{"id":1197,"date":"2013-06-06T08:43:40","date_gmt":"2013-06-06T08:43:40","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=1197"},"modified":"2026-03-17T15:43:31","modified_gmt":"2026-03-17T20:43:31","slug":"pre-algebra","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/pre-algebra\/","title":{"rendered":"Pre-Algebra"},"content":{"rendered":"<p>Mometrix\u2019s pre-algebra videos are general reviews of the concepts, ideas, and topics that may be presented on an exam. Each of these videos will give a wide-scope review of what a test taker may need to know as they prepare to take a test.<\/p>\n<a href=\"https:\/\/www.mometrix.com\/university\/pre-algebra\/\" class=\"mobile-ad\" style=\"color:black;\" onclick=\"_paq.push(['trackEvent', 'Mobile Ad', 'Mobile Click', 'PreAlgebra Mobile Click']);\"><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/03\/PreAlgebra-Mobile-Ad.webp\" alt=\"20% off coupon for the Pre-Algebra online course.\" width=\"353\" height=\"354\"><br \/>\n<\/a>\n<h2 class=\"pt-page\"><span id=\"Numbers\" class=\"m-toc-anchor\"><\/span>Numbers<\/h2>\n<ul class=\"yellow_buttons\">\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/absolute-value\/\">Absolute Value<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/irrational-numbers-on-a-number-line\/\">Irrational Numbers on a Number Line<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/real-numbers-and-the-number-line\/\">Negative and Positive Number Line<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/prime-and-composite-numbers\/\">Prime and Composite Numbers<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/rational-numbers\/\">What is a Rational Number?<\/a><\/li>\n<\/ul>\n<h2 class=\"pt-page\"><span id=\"Operations\" class=\"m-toc-anchor\"><\/span>Operations<\/h2>\n<ul class=\"yellow_buttons\">\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/addition-and-subtraction-with-exponents\/\">Adding and Subtracting Exponents<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/associative-property\/\">Commutative, Associative, and Distributive Properties<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/divisibility-tests\/\">Divisibility Tests<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/laws-of-exponents\/\">Laws of Exponents<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/addition-subtraction-multiplication-and-division\/\">Mathematical Operations<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/roots\/\">Roots<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/exponents\/\">What is an Exponent?<\/a><\/li>\n<\/ul>\n<h2 class=\"pt-page\"><span id=\"Factoring\" class=\"m-toc-anchor\"><\/span>Factoring<\/h2>\n<ul class=\"yellow_buttons\">\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/intro-to-factoring-in-math\/\">An Introduction to Factoring<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/factors\/\">Factors<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/greatest-common-factor\/\">Greatest Common Factor and Least Common Multiple<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/multiples\/\">Multiples<\/a><\/li>\n<\/ul>\n<h2 class=\"pt-page\"><span id=\"Rational_Numbers\" class=\"m-toc-anchor\"><\/span>Rational Numbers<\/h2>\n<ul class=\"yellow_buttons\">\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/adding-and-subtracting-fractions\/\">Adding and Subtracting Fractions<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/converting-decimals-to-fractions-and-percentages\/\">Converting Decimals to Fractions and Percentages<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/converting-decimals-to-improper-fractions-and-mixed-numbers\/\">Converting Decimals, Improper Fractions, and Mixed Numbers<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/converting-fractions-to-percentages-and-decimals\/\">Converting Fractions into Decimals and Percentages<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/converting-percentages-to-decimals-and-fractions\/\">Converting Percentages to Decimals and Fractions<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/decimals\/\">Decimals<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/dividing-decimals-by-whole-numbers\/\">Dividing Decimals by Whole Numbers<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/proper-and-improper-fractions-and-mixed-numbers\/\">Improper Fractions and Mixed Numbers<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/multiplying-and-dividing-fractions\/\">Multiplying and Dividing Fractions<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/ordering-rational-numbers\/\">Ordering Rational Numbers<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/square-root-and-perfect-square\/\">Perfect Squares and Square Roots<\/a><\/li>\n<\/ul>\n<h2 class=\"pt-page\"><span id=\"Proportions_and_Ratios\" class=\"m-toc-anchor\"><\/span>Proportions and Ratios<\/h2>\n<ul class=\"yellow_buttons\">\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/computation-with-percentages\/\">Computation with Percentages<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/distance-apart\/\">Distance, Rate, and Time<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/proportional-change-of-dimensions\/\">Proportional Change of Dimensions<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/proportions\/\">Proportions<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/rates-and-unit-rates\/\">Rates and Unit Rates<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/ratios\/\">Ratios<\/a><\/li>\n<\/ul>\n<h2 class=\"pt-page\"><span id=\"Measurement_Principles\" class=\"m-toc-anchor\"><\/span>Measurement Principles<\/h2>\n<ul class=\"yellow_buttons\">\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/measurement-conversions\/\">Measurement Conversions<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/metric-system-conversions\/\">Metric System Conversions<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/precision-accuracy-and-error\/\">Precision, Accuracy, and Error<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/scientific-notation\/\">Scientific Notation<\/a><\/li>\n<\/ul>\n<h2 class=\"pt-page\"><span id=\"Statistical_Analysis\" class=\"m-toc-anchor\"><\/span>Statistical Analysis<\/h2>\n<ul class=\"yellow_buttons\">\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/average\/\">All About Averages<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/statistical-range\/\">Statistical Range<\/a><\/li>\n<\/ul>\n<h2 class=\"pt-page\"><span id=\"Displaying_Information\" class=\"m-toc-anchor\"><\/span>Displaying Information<\/h2>\n<ul class=\"yellow_buttons\">\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/box-and-whisker-plots\/\">Box and Whisker Plots<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/data-interpretation-of-graphs\/\">Data Interpretation of Graphs<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/line-graph\/\">Line Graphs<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/pictographs\/\">Pictographs<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/stem-and-leaf-plots\/\">Stem-and-Leaf Plots<\/a><\/li>\n<li><a href=\"https:\/\/www.mometrix.com\/academy\/line-plot\/\">What is a Line Plot?<\/a><\/li>\n<\/ul>\n<h2 id=\"PreAlgebraCourse\" class=\"pt-page\"><span id=\"PreAlgebra_Online_Prep_Course\" class=\"m-toc-anchor\"><\/span>Pre-Algebra Online Prep Course<\/h2>\n<p>If you want to be fully prepared, Mometrix offers an <strong>online Pre-Algebra prep course<\/strong> designed to give you everything you need to succeed!<\/p>\n<p>Here&#8217;s what you&#8217;ll find in the Pre-Algebra course:<\/p>\n<div class=\"mocblurb\">\n<ul>\n<li class=\"moclessons\"><\/li>\n<li class=\"mocpqs\"><\/li>\n<li class=\"mocvideos\"><\/li>\n<li class=\"mocflash\"><\/li>\n<li class=\"mocmoney\"><\/li>\n<li class=\"mocmobile\"><\/li>\n<\/ul>\n<\/div>\n<p>Everyone learns differently, so we&#8217;ve tailored the Pre-Algebra online prep course to ensure every learner has what they need to prepare for the Pre-Algebra exam.<\/p>\n<p>Click below to check it out!<\/p>\n<div style=\"text-align: center\">\n<a href=\"https:\/\/www.mometrix.com\/university\/pre-algebra\/?utm_source=academy&amp;utm_medium=button&amp;utm_campaign=academy-mu-ads&amp;utm_content=pre-algebra\" class=\"class_names\" style=\"color:black;\" onclick=\"_paq.push(['trackEvent', 'Course Button', 'Course Click', 'PreAlgebra Course Click']);\"><button class=\"buttontranscript\">Pre-Algebra Online Course<\/button><\/a><\/div>\n<h2 class=\"pt-page\"><span id=\"PreAlgebra_Problems\" class=\"m-toc-anchor\"><\/span>Pre-Algebra Problems<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\n<strong>LCM and GCF.<\/strong> What is the greatest common factor of 42 and 56?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">7<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">14<\/div><div class=\"PQ\"  id=\"PQ-1-3\">16<\/div><div class=\"PQ\"  id=\"PQ-1-4\">21<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The greatest common factor of two or more numbers is the largest integer that divides evenly into both numbers. It is helpful to list out the prime factors of each number and then collect all of the shared prime factors.<\/p>\n<p>Start with 42. Since it is an even number, 2 must be one of its prime factors. After factoring out a 2, 21 remains. This can then be broken down into its prime factors, 3 and 7. So then \\(42=2\\times3\\times7\\).<\/p>\n<table class=\"ATable\" style=\"border:none; width: 8%; font-size:120%; margin: auto;\">\n<tbody>\n<tr>\n<td style=\"text-align:left; border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\">\\(2\\)<\/td>\n<td style=\"text-align:right; border-right:0px; border-top:0px\">\\(4\\)<\/td>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\"><\/td>\n<td style=\"text-align:left; border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\">\\(3\\)<\/td>\n<td style=\"text-align:right; border-right:0px; border-top:0px\">\\(21\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\"><\/td>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\"><\/td>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\">\\(7\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><\/p>\n<p style=\"text-align: center;\">\\(42=2\\times3\\times7\\)<\/p>\n<p>Now, factor 56 using the same method.<\/p>\n<table class=\"ATable\" style=\"border:none; width: 8%; font-size:120%; margin: auto;\">\n<tbody>\n<tr>\n<td style=\"text-align:left; border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\">\\(2\\)<\/td>\n<td style=\"text-align:right; border-right:0px; border-top:0px\">\\(56\\)<\/td>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\"><\/td>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\"><\/td>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\">\\(2\\)<\/td>\n<td style=\"text-align:right; border-right:0px; border-top:0px\">\\(28\\)<\/td>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\"><\/td>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\"><\/td>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\">\\(2\\)<\/td>\n<td style=\"text-align:right; border-right:0px; border-top:0px\">\\(14\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\"><\/td>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\"><\/td>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\"><\/td>\n<td style=\"border-top:0px; border-left:0px; border-bottom:0px; border-right:0px\">\\(7\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><\/p>\n<p style=\"text-align: center;\">\\(56=2\\times2\\times2\\times7\\)<\/p>\n<p>Now that both prime factorizations are complete, look at the factors for what is common between 42 and 56.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(42=\\mathbf{2}\\times3\\times\\mathbf{7}\\)<br \/>\n\\(56=\\mathbf{2}\\times2\\times2\\times\\mathbf{7}\\)<\/p>\n<p>Both share a 2 and a 7. Because of this, it can then be determined that the GCF of 42 and 56 must equal the product of these shared prime factors, \\(2\\times7\\), which is 14.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\n<strong>Measurement Conversions.<\/strong> Stephanie is on a trip to Japan and is getting used to seeing speed limit signs posted in kilometers per hour (km\/h) rather than miles per hour (mph). She sees a lot of signs that say \u201c80 km\/h\u201d and wonders how fast that would be in miles per hour. Using the fact that 1 mile is approximately 1.6 kilometers, determine which of the following choices is equal to this speed in miles per hour.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">35 mph<\/div><div class=\"PQ\"  id=\"PQ-2-2\">40 mph<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-3\">50 mph<\/div><div class=\"PQ\"  id=\"PQ-2-4\">65 mph<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To convert kilometers per hour to miles per hour, start by writing the known speed as a fraction over 1. In the numerator will be 80 kilometers, and 1 hour will be in the denominator since the speed is \u201cper hour.\u201d<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(\\frac{80\\text{ km}}{1\\text{ hr}}\\)<\/p>\n<p>Now, write the conversion factor as a fraction. Since one mile is approximately 1.6 kilometers, this will be \\(\\frac{1\\text{ mi}}{1.6\\text{ km}}\\). Multiply this with the known speed to cancel out unwanted kilometer units and adjust the number appropriately.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(\\frac{80\\text{ km}}{1\\text{ hr}}\\times\\frac{1\\text{ mi}}{1.6\\text{ km}}=\\frac{80\\text{ mi}}{1.6\\text{ hr}}\\)<\/p>\n<p>Divide 80 by 1.6: \\(80\\div1.6=50\\). Therefore, 80 km\/h is equal to 50 mph.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\n<strong>Scientific Notation.<\/strong> Andre is researching the prevalence of various injuries in the United States and sees that there are 1.5 million cases of traumatic brain injury (TBI) annually among the population of 330 million Americans. Based on this, he calculates that approximately 0.004545 of the population sustains a TBI in a given year. How can he write this number using scientific notation?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(4.545\\times{10}^3\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(-4.545\\times{10}^3\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(4.545\\times{10}^{-4}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-4\">\\(4.545\\times{10}^{-3}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Scientific notation is always written in the format \\(m\\times{10}^n\\), where \\(m\\) is a rational number between 1 and 9, and \\(n\\) is an integer. <\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(m\\times{10}^n\\)<br \/>\n\\(1\\le m\\le9, n\\in\\mathbb{Z}\\)<\/p>\n<p>In order to change 0.004545 into a rational number between 1 and 9, the decimal must be moved into position right behind the first 4. Now the number is 4.545, which will be a <em>part<\/em> of the solution.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(0004.\\underparen {5}\\underparen {4}\\underparen {5.}\\)<\/p>\n<p>In order to equate this 4.545 to the true value of 0.004545, what must be done? The decimal point has to move back to the left three times. The action of moving the decimal to the left by one place is like dividing by 10. Therefore, moving the decimal to the left three times is like dividing by 10 <em>three times<\/em>. Equivalently, we say that 4.545 is being multiplied by \\({10}^{-3}\\). Because of this, \\(0.004545=4.545\\times{10}^{-3}\\).\u2003<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\n<strong>Mathematical Operations.<\/strong> Which of the four mathematical operations is associated with the terms \u201cfactor\u201d and \u201cproduct\u201d?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">Multiplication<\/div><div class=\"PQ\"  id=\"PQ-4-2\">Subtraction<\/div><div class=\"PQ\"  id=\"PQ-4-3\">Division<\/div><div class=\"PQ\"  id=\"PQ-4-4\">Addition<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>In multiplication, the numbers being multiplied together are called the factors, while their result is the product. If you haven\u2019t already, take a moment to commit these terms to memory, as they\u2019ll come more into play down the road.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-141088 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/09\/Academy-Pre-Algebra-SQ-1.png\" alt=\"example of multiplication\" width=\"490\" height=\"181\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/09\/Academy-Pre-Algebra-SQ-1.png 650w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/09\/Academy-Pre-Algebra-SQ-1-300x111.png 300w\" sizes=\"auto, (max-width: 490px) 100vw, 490px\" \/><\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\n<strong>Commutative, Associative, and Distributive Properties.<\/strong> Which of the following statements demonstrates the commutative property?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-5-1\">\\(6\\times2=2\\times6\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(2\\times\\left(5\\times3\\right)=\\left(2\\times5\\right)\\times3\\)<\/div><div class=\"PQ\"  id=\"PQ-5-3\">\\(8\\left(2+4\\right)=8\\left(2\\right)+8\\left(4\\right)\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(\\left(5+3\\right)+1=5+\\left(3+1\\right)\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The commutative property applies to addition and multiplication problems in such a way that appears sort of like a mirror. The numbers and operation on the left of the equals sign are reflected on the right side in a reverse order, as if an actual mirror is placed right in the middle.<\/p>\n<p>Each of the following equations demonstrate the commutative property.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(6\\times2=2\\times6\\)<br \/>\n\\(10+5=5+10\\)<br \/>\n\\(9\\times20=20\\times9\\)<\/p>\n<p>You can remember that this is the commutative property because the word \u201ccommutative\u201d has two m\u2019s in it, which stand for \u201cmirror.\u201d If there are more than 2 numbers on both sides, then the numbers can be arranged in any order and don\u2019t have to be exactly mirrored.<\/p>\n<p>The solution is not choice B or choice D because these are both examples of the associative property, which demonstrates that grouping numbers with parentheses does not affect the outcome of problems involving only addition or only multiplication.<\/p>\n<p>The solution is not choice C because that is an example of the distributive property, where the 8 on the outside is multiplied with both the 2 and the 4 individually inside the parentheses.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #6:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\n<strong>Adding and Subtracting Fractions.<\/strong>Trevor and Max made two pizzas, that were the same size, for lunch. Trevor cut his pizza into 8 slices and ate 3 of them, while Max cut his pizza into 6 slices and ate 2 of them. How much pizza did they consume in total? Express your answer as a fraction of one whole pizza.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-6-1\">\\(\\frac{5}{24}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-6-2\">\\(\\frac{17}{24}\\)<\/div><div class=\"PQ\"  id=\"PQ-6-3\">\\(\\frac{7}{16}\\)<\/div><div class=\"PQ\"  id=\"PQ-6-4\">\\(\\frac{9}{16}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-6\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-6\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-6-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Since Trevor ate 3 slices from his pizza that was cut into 8 slices, it can be said that he consumed \\(\\frac{3}{8}\\) of a pizza. Max, on the other hand, ate 2 slices from his pizza that was cut into 6 pieces. Therefore, Max ate \\(\\frac{2}{6}\\), or \\(\\frac{1}{3}\\), of a pizza. Together, they ate \\(\\frac{3}{8}+\\frac{1}{3}\\) of a pizza.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(\\frac{3}{8}+\\frac{1}{3}\\)<\/p>\n<p>Do not cancel the diagonal 3\u2019s; that can only be done in multiplication problems! Instead, these fractions must be combined using addition, which can be done after getting the fractions to have a common denominator.<\/p>\n<p>The least common denominator is the least common multiple (LCM) of 8 and 3. Since 8 has a prime factorization of \\(2\u00d72\u00d72\\), and 3 is already prime, it can be noticed that these prime factorizations don\u2019t have anything in common. Therefore, the LCM of 8 and 3 will equal \\(2\u00d72\u00d72\u00d73\\), which is 24.<\/p>\n<p>To rewrite each fraction to have a denominator of 24, multiply them by \\(\\frac{3}{3}\\) and \\(\\frac{8}{8}\\), respectively.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\((\\frac{3}{3})\\frac{3}{8}+\\frac{1}{3}(\\frac{8}{8})=\\frac{9}{24}+\\frac{8}{24}\\)<\/p>\n<p>Once both fractions share a common denominator, their numerators may be combined by adding. The denominator will stay as 24 because it doesn\u2019t reflect the quantity of \u201cpieces\u201d but instead the size of each piece.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(\\frac{9+8}{24}=\\frac{17}{24}\\)<\/p>\n<p>So, Trevor and Max ate a combined \\(\\frac{17}{24}\\) of a pizza.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-6-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-6-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #7:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\n<strong>Converting Fractions into Decimals and Percentages.<\/strong> Amber conducted a survey for her statistics class and found that out of 20 people surveyed, 3 people were more than 6 feet tall. What percent of participants were taller than 6 feet?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-7-1\">15%<\/div><div class=\"PQ\"  id=\"PQ-7-2\">18%<\/div><div class=\"PQ\"  id=\"PQ-7-3\">20%<\/div><div class=\"PQ\"  id=\"PQ-7-4\">23%<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-7\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-7\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-7-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The given information can be used to write the proportion of participants over 6 feet tall as a fraction. Since 3 out of 20 people met this qualification, it is true that \\(\\frac{3}{20}\\) of participants were taller than 6 feet.<\/p>\n<p>To write this as a percentage rather than as a fraction, set it up as a division problem.<\/p>\n<table class=\"ATable\" style=\"border:none; width: 8%; font-size:120%; margin: auto;\">\n<tbody>\n<tr>\n<td style=\"border-left:0px; border-right:0px; border-top:0px; border-bottom:0px\"><\/td>\n<td style=\"border-bottom:0px; border-right:0px; border-top:0px; border-left:0px; text-align: right;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align:left; border-top:0px; border-left:0px; border-bottom:0px\">\\(20\\)<\/td>\n<td style=\"text-align:right; border-left:0px; border-right:0px; border-bottom:0px\">\\(3\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Since 20 is larger than 3, write in the decimal point and tenths place, then proceed with the division.<\/p>\n<table class=\"ATable\" style=\"border: none; font-size: 145%; width: 15%; margin: auto;\">\n<tbody>\n<tr>\n<td style=\"border: 0px;\"><\/td>\n<td style=\"text-align:right; line-height: 3px; padding-bottom: -10px; border: 0px;\"><\/td>\n<td style=\"width:0.5px; border: 0px;\">.<\/td>\n<td style=\"border: 0px;\"><\/td>\n<td style=\"border: 0px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 0px;\">\\(20\\)<\/td>\n<td style=\"text-align:right; border-right: 0px; border-bottom: 0px;\">\\(\\phantom{.}3\\)<\/td>\n<td style=\"width:0.5px; border-bottom: 0px; border-left: 0px; border-right: 0px;\">.<\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\">\\(0\\)<\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<br \/>\n&nbsp;<\/p>\n<table class=\"ATable\" style=\"border: none; font-size: 145%; width: 15%; margin: auto;\">\n<tbody>\n<tr>\n<td style=\"border: 0px;\"><\/td>\n<td style=\"text-align:right; line-height: 3px; padding-bottom: -10px; border: 0px;\"><\/td>\n<td style=\"width:0.5px; border: 0px;\">.<\/td>\n<td style=\"border: 0px;\">\\(1\\)<\/td>\n<td style=\"border: 0px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 0px;\">\\(20\\)<\/td>\n<td style=\"text-align:right; border-right: 0px; border-bottom: 0px;\">\\(\\phantom{.}3\\)<\/td>\n<td style=\"width:0.5px; border-bottom: 0px; border-left: 0px; border-right: 0px;\">.<\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\">\\(0\\)<\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\"><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" style=\"text-align:right; border: 0px;\">\\(-\\phantom{.}2\\)<\/td>\n<td style=\"border: 0px;\">.<\/td>\n<td style=\"border: 0px;\">\\(0\\)<\/td>\n<td colspan=\"2\" style=\"border: 0px;\"><\/td>\n<\/tr>\n<tr style=\"margin-bottom:0px\">\n<td style=\"border: 0px;\"><\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\"><\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\"><\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\"><\/td>\n<td colspan=\"2\" style=\"border: 0px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 0px;\"><\/td>\n<td style=\"text-align:right; border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px;\">\\(\\phantom{.}1\\)<\/td>\n<td style=\"width:0.5px; border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px;\">.<\/td>\n<td style=\"border-bottom: 0px; border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px;\">\\(0\\)<\/td>\n<td style=\"border-bottom: 0px; border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>This division isn\u2019t finished yet, so add the hundredths place and continue dividing.<\/p>\n<table class=\"ATable\" style=\"border: none; font-size: 145%; width: 15%; margin: auto;\">\n<tbody>\n<tr>\n<td style=\"border: 0px;\"><\/td>\n<td style=\"text-align:right; line-height: 3px; padding-bottom: -10px; border: 0px;\"><\/td>\n<td style=\"width:0.5px; border: 0px;\">.<\/td>\n<td style=\"border: 0px;\">\\(1\\)<\/td>\n<td style=\"border: 0px;\">\\(5\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 0px;\">\\(20\\)<\/td>\n<td style=\"text-align:right; border-right: 0px; border-bottom: 0px;\">\\(\\phantom{.}3\\)<\/td>\n<td style=\"width:0.5px; border-bottom: 0px; border-left: 0px; border-right: 0px;\">.<\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\">\\(0\\)<\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\">\\(0\\)<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" style=\"text-align:right; border: 0px;\">\\(-\\phantom{.}2\\)<\/td>\n<td style=\"border: 0px;\">.<\/td>\n<td style=\"border: 0px;\">\\(0\\)<\/td>\n<td colspan=\"2\" style=\"border: 0px;\"><\/td>\n<\/tr>\n<tr style=\"margin-bottom:0px\">\n<td style=\"border: 0px;\"><\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\"><\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\"><\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\"><\/td>\n<td colspan=\"2\" style=\"border: 0px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 0px;\"><\/td>\n<td style=\"text-align:right; border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px;\">\\(\\phantom{.}1\\)<\/td>\n<td style=\"width:0.5px; border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px;\">.<\/td>\n<td style=\"border-bottom: 0px; border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px;\">\\(0\\)<\/td>\n<td style=\"border-bottom: 0px; border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px;\">\\(0\\)<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" style=\"text-align:right; border: 0px;\">\\(-\\phantom{.}1\\)<\/td>\n<td style=\"border: 0px;\">.<\/td>\n<td style=\"border: 0px;\">\\(0\\)<\/td>\n<td colspan=\"2\" style=\"border: 0px;\">\\(0\\)<\/td>\n<\/tr>\n<tr style=\"margin-bottom:0px\">\n<td style=\"border: 0px;\"><\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\"><\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\"><\/td>\n<td style=\"border-bottom: 0px; border-left: 0px; border-right: 0px;\"><\/td>\n<td colspan=\"2\" style=\"border: 0px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"border-bottom: 0px; border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px;\"><\/td>\n<td style=\"border-bottom: 0px; border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px;\"><\/td>\n<td style=\"border-bottom: 0px; border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px;\"><\/td>\n<td style=\"border-bottom: 0px; border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px;\"><\/td>\n<td style=\"border-bottom: 0px; border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px;\">\\(0\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Now the division is complete, and \\(\\frac{3}{20}\\) is equal to 0.15. This decimal can be converted to a percentage by multiplying by 100%.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(0.15=\\left(0.15\\times100\\%\\right)=15\\%\\)<\/p>\n<p>Therefore, \\(\\frac{3}{20}=0.15=15\\%\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-7-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-7-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #8:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\n<strong>Computations with Percentages.<\/strong> Fill in the blank: 10 is 40% of _____.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-8-1\">14<\/div><div class=\"PQ\"  id=\"PQ-8-2\">17.5<\/div><div class=\"PQ\"  id=\"PQ-8-3\">21<\/div><div class=\"PQ correct_answer\"  id=\"PQ-8-4\">25<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-8\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-8\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-8-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To determine the solution to this problem, use the mathematical equivalents of the words \u201cis\u201d and \u201cof.\u201d For example, the word \u201cis\u201d represents that one thing is the same as something else; in other words, it represents equality. Replace the word \u201cis\u201d with an equal sign.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(10\\text{ is }40%\\text{ of }\\)_____<br \/>\n\\(10=40%\\text{ of }\\)_____<\/p>\n<p>Now, replace the word \u201cof\u201d with a multiplication symbol. <\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(10=40%\\times\\) _____<\/p>\n<p>To find the appropriate value for the blank, use a variable, like the letter \\(n\\), as a placeholder.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(10=40%\\times n\\)<\/p>\n<p>From here, convert 40% to a decimal place and solve for \\(n\\) by getting it by itself on one side of the equation.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(10=0.40n\\)<\/p>\n<p>Divide both sides by 0.40.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(\\frac{10}{0.40}=\\frac{0.40n}{0.40}\\)<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(25=n\\)<\/p>\n<p>Since \\(10\\div0.40=25\\), \\(n\\) must be 25. Therefore, 10 is 40% of 25.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-8-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-8-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #9:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\n<strong>Proportions.<\/strong> Sandra has a photograph that is 8 inches in length and 5 inches in width, and she wants to have the photo enlarged. In order to ensure that none of the image is lost along the sides, she needs the dimensions to remain proportional. If the enlarged photograph is to be 15 inches wide, what will its length be? <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-141091 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/09\/I09790-Resized.png\" alt=\"two proportional rectangles\" width=\"537\" height=\"181\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/09\/I09790-Resized.png 650w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/09\/I09790-Resized-300x101.png 300w\" sizes=\"auto, (max-width: 537px) 100vw, 537px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-9-1\">24 inches<\/div><div class=\"PQ\"  id=\"PQ-9-2\">28 inches<\/div><div class=\"PQ\"  id=\"PQ-9-3\">30 inches<\/div><div class=\"PQ\"  id=\"PQ-9-4\">32 inches<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-9\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-9\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-9-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The dimensions of the initial photograph may be written as the ratio \\(\\frac{8}{5}\\). Because the enlarged photograph will have a new width of 15 inches instead of 5, write a new ratio with 15 in the denominator. These two ratios will be equal because the photo enlargement will have the same proportions as the original.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(\\frac{8}{5}=\\frac{?}{15}\\)<\/p>\n<p>To determine the missing value of the new length, notice that the width is increasing by a factor of three. To preserve the proportion of the dimensions, the length must also be multiplied by three.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(8\\times3=24\\)<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(5\\times3=15\\)<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(\\frac{8}{5}=\\frac{24}{15}\\)<\/p>\n<p>Therefore, the length of the enlarged photograph is 24 inches. \u2003<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-9-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-9-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #10:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\n<strong>Average.<\/strong> Determine the average of the following set of numbers: 12, 15, 19, 25, 31, 36.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-10-1\">15%<\/div><div class=\"PQ\"  id=\"PQ-10-2\">18%<\/div><div class=\"PQ\"  id=\"PQ-10-3\">20%<\/div><div class=\"PQ\"  id=\"PQ-10-4\">23%<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-10\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-10\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-10-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The average is the weighted \u201ccenter value\u201d of a set of numbers, it can be found by adding up all the numbers and then dividing that sum by the number of values in the set. In this case, adding up all of the numbers in the set results in a sum of 138.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(12+15+19+25+31+36=138\\)<\/p>\n<p>Because this set included 6 numbers, divide the sum, 138, by 6.<\/p>\n<p><\/p>\n<p style=\"text-align: center;\">\\(138\\div6=23\\)<\/p>\n<p>Therefore, 23 is the average of this set of numbers.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-10-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-10-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/\">Mometrix Academy &#8211; Home<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Mometrix\u2019s pre-algebra videos are general reviews of the concepts, ideas, and topics that may be presented on an exam. Each of these videos will give a wide-scope review of what a test taker may need to know as they prepare to take a test. 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