Converting Decimals, Improper Fractions, and Mixed Numbers

Hello, and welcome to this video about converting decimals, improper fractions, and mixed numbers! In this video, we will explore the steps to convert a decimal to a fraction and a mixed number to an improper fraction and vice versa. Let’s learn about converting decimals to fractions and mixed numbers to improper fractions!

We use fractions and decimals daily. All our money transactions are done in decimal form. When we bake, we use half cups and one-third cups. Being able to convert between a decimal and a fraction is a math skill you will use every single day.

The table shows a decimal, an improper fraction, and a mixed number that are all equivalent.

Decimal\(3.25\)
Improper fraction\(\frac{13}{4}\)
Mixed number\(3\frac{1}{4}\)

Converting a Decimal to a Fraction:

When converting a decimal to a fraction, we start by multiplying the decimal by a fraction that is equivalent to 1, so the value of the decimal does not change. For example, if there is only one number after the decimal (in other words, a number in the tenths place), the number would be multiplied by \(\frac{10}{10}\). If there are two numbers after the decimal (the last digit is in the hundredths place), we would multiply the number by \(\frac{100}{100}\), and so on. After multiplying, we simplify the fraction.

Let’s take a look at an example.

We will convert 5.85 into fraction form. Since there are 2 numbers after the decimal, we will multiply 5.85 by \(\frac{100}{100}\).

\(5.58\times \frac{100}{100}=\frac{585}{100}\)

To simplify the fraction, we will start by breaking down the number into its factors. Then we will cancel out the common factors in the numerator and denominator. Both numbers have a factor of 5, so \(\frac{585}{100}\) can be simplified to \(\frac{117}{20}\).

\(\frac{585}{100}=\frac{5\times 3\times 3\times 13}{5\times 5\times 2\times 2}=\frac{117}{20}\)

The fraction equivalent to 5.85 is \(\frac{117}{20}\), which is also called an improper fraction. We will now convert the improper fraction into a mixed number.

Converting an Improper Fraction to a Mixed Number:

We will convert the improper fraction, \(\frac{117}{20}\), to a mixed number by first dividing the numerator by the denominator. The whole number becomes the number in the front of the fraction, the remainder becomes the numerator of the fraction, and the denominator of the fraction remains the same. Therefore, \(\frac{117}{20}\), converted to a mixed number is \(5\frac{17}{20}\).

Here’s an example of how we use conversions in real life.

Samm owns a bakery. She has \(5\frac{3}{4}\) kg of sugar. She buys another bag with 10.75 kg of sugar. What is the total amount of sugar, in kilograms, that Samm has for baking? Give your answer in fraction form.

First, we will start by converting 10.75 to fraction form by multiplying it by \(\frac{100}{100}\), which is \(\frac{1,075}{100}\). Once the fraction is simplified, we get \(\frac{43}{4}\), which when converted to a mixed number is \(10\frac{3}{4}\).

Now that both numbers are in mixed number form, we can easily combine to find the total amount of sugar that Samm has for her baking. So all we’re gonna do is add, \(5\frac{3}{4}+10\frac{3}{4}\). When we add mixed numbers, we want to start by adding the fractional parts, so let’s do \(\frac{3}{4}+\frac{3}{4}\). That gives us \(\frac{6}{4}\) because we add our numerators and our denominator stays the same. Now, if you notice, we have an improper fraction. So let’s convert that to a mixed number. If we divide the numerator by the denominator, we’ll get \(1\frac{2}{4}\), which can be simplified to \(1\frac{1}{2}\). Now we’re gonna add this part to our whole number parts from earlier. So \(5+10=15+1\frac{1}{2}=16\frac{1}{2}\). So Samm has \(16\frac{1}{2}\) kg of sugar for baking.

I hope this video on converting decimals, improper fractions, and mixed numbers was helpful. Thanks for watching, and happy studying!

Practice Questions

Question #1:

 
Convert the decimal number 6.8 to a mixed number.

\(6\frac{4}{5}\)
\(6\frac{3}{4}\)
\(6\frac{5}{8}\)
\(6\frac{1}{2}\)
Answer:

A mixed number is a whole number along with a proper fraction next to it.

Step 1. Convert the decimal number to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change. The number 8 after the decimal is in the tenths place, so we can multiply our decimal number by \(\frac{10}{10}\) to convert it to an improper fraction.

\(6.8\times\frac{10}{10}=\frac{68}{10}\)

Step 2. Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.

\(\frac{68}{10}=\frac{2\times 2\times 17}{2\times 5}=\frac{34}{5}\)

Step 3. Convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator.

\(\phantom{0}6\)
\(5\)\(34\)
\(–\)\(30\)
\(4\)

 
The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of \(6\). The numerator of the proper fraction is the remainder of \(4\), and the denominator is the divisor of \(5\). So, \(\frac{34}{5}=6\frac{4}{5}\).

Thus, \(6.8=6\frac{4}{5}\).

Question #2:

 
Convert the decimal number 3.25 to a mixed number.

\(3\frac{1}{8}\)
\(3\frac{1}{4}\)
\(3\frac{2}{5}\)
\(3\frac{3}{4}\)
Answer:

A mixed number is a whole number along with a proper fraction next to it.

Step 1. Convert the decimal number to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change. The number 5 after the decimal is in the hundredths place, so we can multiply our decimal number by \(\frac{100}{100}\) to convert it to an improper fraction.

\(3.25\times\frac{100}{100}=\frac{325}{100}\)

Step 2. Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.

\(\frac{325}{100}=\frac{5\times5\times13}{2\times2\times\times5}=\frac{13}{4}\)

Step 3. Convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator.

\(\phantom{0}3\)
\(4\)\(13\)
\(–\)\(12\)
\(1\)

 
The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 3. The numerator of the proper fraction is the remainder of 1, and the denominator is the divisor of 4. So, \(\frac{13}{4}=3\frac{1}{4}\).

Thus, \(3.25=3\frac{1}{4}\).

Question #3:

 
Convert the decimal number 8.275 to a mixed number.

\(8\frac{25}{49}\)
\(8\frac{22}{45}\)
\(8\frac{11}{40}\)
\(8\frac{29}{40}\)
Answer:

A mixed number is a whole number along with a proper fraction next to it.

Step 1. Convert the decimal number to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change. The number 5 after the decimal is in the thousandths place, so we can multiply our decimal number by \(\frac{1{,}000}{1{,}000}\) to convert it to an improper fraction.

\(8.275\times\frac{1{,}000}{1{,}000}=\frac{8{,}275}{1{,}000}\)

Step 2. Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.

\(\frac{8{,}275}{1{,}000}=\frac{5\times5\times331}{2\times2\times2\times5\times5\times5}=\frac{331}{40}\)

Step 3. Convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator.

\(\phantom{00}8\)
\(40\)\(331\)
\(–\)\(320\)
\(11\)

 
The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 8. The numerator of the proper fraction is the remainder of 11, and the denominator is the divisor of 40. So, \(\frac{331}{40}=8\frac{11}{40}\).

Thus, \(8.275=8\frac{11}{40}\).

Question #4:

 
A fruit drink recipe that is made with several types of fruit is mixed with 20 ounces of water, 10.2 ounces of apple juice, and \(\frac{13}{5}\) ounces of lemon juice. How much liquid is needed for the recipe?

\(32\frac{4}{5}\text{ ounces}\)
\(32\frac{1}{5}\text{ ounces}\)
\(32\frac{1}{4}\text{ ounces}\)
\(32\frac{3}{4}\text{ ounces}\)
Answer:

We need to combine the amounts of water, apple juice, and lemon juice to find the total amount of liquid needed to mix into the fruit drink. We will convert the amounts of apple juice and lemon juice to mixed numbers first before combining all of the amounts of liquid. A mixed number is a whole number along with a proper fraction next to it.

Step 1. Convert the decimal number of 10.2 to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change, before converting it to a mixed number. The number 2 after the decimal is in the tenths place, so we can multiply our decimal number by \(\frac{10}{10}\) to convert it to an improper fraction.

\(10.2\times\frac{10}{10}=\frac{102}{10}\)

Step 2. Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.

\(\frac{102}{10}=\frac{2\times51}{2\times5}=\frac{51}{5}\)

Step 3. Convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator.

\(10\)
\(5\)\(51\)
\(–\)\(50\)
\(1\)

 
The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 10. The numerator of the proper fraction is the remainder of 1, and the denominator is the divisor of 5. So, \(\frac{51}{5}=10\frac{1}{5}\).

Step 4. Next, convert \(\frac{13}{5}\) to a mixed number by dividing the numerator by the denominator.

\(\phantom{0}2\)
\(5\)\(13\)
\(–\)\(10\)
\(3\)

 

The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 2. The numerator of the proper fraction is the remainder of 3, and the denominator is the divisor of 5. So, \(\frac{13}{5}=2\frac{3}{5}\).

Step 5. Now that we have converted the amounts of apple juice and lemon juice to mixed numbers, we can combine the 3 amounts by adding the proper fractions for the mixed numbers, then adding the whole numbers for each mixed number.

\(20+10\frac{1}{5}+2\frac{3}{5}=32\frac{4}{5}\)

So, there is a total of \(32\frac{4}{5}\) ounces of liquid needed for the fruit drink recipe.

Question #5:

 
You are on a fishing trip, hoping to catch a certain fish. The daily weight limit for keeping the fish is \(9\frac{1}{2}\) pounds. You catch two fish, one weighing 4.75 pounds, and the other weighing \(\frac{9}{2}\) pounds. Will you need to release one of the fish back into the water due to exceeding the daily weight limit?

Yes, since the total weight of fish you caught is \(9\frac{3}{4}\) pounds, which is greater than the daily weight limit of \(9\frac{1}{2}\) pounds.

Yes, since the total weight of fish you caught is \(9\frac{1}{4}\) pounds, which is greater than the daily weight limit of \(9\frac{1}{2}\) pounds.

No, since the total weight of fish you caught is \(9\frac{1}{4}\) pounds, which is less than the daily weight limit of \(9\frac{1}{2}\) pounds.

No, since the total weight of fish you caught is \(9\frac{3}{4}\) pounds, which is less than the daily weight limit of \(9\frac{1}{2}\) pounds.

Answer:

We will combine the total weight of the 2 fish you caught using mixed numbers and compare it with the daily weight limit to determine if one of the fish needs to be released. A mixed number is a whole number along with a proper fraction next to it.

Step 1. Convert the weight of the fish given as a decimal number to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change, before converting it to a mixed number. The number 5 after the decimal is in the hundredths place value, so we can multiply our decimal number by \(\frac{100}{100}\) to convert it to an improper fraction.

\(4.75\times\frac{100}{100}=\frac{475}{100}\)

Step 2. Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.

\(\frac{475}{100}=\frac{5×5×19}{2×2×5×5}=\frac{19}{4}\)

Next, convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator.

\(4\)
\(4\)\(19\)
\(–\)\(16\)
\(3\)

 
The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 4. The numerator of the proper fraction is the remainder of 3, and the denominator is the divisor of 4. So, \(4.75=\frac{19}{4}=4\frac{3}{4}\).

Step 3. Convert the weight of the fish given as an improper fraction to a mixed number by dividing the numerator by the denominator.

\(4\)
\(2\)\(9\)
\(–\)\(8\)
\(1\)

 

The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 4. The numerator of the proper fraction is the remainder of 1, and the denominator is the divisor of 2. So, \(\frac{9}{2}=4\frac{1}{2}\).

Step 4. Now that we have converted the weights of the two fish caught to mixed numbers, we can combine them by adding the proper fractions for each mixed number, then adding the whole numbers for each mixed number.

\(4\frac{3}{4}+4\frac{1}{2}=4\frac{3}{4}+4\frac{2}{4}=8\frac{5}{4}\)

Since the fractional part of the mixed number is an improper fraction, we need to convert it to a mixed number and add it to 8 to determine the total weight of the fish caught as a proper mixed number.

We can convert \(\frac{5}{4}\) to a mixed number by dividing the numerator by the denominator.

\(1\)
\(4\)\(5\)
\(–\)\(4\)
\(1\)

 
The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 1. The numerator of the proper fraction is the remainder of 1, and the denominator is the divisor of 4. So, \(\frac{5}{4}=1\frac{1}{4}\).

Therefore, the proper mixed number is:

\(8\frac{5}{4}=8+1\frac{1}{4}=9\frac{1}{4}\)

The total weight of the two game fish you caught is \(9\frac{1}{4}\) pounds. The daily weight limit for the game fish is \(9\frac{1}{2}\) pounds, or \(9\frac{2}{4}\) pounds. Since your total weight for the fish caught is less than the daily weight limit, you do not need to release any of the fish.

 
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by Mometrix Test Preparation | This Page Last Updated: March 4, 2022