# Ratios

Hi, and welcome to this video on ratios! Ratios are used all the time in many aspects of our lives. In this video, we will review what ratios represent and how they should be interpreted.

## What is a Ratio?

As mentioned, ratios are frequently used, but sometimes not fully understood. Simply put, ratios are an efficient way to compare numeric values of different categories. For example, let’s say that you have a room of twenty people comprised of 12 women and 8 men. The two categories are men and women, so your ratios would look like this: the ratio of women to men is 12 to 8, and the ratio of men to women is 8 to 12:

Ratio | Numeric Representation |
---|---|

W:M | 12:8 |

M:W | 8:12 |

Note that ratios can be **simplified** by dividing both values by the common factor of 4, which will not change the meaning of the ratio. The simplified ratio still represents the relationship of the number of women to men, 3:2, and the number of men to women, 2:3.

## Writing Ratios

There are two ways that ratios can be written. This example uses a colon, but you could also use a division bar to form a fraction:

Ratio | Fraction Representation |
---|---|

W:M | \(\frac{12}{8}\), simplifies to \(\frac{3}{2}\) |

It is very important to note that the order of the categories matters when building a ratio. The first value is technically referred to as the **antecedent** and the second value is referred to as the **consequent**. The antecedent is always compared to the consequent. Interpreting the ratio in context can sometimes be tricky, but becomes easier with practice.

## Examples of Using Ratios

Let’s look at some examples of ratios you might come across in day-to-day life:

### Cooking

You are making a batch of your mom’s delicious salad dressing. The recipe calls for many ingredients, including 2 **cups** of extra virgin olive oil and 3 **cloves** of chopped garlic. In this case, the ratio of oil to cloves is 2:3, or \(\frac{2}{3}\), and the ratio of garlic to oil is 3:2, or \(\frac{3}{2}\). In cooking, you might hear this referred to as “two parts oil, three parts garlic.” This is because the “units” here are different (cloves vs. cups).

### Shopping

Grocery store displays allow us to compare the value of products based on their “unit cost.” Many times, this is simply a quick ratio of “cost to unit,” with the unit being ounce, pound, etc.

#### Example 1

Suppose you are scanning the cereal aisle and narrow your choice down to your two favorites. You decide to be practical and base your decision purely on cost. Both have similar prices, but the volume of the packaging is different. Calculating a quick ratio of cost to unit for each box will reveal the better value: brand A costs $5.79 and has a volume of 20.35 ounces. Dividing the price by the volume gives us the cost of the cereal per ounce, $0.28. Brand B costs $6.39 and has a volume of 24.15 ounces. Dividing the price by the volume gives us $0.26 per ounce.

Brand | Cost | Unit Price (Ratio) | ||
---|---|---|---|---|

Choice A | \(\frac{$5.79}{20.35 \text{ oz.}}\) | \(=\) | $0.28 per oz. | |

Choice B | \(\frac{$6.39}{24.15 \text{ oz.}}\) | \(=\) | $0.12 per oz. |

Despite being a higher cost per package, Choice B is a better value by unit price.

This example was fairly straightforward because the volume of the cereal packages was measured in ounces.

#### Example 2

Many times a unit conversion must be made before a unit price can be determined. For example, if we are trying to compare the unit cost of a pound of fresh broccoli to a package of frozen broccoli measured in ounces, we would need to know that 1 pound is equal to 16 ounces before we could calculate the unit cost ratio.

Type | Cost | Unit Price (Ratio) | ||
---|---|---|---|---|

Fresh | \(\frac{$2.37}{16 \text{ oz. (1 lb)}}\) | \(=\) | $0.15 per oz. | |

Frozen | \(\frac{$1.47}{12 \text{ oz.}}\) | \(=\) | $0.12 per oz. |

In this case, the frozen broccoli would be the better value based on the smaller unit price per ounce.

So, as you can see, ratios are common in our everyday lives, and you’ve probably been using them whether you have realized it or not!

Thanks for watching, and happy studying!

## Frequently Asked Questions

#### Q

### What is a ratio?

#### A

A ratio is a comparison of two quantities in a particular order.

Ex. If a preschool has 3 adults in a classroom with 25 kids, the ratio of adults to kids in the classroom is 3:25 or \(\frac{3}{25}\).

#### Q

### How do you calculate a ratio?

#### A

Calculate a ratio by comparing two quantities to another in a particular order.

Ex. There are 140 students in a cafeteria and 7 teachers. What is the ratio of students to teachers?

140:7, which simplifies to 20:1

#### Q

### What are equivalent ratios?

#### A

Equivalent ratios are two different ratios that equal one another.

Ex. 2:4 and 1:2

## Practice Questions

**Question #1:**

Which of the following is not a proper way to write a ratio?

3 over 2

3:2

3 to 2

**Answer:**

The correct answer is 3 over 2. A ratio compares one thing to another and can be written three different ways: 3 to 2, 3:2, or \(\frac{3}{2}\).

**Question #2:**

There are 8 men in an office building and 2 women. What is the ratio of men to women in the building?

4:1

3:2

2:3

1:4

**Answer:**

The correct answer is 4:1. The ratio of men to women is 8 : 2, which can be simplified to 4:1 by dividing both parts by 2.

**Question #3:**

A school has 420 students and 40 teachers. What is the ratio of teachers to students?

**Answer:**

The correct answer is \(\frac{2}{21}\). The ratio of teachers to students is \(\frac{4}{420}\), which can be simplified to \(\frac{2}{21}\) by dividing both numbers by 20.

**Question #4:**

A cell phone company has two different texting plans. Plan A offers texting at $0.25 per 5 text messages and Plan B offers texting at $0.18 per 3 text messages. Which plan has the cheaper texting option?

Plan A

Plan B

They are the same price

Cannot be determined from given information

**Answer:**

The correct answer is Plan A. This problem can be solved by using ratios to find the unit price of one text message for each plan. First, set up a ratio for Plan A.

\(\frac{$0.25}{5\text{ text messages}}\)

Then, divide both numbers by 5 to determine the price of 1 text message.

\(\frac{$0.25}{5\text{ text messages}}=\frac{$0.05}{1\text{ text message}}\)

Plan A costs $0.05 per text message. Then, do the same for Plan B.

\(\frac{0.18}{3\text{ text messages}}\)

Divide both numbers by 3.

\(\frac{0.18}{3\text{ text messages}}=\frac{$0.06}{1\text{ text message}}\)

Plan B costs $0.06 per text message. Therefore, Plan A is the cheaper of the two options.

**Question #5:**

There are 763 employees in a company. 537 of them are women. What is the ratio of men to women in this company?

537:763

226:537

537:226

763:226

**Answer:**

The correct answer is 226:537. Be sure to read this question carefully! It asks for the ratio of men to women but the number of men is not given. Subtract 537 from 762 to find the number of men in the company.

\(763-537=226\)

So the ratio of men to women is 226:537.