## Equivalent Ratios

#### Aligned To Common Core Standard:

**Grade 7 Proportional Relationships** - 7.RP.A.2c

How to Determine if Two Ratios Are Equivalent - A ratio is a mathematical concept which determines the relationship between two numbers. It tells us how many times one number contains the other. In the case of multiple rations, you can find out if two ratios are equivalent or not. It helps us find out if one ratio is larger or smaller than the other. The primary requirement for comparing two ratios is to have a common second number. However, if you want to determine whether two ratios are equivalent, you need to follow these steps. If you have two ratios, you need to multiply each ratio by the second number of the second ratio. Consider two ratios; 9:15 and 3:5. Here, you have to multiply 9 and 15 by 5. It will give you 45:75. Now you have to multiply 3 and 5 by 15 and it will give you 45:75. The results are equal this means that both ratios are equivalent. These worksheets and lessons help students learn how to generate and identify ratios that are equal values.

### Printable Worksheets And Lessons

- Proportion Word Problem Step-by-step Lesson- See if you can figure out how far Mikai walks her dog Rufus.
- Ratio Equation Step-by-step Lesson - George sure paints a lot of walls. I wonder what color they are going for?
- Making Equivalent Ratios Worksheet 1 - Simple horizontal ratio sets for you to make sense of.
- Proportion Word Problems Worksheet 2 - Julie's apples, how many points does Tim score, and Jenna loves mittens.
- Story Ratios Worksheet 3 - Jackie's lemonade and Gina's Fudge shop.
- Ratio Tables Worksheet 4 - A scattering of tables that will make you work.

#### Homework Sheets

Simple ratio tables followed by word problems and a little dash of algebra.

- Homework 1 - Fill in the blank to make an equivalent ratio.
- Homework 2 - Jenny earns $9.50 per hour for babysitting. If she worked 11 hours, how much does she get paid?
- Homework 3 - Solve for the missing proportions. You will replace the unknown variable with the correct value.

#### Practice Worksheets

Fill in all the missing holes with whole numbers.

- Practice 1 - We can easily create a proportion just by placing the proper units in the proportion.
- Practice 2 - Fletcher and Jim raced to the park. Fletcher arrived in 12 minutes while Jim arrived in 14 minutes. Write the ratio of their race times, beginning with the winner.
- Practice 3 - Complete each ratio table. There are several missing pieces found in here.
- Practice 4 - At the gym, eight people can fit in one hot tub. This can be expressed as y x 8 = Z. If y = # of hot tubs and Z = # of people, find the total number of people that can fit in the gym's 9 hot tubs.
- Practice 5 - Every foot is 12 inches. This can be expressed as y x 12 = Z. If y = # of feet and Z = # of inches, find the total number of inches in 4 feet.

#### Math Skill Quizzes

The third quiz is a bit of a challenging set for this level.

- Quiz 1 - Fill in the blank to make an equivalent ratio.
- Quiz 2 - Name each variable to make these values equal.
- Quiz 3 - In the past year, Johnny received 12 gold stars and Jimmy received 15. Write the ratio of gold stars that Johnny and Jimmy received.

### How Does This Skill Apply to Everyday Life?

This is a skill that we use almost everyday without realize it. When we are growing up, we often love to learn to cook. Following a recipe that we wish to scale up or size down, is this skill to the T. Think about it, every single recipe you come across is just a series of ingredients in a ratio with one another. Every recipe is designed, with the ingredients in proportion, to produce a fixed amount of the item you are making. If you want more or less of that item, you will just create an equivalent ratio up or down. Take a look at what it takes to create a standard loaf of bread. The recipe calls for 5 cups of flour, 1 tablespoon of sugar, 2 teaspoons of salt, 2 teaspoons of yeast, and 2 cups of water. If you wanted to make 2 loaves of bread, guess what ingredients you would need? It would be everything we just stated, but twice as much. If you wanted a half a loaf, you would need half the amount of ingredients. As you can see. As long as you create an equivalent ratio, the bread will be the same consistence and taste you were looking for in a single loaf. Beyond recipes you will find this skill helpful when you are comparison shopping. I find this extremely helpful on the cereal aisle. They will often package the same cereal in a variety of different sizes. Using this skill, you can determine the best buy. Most retailers will display the unit price which displays the cost of single unit of what you are buying. That is a quick and easy way to compare which is the best price for you.