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Introduction to Ratios

More Lessons for Grade 6

A ratio is a comparison of any two quantities. It can be written as a to b, a: b or a/b.

Percent is a ratio. Percent should be viewed as a part-to-whole ratio that compares a number to a whole divided into 100 equal parts.

In these lessons, we will learn how to solve ratio word problems and how to use ratios to help us solve percent word problems.

Some of the strategies that we can use to solve ratio word problems are:

1) Table with multiplication

2) Double number lines

3) Tape diagrams

4) Graphing

### Ratio Word Problems

### Using Table with Multiplication

In this lesson you will learn to solve for missing values in a ratio problem by using a table and multiplicative reasoning.

Example:

A recipe calls for 3 cups of orange juice for every 4 cups of fruit punch. If a person makes a large batch of this recipe, how many cups of fruit punch will be needed if 12 cups of orange juice are used?### Using Double Number Lines

In this lesson you will learn to solve for missing values in a ratio problem by setting up a double number line. We can use either addition or multiplication.

Examples:

1. The ratio of boys to girls in a class is 5 to 2. If there are 15 boys in a class, how many girls are there?

2. Mrs. Schreier can grade 30 papers in 4 minutes. How many papers can she grade in 30 minutes?

### Using Tape Diagram

In this lesson you will learn to solve ratio problems by using a tape diagram.

1. Write your ratio as a fraction and label next to each part.

2. Draw your boxes (connected or separated).

3. Match the additional info. with the part of your ratio.

4. Fill your boxes with the SAME number.

5. Multiply (or skip count) to get your new parts.

Example:

Paige wanted to bake cookies for her teachers at school. She decided to make both sugar and chocolate chip cookies. For every 5 chocolate chip cookies, Paige baked 2 sugar cookies. If Paige baked 25 chocolate chip cookies, how many sugare cookies did she bake?### Using Graphs

In this lesson you will learn to graph ratios on a coordinate plane by setting up a table.

Example:

The table below shows how many football players Coach Whistle can feed for each pizza that he buys.

Graph the data and use the information to answer the questions below.

a. How many football players can be fed if Coach Whistle orders 7 pizzas?

b. If there are 24 players to feed, how many pizzas should the coach order?

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Introduction to Ratios

More Lessons for Grade 6

A ratio is a comparison of any two quantities. It can be written as a to b, a: b or a/b.

Percent is a ratio. Percent should be viewed as a part-to-whole ratio that compares a number to a whole divided into 100 equal parts.

In these lessons, we will learn how to solve ratio word problems and how to use ratios to help us solve percent word problems.

Some of the strategies that we can use to solve ratio word problems are:

1) Table with multiplication

2) Double number lines

3) Tape diagrams

4) Graphing

Example:

A recipe calls for 3 cups of orange juice for every 4 cups of fruit punch. If a person makes a large batch of this recipe, how many cups of fruit punch will be needed if 12 cups of orange juice are used?

Examples:

1. The ratio of boys to girls in a class is 5 to 2. If there are 15 boys in a class, how many girls are there?

2. Mrs. Schreier can grade 30 papers in 4 minutes. How many papers can she grade in 30 minutes?

1. Write your ratio as a fraction and label next to each part.

2. Draw your boxes (connected or separated).

3. Match the additional info. with the part of your ratio.

4. Fill your boxes with the SAME number.

5. Multiply (or skip count) to get your new parts.

Example:

Paige wanted to bake cookies for her teachers at school. She decided to make both sugar and chocolate chip cookies. For every 5 chocolate chip cookies, Paige baked 2 sugar cookies. If Paige baked 25 chocolate chip cookies, how many sugare cookies did she bake?

Example:

The table below shows how many football players Coach Whistle can feed for each pizza that he buys.

Graph the data and use the information to answer the questions below.

a. How many football players can be fed if Coach Whistle orders 7 pizzas?

b. If there are 24 players to feed, how many pizzas should the coach order?

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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