### Illustrative Mathematics

A ratio is one thing or value compared with or related to another thing or value; it is just a statement On the other hand, a proportion is two ratios which have been set equal to each other; . The cross-multiplication solution of the above exercise looks like this: . 6 y = 2 3 4 \small{ 6y = } 6y= (13 × 18) ÷ 6 = 39 = y. Equivalent Ratios. 2.) This is an example of scaling down by a scale factor of 5. The ratio 8 to 11 is the 1: 3 = 2: 6 = 3: 9 = 4: 12 = 5: 15 = 6: 18 = 7: Lesson Comparing Additive and Multiplicative DAY 6. DAY 7. Lesson Ready to Go On? Texas Test Prep. Module 8. DAY 1. DAY 2 . Remind students that a ratio is a comparison of two quantities expressed with the same units of . You can solve rate problems by using a unit rate or by using equivalent rates.

Ratios often look like fractions, but they are read differently. Read on to find out how to solve algebraic ratio problems using two methods: Using Equivalent Ratios When you first begin studying ratios, you will encounter equivalent ratio problems. The word equivalent means equal value.

### 6th Grade Math - Unit 1: Understanding and Representing Ratios | Common Core Lessons

You have probably come across this term when you learned about fractions. Equivalent fractions are two fractions with the same value. Equivalent ratios are very similar to equivalent fractions. Let's use the following problem as an example for solving equivalent ratio problems: First, identify the set of terms with the variable.

A variable is a letter or symbol that represents a number. In this case, the second set of terms and n--has has the variable. Note that if we were talking about fractions, we could call the numbers in the second set "denominators.

We will be using the known value in this set 12 to determine the value of the variable Sciencing Video Vault In order to determine the relationship between the second set of terms in our ratio, we must first determine the relationship between the values in the first set.

This should be relatively easy because both values in this set are known: Now, ask yourself, "How are these values related?

## Equivalent ratios

In this case, we know that 5 times 4 equals This will be the key to solving the ratio. Once you have determined how the terms in one set are related, you can solve the ratio. To create an equivalent ratio, you must multiply or divide both terms in the ratio by the same whole number.

This is the same way we create equivalent fractions.

We know that if we multiply 5 by 4, we will get So, we need to also multiply 12 by 4 to find the value of n. Since 12 times 4 is 48, n equals Using Cross-Multiplication When you have moved into more advanced studies of ratios, you will begin to encounter proportions.

- Using Equivalent Ratios
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Proportions are statements that show two ratios as equivalent. Obviously, proportions are very similar to equivalent ratio problems. When students work with tables in the second half of the unit, they will discover how the structure of a ratio table can shine light on a relationship, especially when they compare multiple ratio situations standard for Math Practice 7.

Throughout the unit, students will see similar problems posed to them in different lessons. This is to support students learning new strategies to solve ratio problems and to compare and contrast different approaches.

## Equivalent Ratios

By the end of the unit, students should be able to select a strategy they think is best for a problem and to explain their choice. In fourth and fifth grade, students learned the difference between multiplicative and additive comparisons and they interpreted multiplication as a way to scale. Students will access these prior concepts in this unit as they investigate patterns and structures in ratio tables and use multiplication to create equivalent ratios.

In fifth grade, students also developed their concept of a fraction as division of the numerator and denominator.

### Sixth Grade / Ratios as Multiplicative Comparisons

The work students do in this unit connects directly to unit 2: Beyond sixth grade, students extend their understanding of ratios and rates to investigate proportional relationships in seventh grade. This sets the groundwork for the study of functions, linear equations, and systems of equations, which students will study in eighth grade and high school. This unit includes the MA-specific standard 6. While this context is specific to this MA standard, it poses a real-world example of ratio problems that is worthwhile to solve.