All About 7th Grade Fractions and Decimals

What Do 7th Graders Learn about Fractions and Decimals?

Ratios and Proportions

A ratio demonstrates a relationship between two amounts. It can be written using a colon (1:3) or a fraction (1/3). In 7th grade, students learn to use ratios to calculate rate. For instance, if a car has traveled 500 miles in 20 hours, the car's rate of speed can be calculated by creating a ratio and simplifying it, like this: 500/20 = 25/1 = 25 miles per hour.

Proportional relationships compare two equivalent ratios. Often, 7th graders have to solve a proportion, like 4/5 = x/30, for an unknown variable. To solve proportions, students learn to cross-multiply and then isolate the variable. For this problem, cross-multiplication gives the following result: 5x = 120. Then, your student can divide both sides by five to get x = 24.

Your 7th grader will likely have to solve real-world word problems using proportions. Here's an example:

Max bought five cupcakes for $32. How much money would he have spent if he bought 15 cupcakes?

To solve this problem, your 7th grader should identify the variable. In this case, the variable is how much 15 cupcakes would cost. Then, your student can create a proportional relationship by writing the two ratios and adding an equals sign (5/32 = 15/x). The next step is to cross-multiply and isolate the variable as shown in the previous example. The answer is x = $96.

Rational Numbers

In 7th grade, students study the relationship between fractions, decimals and percents, which are all representations of rational numbers. Rational numbers include whole numbers, decimals, fractions and even negative numbers. You can determine whether or not a number is rational by writing it as a fraction. If both the numerator and the denominator are integers, and the denominator doesn't equal zero, then the number is rational.

Your 7th grader may convert decimals with a hundredths place to fractions by putting them over 100, like this: 0.24 = 24/100. Decimals with just a tenths place can be written over ten (0.4 = 4/10). These fractions can then be simplified to 6/25 and 2/5, respectively.

Your student can also convert decimals to percentages by multiplying them by 100 (0.24 x 100 = 24%). Fractions can be converted to decimals by simply dividing the numerator by the denominator. For example, 6/25 = 6 ÷ 25 = 0.24.