Ratio & Proportion Worksheet for 12-Year-Olds — Middle School Math (Grade 7) Practice

Instructions

Read each section carefully and answer the questions. Show your work where necessary. Ratios compare two quantities, and proportions state that two ratios are equal. Good luck!

Part 1: Writing and Simplifying Ratios

A ratio compares two numbers. It can be written in three ways: a to b, a:b, or as a fraction a/b. Always simplify your ratio to its lowest terms, just like a fraction!

1. In a school choir, there are 12 sopranos, 5 altos, and 8 tenors. Write the following ratios in their simplest form (using the a:b format).
   
   a) Sopranos to tenors: _______________
   b) Altos to sopranos: _______________
   c) Tenors to the total number of choir members: _______________


2. A video game character has 100 health points and 50 magic points. What is the simplified ratio of health points to magic points?
   
   Ratio: _______________


3. Simplify the following ratios:
   
   a) 15:20 = _______________
   b) 24:8 = _______________
   c) 18:45 = _______________

Part 2: Solving Proportions

A proportion is an equation stating that two ratios are equal. You can use cross-multiplication to find the missing value (represented by a letter like x).

Example:   2/3 = x/9   →   2 × 9 = 3 × x   →   18 = 3x   →   x = 6

1. Solve for the missing value in each proportion.
   
   a) 5 / 8 = x / 32           x = _______________
   
   b) 7 / n = 21 / 24           n = _______________
   
   c) 10 / 12 = 15 / y           y = _______________

Part 3: Ratio and Proportion Word Problems

Set up a proportion to solve each problem. Make sure to keep your units consistent!

1. A recipe for lemonade requires 3 cups of water for every 1 cup of lemon juice. If you want to make a big batch with 6 cups of lemon juice, how much water will you need?
   
   Answer: _______________


2. If 4 movie tickets cost $50, how much would it cost to buy 6 movie tickets?
   
   Answer: _______________


3. A car can travel 120 miles on 5 gallons of gas. How many gallons of gas would be needed to travel 300 miles?
   
   Answer: _______________


4. Challenge: In a park, the ratio of oak trees to maple trees is 4:3. If there are 36 maple trees in the park, how many trees are there in total (oaks and maples combined)?
   
   Answer: _______________

Answer Key

Part 1: Writing and Simplifying Ratios

1. a) 12:8 simplifies to 3:2
   b) 5:12 (cannot be simplified)
   c) Total members = 12 + 5 + 8 = 25. The ratio is 8:25. 8:25 (cannot be simplified)
2. 100:50 simplifies to 2:1
3. a) 15:20 = 3:4 (dividing both by 5)
   b) 24:8 = 3:1 (dividing both by 8)
   c) 18:45 = 2:5 (dividing both by 9)

Part 2: Solving Proportions

1. a) 5 × 32 = 8 × x → 160 = 8x → x = 20
   b) 7 × 24 = n × 21 → 168 = 21n → n = 8
   c) 10 × y = 12 × 15 → 10y = 180 → y = 18

Part 3: Ratio and Proportion Word Problems

1. Proportion: 3/1 = x/6.   3 × 6 = 1 × x.   x = 18.
   Answer: 18 cups of water
2. Proportion: 50/4 = x/6.   50 × 6 = 4 × x.   300 = 4x.   x = 75.
   Answer: $75
3. Proportion: 120/5 = 300/x.   120 × x = 5 × 300.   120x = 1500.   x = 12.5.
   Answer: 12.5 gallons of gas
4. Challenge:
   First find the number of oak trees. Proportion: 4/3 = x/36.   4 × 36 = 3 × x.   144 = 3x.   x = 48 oak trees.
   Total trees = Oak trees + Maple trees = 48 + 36 = 84.
   Answer: 84 trees in total