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Understanding Ratios - Worksheet 10 - 6th Grade

Hard

Understand ratios as comparisons of two quantities (Hard)

23 problems · 15-20 minutes · Skills: ratios, number sense

About This Worksheet

This hard-level worksheet contains 23 problems designed for 6th Grade students practicing understanding ratios. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Ratios are the language of comparison in mathematics and everyday life. Mastering ratio notation and meaning unlocks proportional reasoning — the backbone of percents, scale, probability, and algebra.

  • Write ratios in three forms: fraction, colon, and word form
  • Understand a ratio as a comparison of two quantities
  • Identify part-to-part and part-to-whole ratios
  • Simplify ratios to lowest terms using common factors
  • Recognize equivalent ratios in real-world contexts like recipes

How to Solve: Worked Example

Example Problem: A car travels 240 miles using 8 gallons of fuel. What is the unit rate in miles per gallon?
Solution Steps:
  1. A unit rate compares a quantity to 1 unit.
  2. Divide the total miles by the number of gallons: 240 ÷ 8 = 30.
  3. The car travels 30 miles per gallon.
Answer: 30 miles per gallon
Tip: To find a unit rate, divide to make the second quantity equal to 1.
1
Simplify the ratio 8:2
2
Simplify the ratio 12:24
3
Simplify the ratio 6:12
4
Simplify the ratio 20:8
5
A recipe uses 30 cups of flour and 5 cups of sugar. What is the ratio in simplest form?
6
A recipe uses 10 cups of flour and 8 cups of sugar. What is the ratio in simplest form?
7
A recipe uses 25 cups of flour and 5 cups of sugar. What is the ratio in simplest form?
8
Simplify the ratio 24:16
9
A recipe uses 2 cups of flour and 12 cups of sugar. What is the ratio in simplest form?
10
A recipe uses 4 cups of flour and 2 cups of sugar. What is the ratio in simplest form?
11
Simplify the ratio 5:30
12
Simplify the ratio 9:15
13
Simplify the ratio 12:2
14
A recipe uses 24 cups of flour and 12 cups of sugar. What is the ratio in simplest form?
15
A recipe uses 10 cups of flour and 8 cups of sugar. What is the ratio in simplest form?
16
Simplify the ratio 24:12
17
A recipe uses 9 cups of flour and 15 cups of sugar. What is the ratio in simplest form?
18
A recipe uses 6 cups of flour and 18 cups of sugar. What is the ratio in simplest form?
19
Simplify the ratio 6:6
20
Simplify the ratio 20:12
21
Simplify the ratio 9:6
22
Simplify the ratio 12:20
23
A recipe uses 6 cups of flour and 6 cups of sugar. What is the ratio in simplest form?

Answer Key

1. 4:12. 1:23. 1:24. 5:25. 6:16. 5:47. 5:18. 3:29. 1:610. 2:111. 1:612. 3:513. 6:114. 2:115. 5:416. 2:117. 3:518. 1:319. 1:120. 5:321. 3:222. 3:523. 1:1

Frequently Asked Questions

How do I download this understanding ratios - worksheet 10 worksheet?

Click the "Download PDF / Print" button at the top of the worksheet. You can save it as a PDF or print it directly. The answer key will be on a separate page.

How do I find worksheets at different difficulty levels?

Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.

What skills does this ratios and proportional relationships worksheet cover?

This worksheet focuses on ratios, number sense. It is designed for 6th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 23 problems. It typically takes 15-20 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.