6th Grade Ratio Problems- Practice Worksheets and Solutions

What 6th Graders Actually Struggle With in Ratio Problems

Most 6th graders don't struggle with the concept of ratios. They understand that if you have 2 apples for every 3 oranges, that's a ratio. The problem starts when they have to write it, solve it, or apply it to word problems.

Teachers spend weeks on this unit because ratio reasoning shows up in everything from unit rates to percentages to proportional relationships in 7th grade. If your kid is bombing tests right now, they're not alone. Here's what actually needs to happen for this to click.

The Core Skill: Writing Ratios Three Different Ways

Every ratio problem assumes students can write the same ratio in three formats. If they're only writing one, they'll lose points.

• Word form: 2 to 3
• Colon form: 2:3
• Fraction form: 2/3

Students need to know these are identical. The fraction form trips most kids up because they think 2/3 means something different than 2:3. It doesn't.

Types of Ratio Problems You'll See in 6th Grade

Type 1: Finding Equivalent Ratios

Given one ratio, find another equivalent ratio by multiplying or dividing both terms by the same number.

Example: If the ratio of boys to girls is 3:5 and there are 15 girls, how many boys are there?

Solution: 3:5 = ? : 15. Since 5 × 3 = 15, multiply 3 × 3 = 9. There are 9 boys.

Type 2: Simplifying Ratios

Divide both terms by their greatest common factor.

Example: Simplify 12:18

Solution: GCF of 12 and 18 is 6. Divide both: 12 ÷ 6 = 2, 18 ÷ 6 = 3. The simplified ratio is 2:3.

Type 3: Ratio Table Problems

Students fill in missing values in a ratio table, often requiring multiplication or division.

These appear on almost every state test. The trick: identify the multiplier or divisor first, then apply it consistently.

Type 4: Real-World Word Problems

Recipes, map scales, speed/distance, cost per item. These require students to identify the ratio, set it up correctly, then solve.

Example: A recipe uses 4 cups of flour for every 6 cups of sugar. How much flour is needed for 18 cups of sugar?

Solution: Ratio is 4:6. 6 × 3 = 18, so 4 × 3 = 12. You need 12 cups of flour.

Practice Worksheet #1: Equivalent Ratios

Solve each problem. Show your work.

1. If the ratio of dogs to cats at a shelter is 4:7 and there are 28 cats, how many dogs are there?
2. Simplify the ratio 24:36.
3. Complete the ratio table: 3:5 = 6:__ = __:20 = 15:__
4. A map uses 2 inches to represent 50 miles. How many miles does 7 inches represent?
5. If 5 pencils cost $3.75, how much do 12 pencils cost?

Solutions

1. 4:7 = 16:28. 16 dogs (7 × 4 = 28, so 4 × 4 = 16)
2. 24:36 simplifies to 2:3 (divide both by 12)
3. 3:5 = 6:10 = 12:20 = 15:25
4. 2:50 = 7:175. 175 miles (multiply by 3.5)
5. $3.75 ÷ 5 = $0.75 per pencil. $0.75 × 12 = $9.00

Practice Worksheet #2: Ratio Word Problems

Read carefully. Circle the ratio, box the question, then solve.

1. At a party, the ratio of soda to pizza slices is 3:8. If there are 24 pizza slices, how many sodas are there?
2. A baseball team won 15 games and lost 10. What is the ratio of wins to total games played? Simplify your answer.
3. In a garden, the ratio of roses to tulips is 5:3. If there are 40 flowers total, how many are roses?
4. A car travels 180 miles on 6 gallons of gas. How many miles per gallon does it get?
5. The ratio of boys to girls in a class is 8:7. There are 45 students total. How many are boys?

Solutions

1. 3:8 = 9:24. 9 sodas
2. 15 wins out of 25 total = 15:25 = 3:5
3. 5:3 ratio, 8 parts total (5+3). 40 ÷ 8 = 5. Roses: 5 × 5 = 20 roses
4. 180 ÷ 6 = 30 miles per gallon
5. 8+7 = 15 parts. 45 ÷ 15 = 3. Boys: 8 × 3 = 24 boys

The Method That Actually Works: Cross Multiplication

When students get stuck, this is the failsafe method:

For ratios a/b = c/d, cross multiply: a × d = b × c

Example: 4/x = 2/6

4 × 6 = 2 × x

24 = 2x

x = 12

This works every time. If your kid is guessing and checking, teach them this instead. It's faster and more reliable.

Where This Goes Next: Unit Rates

Unit rates are ratios where the second term is 1. They're the natural next step and show up constantly in algebra.

Example: 150 miles in 3 hours = 50 miles per hour

Students who master ratio tables usually pick up unit rates quickly. The ones who don't usually never solidified the equivalent ratio concept first.

When to Get a Tutor

If your kid has seen these problems for more than 3 weeks and still can't set up a ratio from a word problem, they need intervention. This isn't about being "bad at math." It's about a missing foundation piece.

Common red flags:

• Can't identify which number goes first in the ratio
• Doesn't realize 2:3 and 3:2 are completely different
• Solves by guessing instead of using the ratio structure
• Can do the numbers but can't explain what the ratio means

These aren't character flaws. They're fixable gaps. But they won't fix themselves by doing more of the same worksheet.

Free Resources Worth Using

Not all practice sites are equal. Here's what's actually useful:

Khan Academy is free and actually aligns with most state standards. Start there before paying for anything.

The Bottom Line

Ratios aren't hard. They're systematic. Students who struggle usually don't need more practice—they need to understand the system: write the ratio, find the multiplier, apply it to find the missing value.

Once that clicks, word problems stop being intimidating and start being straightforward. The worksheets above give enough practice to get there. Run through them until it's automatic.