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Ratio worksheet

Grade 6 · CCSS 6.RP.A.3, 6.RP.A.1

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Calculation: Simplify A : B
- A: 3
- B: 4
Find: Simplified ratio
Answer
2.
Problem 2.
- Calculation: Simplify A : B
- A: 3
- B: 3
Find: Simplified ratio
Answer
3.
Problem 3.
- Calculation: Solve A : B = C : D for D
- A: 3
- B: 5
- C: 15
Find: D
Answer
4.
Problem 4.
- Calculation: Solve A : B = C : D for D
- A: 4
- B: 4
- C: 12
Find: D
Answer
5.
Problem 5.
- Calculation: Simplify A : B
- A: 2
- B: 5
Find: Simplified ratio
Answer
6.
Problem 6.
- Calculation: Solve A : B = C : D for D
- A: 4
- B: 6
- C: 13
Find: D
Answer
7.
Problem 7.
- Calculation: Simplify A : B
- A: 4
- B: 4
Find: Simplified ratio
Answer
8.
Problem 8.
- Calculation: Solve A : B = C : D for D
- A: 2
- B: 4
- C: 18
Find: D
Answer
9.
Problem 9.
- Calculation: Solve A : B = C : D for D
- A: 3
- B: 3
- C: 13
Find: D
Answer
10.
Problem 10.
- Calculation: Solve A : B = C : D for D
- A: 3
- B: 5
- C: 9
Find: D
Answer

Answer key: Ratio worksheet

1. Simplified ratio: 3 : 4
1. Find the greatest common divisor (GCD), the largest number that divides both terms
  $GCD (3, 4)$ $= 1$
2. The GCD is 1, so the ratio is already as simple as it gets
  $\frac{3}{1} : \frac{4}{1}$ $= 3 : 4$
2. Simplified ratio: 1 : 1
1. Find the greatest common divisor (GCD), the largest number that divides both terms
  $GCD (3, 3)$ $= 3$
2. Divide both terms by 3 to get the smallest whole numbers
  $\frac{3}{3} : \frac{3}{3}$ $= 1 : 1$
3. D: 25
1. Write both ratios as fractions that are equal, with D as the missing number
  $\frac{3}{5}$ $= \frac{15}{D}$
2. Cross-multiply: the first top number times D equals the first bottom number times the second top number
  $3 \times D$ $= 5 \times 15$ $= 75$
3. Divide both sides by the first top number to get D on its own
  $D$ $= \frac{75}{3}$ $= 25$
4. D: 12
1. Write both ratios as fractions that are equal, with D as the missing number
  $\frac{4}{4}$ $= \frac{12}{D}$
2. Cross-multiply: the first top number times D equals the first bottom number times the second top number
  $4 \times D$ $= 4 \times 12$ $= 48$
3. Divide both sides by the first top number to get D on its own
  $D$ $= \frac{48}{4}$ $= 12$
5. Simplified ratio: 2 : 5
1. Find the greatest common divisor (GCD), the largest number that divides both terms
  $GCD (2, 5)$ $= 1$
2. The GCD is 1, so the ratio is already as simple as it gets
  $\frac{2}{1} : \frac{5}{1}$ $= 2 : 5$
6. D: 19.5
1. Write both ratios as fractions that are equal, with D as the missing number
  $\frac{4}{6}$ $= \frac{13}{D}$
2. Cross-multiply: the first top number times D equals the first bottom number times the second top number
  $4 \times D$ $= 6 \times 13$ $= 78$
3. Divide both sides by the first top number to get D on its own
  $D$ $= \frac{78}{4}$ $= 19.5$
7. Simplified ratio: 1 : 1
1. Find the greatest common divisor (GCD), the largest number that divides both terms
  $GCD (4, 4)$ $= 4$
2. Divide both terms by 4 to get the smallest whole numbers
  $\frac{4}{4} : \frac{4}{4}$ $= 1 : 1$
8. D: 36
1. Write both ratios as fractions that are equal, with D as the missing number
  $\frac{2}{4}$ $= \frac{18}{D}$
2. Cross-multiply: the first top number times D equals the first bottom number times the second top number
  $2 \times D$ $= 4 \times 18$ $= 72$
3. Divide both sides by the first top number to get D on its own
  $D$ $= \frac{72}{2}$ $= 36$
9. D: 13
1. Write both ratios as fractions that are equal, with D as the missing number
  $\frac{3}{3}$ $= \frac{13}{D}$
2. Cross-multiply: the first top number times D equals the first bottom number times the second top number
  $3 \times D$ $= 3 \times 13$ $= 39$
3. Divide both sides by the first top number to get D on its own
  $D$ $= \frac{39}{3}$ $= 13$
10. D: 15
1. Write both ratios as fractions that are equal, with D as the missing number
  $\frac{3}{5}$ $= \frac{9}{D}$
2. Cross-multiply: the first top number times D equals the first bottom number times the second top number
  $3 \times D$ $= 5 \times 9$ $= 45$
3. Divide both sides by the first top number to get D on its own
  $D$ $= \frac{45}{3}$ $= 15$