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Proportion worksheet

Grades 6–7 · CCSS 6.RP.A.3, 7.RP.A.3

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

1.
Problem 1.
- Solve A/B = C/D for: C
- A (first numerator): 3
- B (first denominator): 4
- D (second denominator): 24
Find: Missing value C
Answer
2.
Problem 2.
- Solve A/B = C/D for: B
- A (first numerator): 2
- C (second numerator): 15
- D (second denominator): 18
Find: Missing value B
Answer
3.
Problem 3.
- Solve A/B = C/D for: B
- A (first numerator): 3
- C (second numerator): 14
- D (second denominator): 24
Find: Missing value B
Answer
4.
Problem 4.
- Solve A/B = C/D for: B
- A (first numerator): 2
- C (second numerator): 12
- D (second denominator): 22
Find: Missing value B
Answer
5.
Problem 5.
- Solve A/B = C/D for: C
- A (first numerator): 3
- B (first denominator): 6
- D (second denominator): 18
Find: Missing value C
Answer
6.
Problem 6.
- Solve A/B = C/D for: B
- A (first numerator): 4
- C (second numerator): 17
- D (second denominator): 20
Find: Missing value B
Answer
7.
Problem 7.
- Solve A/B = C/D for: B
- A (first numerator): 3
- C (second numerator): 16
- D (second denominator): 20
Find: Missing value B
Answer
8.
Problem 8.
- Solve A/B = C/D for: A
- B (first denominator): 4
- C (second numerator): 10
- D (second denominator): 18
Find: Missing value A
Answer
9.
Problem 9.
- Solve A/B = C/D for: A
- B (first denominator): 5
- C (second numerator): 13
- D (second denominator): 24
Find: Missing value A
Answer
10.
Problem 10.
- Solve A/B = C/D for: A
- B (first denominator): 5
- C (second numerator): 10
- D (second denominator): 22
Find: Missing value A
Answer

Answer key: Proportion worksheet

1. Missing value C: 18
1. Write the proportion with the unknown C as x
  $\frac{3}{4}$ $= \frac{x}{24}$
2. Cross-multiply: the product of one diagonal equals the product of the other (A × D = B × C)
  $3 \times 24$ $= 4 \times x$
3. Multiply out the side with two known numbers
  $4 x$ $= 3 \times 24$ $= 72$
4. Divide both sides by 4 so x is left on its own
  $x$ $= \frac{72}{4}$ $= 18$
5. Check the answer: both ratios should now have the same value
  $\frac{3}{4} = 0.75, \frac{18}{24} = 0.75$
2. Missing value B: 2.4
1. Write the proportion with the unknown B as x
  $\frac{2}{x}$ $= \frac{15}{18}$
2. Cross-multiply: the product of one diagonal equals the product of the other (A × D = B × C)
  $2 \times 18$ $= x \times 15$
3. Multiply out the side with two known numbers
  $15 x$ $= 2 \times 18$ $= 36$
4. Divide both sides by 15 so x is left on its own
  $x$ $= \frac{36}{15}$ $= 2.4$
5. Check the answer: both ratios should now have the same value
  $\frac{2}{2.4} = 0.833333, \frac{15}{18} = 0.833333$
3. Missing value B: 5.14
1. Write the proportion with the unknown B as x
  $\frac{3}{x}$ $= \frac{14}{24}$
2. Cross-multiply: the product of one diagonal equals the product of the other (A × D = B × C)
  $3 \times 24$ $= x \times 14$
3. Multiply out the side with two known numbers
  $14 x$ $= 3 \times 24$ $= 72$
4. Divide both sides by 14 so x is left on its own
  $x$ $= \frac{72}{14}$ $= 5.142857$
5. Check the answer: both ratios should now have the same value
  $\frac{3}{5.142857} = 0.583333, \frac{14}{24} = 0.583333$
4. Missing value B: 3.67
1. Write the proportion with the unknown B as x
  $\frac{2}{x}$ $= \frac{12}{22}$
2. Cross-multiply: the product of one diagonal equals the product of the other (A × D = B × C)
  $2 \times 22$ $= x \times 12$
3. Multiply out the side with two known numbers
  $12 x$ $= 2 \times 22$ $= 44$
4. Divide both sides by 12 so x is left on its own
  $x$ $= \frac{44}{12}$ $= 3.666667$
5. Check the answer: both ratios should now have the same value
  $\frac{2}{3.666667} = 0.545455, \frac{12}{22} = 0.545455$
5. Missing value C: 9
1. Write the proportion with the unknown C as x
  $\frac{3}{6}$ $= \frac{x}{18}$
2. Cross-multiply: the product of one diagonal equals the product of the other (A × D = B × C)
  $3 \times 18$ $= 6 \times x$
3. Multiply out the side with two known numbers
  $6 x$ $= 3 \times 18$ $= 54$
4. Divide both sides by 6 so x is left on its own
  $x$ $= \frac{54}{6}$ $= 9$
5. Check the answer: both ratios should now have the same value
  $\frac{3}{6} = 0.5, \frac{9}{18} = 0.5$
6. Missing value B: 4.71
1. Write the proportion with the unknown B as x
  $\frac{4}{x}$ $= \frac{17}{20}$
2. Cross-multiply: the product of one diagonal equals the product of the other (A × D = B × C)
  $4 \times 20$ $= x \times 17$
3. Multiply out the side with two known numbers
  $17 x$ $= 4 \times 20$ $= 80$
4. Divide both sides by 17 so x is left on its own
  $x$ $= \frac{80}{17}$ $= 4.705882$
5. Check the answer: both ratios should now have the same value
  $\frac{4}{4.705882} = 0.85, \frac{17}{20} = 0.85$
7. Missing value B: 3.75
1. Write the proportion with the unknown B as x
  $\frac{3}{x}$ $= \frac{16}{20}$
2. Cross-multiply: the product of one diagonal equals the product of the other (A × D = B × C)
  $3 \times 20$ $= x \times 16$
3. Multiply out the side with two known numbers
  $16 x$ $= 3 \times 20$ $= 60$
4. Divide both sides by 16 so x is left on its own
  $x$ $= \frac{60}{16}$ $= 3.75$
5. Check the answer: both ratios should now have the same value
  $\frac{3}{3.75} = 0.8, \frac{16}{20} = 0.8$
8. Missing value A: 2.22
1. Write the proportion with the unknown A as x
  $\frac{x}{4}$ $= \frac{10}{18}$
2. Cross-multiply: the product of one diagonal equals the product of the other (A × D = B × C)
  $x \times 18$ $= 4 \times 10$
3. Multiply out the side with two known numbers
  $18 x$ $= 4 \times 10$ $= 40$
4. Divide both sides by 18 so x is left on its own
  $x$ $= \frac{40}{18}$ $= 2.222222$
5. Check the answer: both ratios should now have the same value
  $\frac{2.222222}{4} = 0.555556, \frac{10}{18} = 0.555556$
9. Missing value A: 2.71
1. Write the proportion with the unknown A as x
  $\frac{x}{5}$ $= \frac{13}{24}$
2. Cross-multiply: the product of one diagonal equals the product of the other (A × D = B × C)
  $x \times 24$ $= 5 \times 13$
3. Multiply out the side with two known numbers
  $24 x$ $= 5 \times 13$ $= 65$
4. Divide both sides by 24 so x is left on its own
  $x$ $= \frac{65}{24}$ $= 2.708333$
5. Check the answer: both ratios should now have the same value
  $\frac{2.708333}{5} = 0.541667, \frac{13}{24} = 0.541667$
10. Missing value A: 2.27
1. Write the proportion with the unknown A as x
  $\frac{x}{5}$ $= \frac{10}{22}$
2. Cross-multiply: the product of one diagonal equals the product of the other (A × D = B × C)
  $x \times 22$ $= 5 \times 10$
3. Multiply out the side with two known numbers
  $22 x$ $= 5 \times 10$ $= 50$
4. Divide both sides by 22 so x is left on its own
  $x$ $= \frac{50}{22}$ $= 2.272727$
5. Check the answer: both ratios should now have the same value
  $\frac{2.272727}{5} = 0.454545, \frac{10}{22} = 0.454545$