Grade 6 Equivalent Fractions Worksheet with 14 math problems for finding missing values in fraction equations.

Problem: Equivalent Fractions Worksheet

The task is to find the missing numbers in each fraction to make them equivalent. This involves understanding how to simplify or scale fractions by multiplying or dividing both the numerator and the denominator by the same number.

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Solution:

#### 1. $\frac{4}{?} = \frac{28}{70}$
- Simplify $\frac{28}{70}$:
$$
\frac{28}{70} = \frac{28 \div 14}{70 \div 14} = \frac{2}{5}
$$
- Now, compare $\frac{4}{?}$ with $\frac{2}{5}$:
- To get from $\frac{2}{5}$ to $\frac{4}{?}$, multiply both the numerator and the denominator by 2.
- Therefore, $\frac{4}{?} = \frac{4}{10}$.
- Answer: $\boxed{10}$

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#### 2. $\frac{?}{8} = \frac{4}{8}$
- The fraction $\frac{4}{8}$ is already given.
- Since the denominators are the same, the numerators must also be the same for the fractions to be equivalent.
- Answer: $\boxed{4}$

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#### 3. $\frac{2}{3} = \frac{?}{27}$
- To find the missing numerator, determine what you multiply the denominator 3 by to get 27:
$$
3 \times 9 = 27
$$
- Multiply the numerator 2 by the same factor (9):
$$
2 \times 9 = 18
$$
- Therefore, $\frac{2}{3} = \frac{18}{27}$.
- Answer: $\boxed{18}$

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#### 4. $\frac{4}{6} = \frac{16}{?}$
- Simplify $\frac{4}{6}$:
$$
\frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}
$$
- Now, compare $\frac{2}{3}$ with $\frac{16}{?}$:
- To get from $\frac{2}{3}$ to $\frac{16}{?}$, multiply both the numerator and the denominator by 8.
- Therefore, $\frac{16}{?} = \frac{16}{24}$.
- Answer: $\boxed{24}$

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#### 5. $\frac{1}{8} = \frac{?}{64}$
- To find the missing numerator, determine what you multiply the denominator 8 by to get 64:
$$
8 \times 8 = 64
$$
- Multiply the numerator 1 by the same factor (8):
$$
1 \times 8 = 8
$$
- Therefore, $\frac{1}{8} = \frac{8}{64}$.
- Answer: $\boxed{8}$

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#### 6. $\frac{2}{?} = \frac{8}{16}$
- Simplify $\frac{8}{16}$:
$$
\frac{8}{16} = \frac{8 \div 8}{16 \div 8} = \frac{1}{2}
$$
- Now, compare $\frac{2}{?}$ with $\frac{1}{2}$:
- To get from $\frac{1}{2}$ to $\frac{2}{?}$, multiply both the numerator and the denominator by 2.
- Therefore, $\frac{2}{?} = \frac{2}{4}$.
- Answer: $\boxed{4}$

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#### 7. $\frac{1}{?} = \frac{10}{50}$
- Simplify $\frac{10}{50}$:
$$
\frac{10}{50} = \frac{10 \div 10}{50 \div 10} = \frac{1}{5}
$$
- Now, compare $\frac{1}{?}$ with $\frac{1}{5}$:
- The denominators must be the same.
- Therefore, $\frac{1}{?} = \frac{1}{5}$.
- Answer: $\boxed{5}$

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#### 8. $\frac{2}{?} = \frac{4}{12}$
- Simplify $\frac{4}{12}$:
$$
\frac{4}{12} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3}
$$
- Now, compare $\frac{2}{?}$ with $\frac{1}{3}$:
- To get from $\frac{1}{3}$ to $\frac{2}{?}$, multiply both the numerator and the denominator by 2.
- Therefore, $\frac{2}{?} = \frac{2}{6}$.
- Answer: $\boxed{6}$

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#### 9. $\frac{7}{12} = \frac{?}{24}$
- To find the missing numerator, determine what you multiply the denominator 12 by to get 24:
$$
12 \times 2 = 24
$$
- Multiply the numerator 7 by the same factor (2):
$$
7 \times 2 = 14
$$
- Therefore, $\frac{7}{12} = \frac{14}{24}$.
- Answer: $\boxed{14}$

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#### 10. $\frac{3}{?} = \frac{6}{10}$
- Simplify $\frac{6}{10}$:
$$
\frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5}
$$
- Now, compare $\frac{3}{?}$ with $\frac{3}{5}$:
- The numerators are the same, so the denominators must also be the same.
- Therefore, $\frac{3}{?} = \frac{3}{5}$.
- Answer: $\boxed{5}$

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#### 11. $\frac{2}{10} = \frac{?}{40}$
- To find the missing numerator, determine what you multiply the denominator 10 by to get 40:
$$
10 \times 4 = 40
$$
- Multiply the numerator 2 by the same factor (4):
$$
2 \times 4 = 8
$$
- Therefore, $\frac{2}{10} = \frac{8}{40}$.
- Answer: $\boxed{8}$

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#### 12. $\frac{?}{4} = \frac{36}{24}$
- Simplify $\frac{36}{24}$:
$$
\frac{36}{24} = \frac{36 \div 12}{24 \div 12} = \frac{3}{2}
$$
- Now, compare $\frac{?}{4}$ with $\frac{3}{2}$:
- To get from $\frac{3}{2}$ to $\frac{?}{4}$, multiply both the numerator and the denominator by 2.
- Therefore, $\frac{?}{4} = \frac{6}{4}$.
- Answer: $\boxed{6}$

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#### 13. $\frac{7}{8} = \frac{?}{72}$
- To find the missing numerator, determine what you multiply the denominator 8 by to get 72:
$$
8 \times 9 = 72
$$
- Multiply the numerator 7 by the same factor (9):
$$
7 \times 9 = 63
$$
- Therefore, $\frac{7}{8} = \frac{63}{72}$.
- Answer: $\boxed{63}$

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#### 14. $\frac{1}{?} = \frac{9}{16}$
- To find the missing denominator, determine what you multiply the numerator 1 by to get 9:
$$
1 \times 9 = 9
$$
- Multiply the denominator ? by the same factor (9):
$$
? \times 9 = 16
$$
- Solve for ?:
$$
? = \frac{16}{9}
$$
- Therefore, $\frac{1}{?} = \frac{1}{\frac{16}{9}} = \frac{9}{16}$.
- Answer: $\boxed{\frac{16}{9}}$

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Final Answers:

1. $\boxed{10}$
2. $\boxed{4}$
3. $\boxed{18}$
4. $\boxed{24}$
5. $\boxed{8}$
6. $\boxed{4}$
7. $\boxed{5}$
8. $\boxed{6}$
9. $\boxed{14}$
10. $\boxed{5}$
11. $\boxed{8}$
12. $\boxed{6}$
13. $\boxed{63}$
14. $\boxed{\frac{16}{9}}$