To find the missing numbers in these equivalent fractions, we need to figure out what number was used to multiply or divide the top and bottom numbers (numerator and denominator) to get from one fraction to the other.
Here is the step-by-step solution for each problem:
1. $\frac{\square}{4} = \frac{2}{8}$
* Look at the denominators (bottom numbers): To get from 8 to 4, we divide by 2 ($8 \div 2 = 4$).
* Do the same to the numerator (top number): $2 \div 2 = 1$.
* The missing number is
1.
2. $\frac{1}{\square} = \frac{3}{9}$
* Look at the numerators: To get from 3 to 1, we divide by 3 ($3 \div 3 = 1$).
* Do the same to the denominator: $9 \div 3 = 3$.
* The missing number is
3.
3. $\frac{2}{3} = \frac{\square}{9}$
* Look at the denominators: To get from 3 to 9, we multiply by 3 ($3 \times 3 = 9$).
* Do the same to the numerator: $2 \times 3 = 6$.
* The missing number is
6.
4. $\frac{1}{3} = \frac{\square}{15}$
* Look at the denominators: To get from 3 to 15, we multiply by 5 ($3 \times 5 = 15$).
* Do the same to the numerator: $1 \times 5 = 5$.
* The missing number is
5.
5. $\frac{1}{\square} = \frac{10}{20}$
* Look at the numerators: To get from 10 to 1, we divide by 10 ($10 \div 10 = 1$).
* Do the same to the denominator: $20 \div 10 = 2$.
* The missing number is
2.
6. $\frac{2}{\square} = \frac{14}{21}$
* Look at the numerators: To get from 14 to 2, we divide by 7 ($14 \div 7 = 2$).
* Do the same to the denominator: $21 \div 7 = 3$.
* The missing number is
3.
7. $\frac{1}{\square} = \frac{11}{66}$
* Look at the numerators: To get from 11 to 1, we divide by 11 ($11 \div 11 = 1$).
* Do the same to the denominator: $66 \div 11 = 6$.
* The missing number is
6.
8. $\frac{3}{4} = \frac{\square}{24}$
* Look at the denominators: To get from 4 to 24, we multiply by 6 ($4 \times 6 = 24$).
* Do the same to the numerator: $3 \times 6 = 18$.
* The missing number is
18.
9. $\frac{1}{5} = \frac{2}{\square}$
* Look at the numerators: To get from 1 to 2, we multiply by 2 ($1 \times 2 = 2$).
* Do the same to the denominator: $5 \times 2 = 10$.
* The missing number is
10.
10. $\frac{1}{\square} = \frac{2}{16}$
* Look at the numerators: To get from 2 to 1, we divide by 2 ($2 \div 2 = 1$).
* Do the same to the denominator: $16 \div 2 = 8$.
* The missing number is
8.
Final Answer:
1. 1
2. 3
3. 6
4. 5
5. 2
6. 3
7. 6
8. 18
9. 10
10. 8
Parent Tip: Review the logic above to help your child master the concept of equivalent fractions.
