Equivalent Fractions - Exercise 5 - Your Home Teacher - Free Printable

To solve the problem of finding the missing values in the equivalent fractions, we need to use the concept of equivalent fractions. Two fractions are equivalent if they represent the same value when simplified. This means that the numerator and denominator of one fraction can be multiplied or divided by the same non-zero number to get the other fraction.

Let's solve each problem step by step:

1. $\frac{1}{2} = \frac{\square}{14}$

- To find the missing numerator, notice that the denominator $2$ is multiplied by $7$ to get $14$. Therefore, the numerator $1$ must also be multiplied by $7$.
- $1 \times 7 = 7$
- So, $\frac{1}{2} = \frac{7}{14}$

2. $\frac{7}{2} = \frac{\square}{18}$

- The denominator $2$ is multiplied by $9$ to get $18$. Therefore, the numerator $7$ must also be multiplied by $9$.
- $7 \times 9 = 63$
- So, $\frac{7}{2} = \frac{63}{18}$

3. $\frac{3}{6} = \frac{\square}{54}$

- The denominator $6$ is multiplied by $9$ to get $54$. Therefore, the numerator $3$ must also be multiplied by $9$.
- $3 \times 9 = 27$
- So, $\frac{3}{6} = \frac{27}{54}$

4. $\frac{6}{1} = \frac{12}{\square}$

- The numerator $6$ is multiplied by $2$ to get $12$. Therefore, the denominator $1$ must also be multiplied by $2$.
- $1 \times 2 = 2$
- So, $\frac{6}{1} = \frac{12}{2}$

5. $\frac{4}{2} = \frac{4}{\square}$

- The numerator $4$ is the same, so the denominator $2$ must remain the same.
- So, $\frac{4}{2} = \frac{4}{2}$

6. $\frac{7}{10} = \frac{\square}{63}$

- The denominator $10$ is multiplied by $6.3$ to get $63$. Therefore, the numerator $7$ must also be multiplied by $6.3$.
- $7 \times 6.3 = 44.1$
- So, $\frac{7}{10} = \frac{44.1}{63}$

7. $\frac{1}{5} = \frac{\square}{35}$

- The denominator $5$ is multiplied by $7$ to get $35$. Therefore, the numerator $1$ must also be multiplied by $7$.
- $1 \times 7 = 7$
- So, $\frac{1}{5} = \frac{7}{35}$

8. $\frac{7}{9} = \frac{\square}{36}$

- The denominator $9$ is multiplied by $4$ to get $36$. Therefore, the numerator $7$ must also be multiplied by $4$.
- $7 \times 4 = 28$
- So, $\frac{7}{9} = \frac{28}{36}$

9. $\frac{7}{6} = \frac{\square}{36}$

- The denominator $6$ is multiplied by $6$ to get $36$. Therefore, the numerator $7$ must also be multiplied by $6$.
- $7 \times 6 = 42$
- So, $\frac{7}{6} = \frac{42}{36}$

10. $\frac{8}{3} = \frac{32}{\square}$

- The numerator $8$ is multiplied by $4$ to get $32$. Therefore, the denominator $3$ must also be multiplied by $4$.
- $3 \times 4 = 12$
- So, $\frac{8}{3} = \frac{32}{12}$

11. $\frac{3}{6} = \frac{6}{\square}$

- The numerator $3$ is multiplied by $2$ to get $6$. Therefore, the denominator $6$ must also be multiplied by $2$.
- $6 \times 2 = 12$
- So, $\frac{3}{6} = \frac{6}{12}$

12. $\frac{1}{8} = \frac{3}{\square}$

- The numerator $1$ is multiplied by $3$ to get $3$. Therefore, the denominator $8$ must also be multiplied by $3$.
- $8 \times 3 = 24$
- So, $\frac{1}{8} = \frac{3}{24}$

13. $\frac{4}{10} = \frac{\square}{30}$

- The denominator $10$ is multiplied by $3$ to get $30$. Therefore, the numerator $4$ must also be multiplied by $3$.
- $4 \times 3 = 12$
- So, $\frac{4}{10} = \frac{12}{30}$

14. $\frac{9}{2} = \frac{\square}{4}$

- The denominator $2$ is multiplied by $2$ to get $4$. Therefore, the numerator $9$ must also be multiplied by $2$.
- $9 \times 2 = 18$
- So, $\frac{9}{2} = \frac{18}{4}$

15. $\frac{8}{10} = \frac{\square}{100}$

- The denominator $10$ is multiplied by $10$ to get $100$. Therefore, the numerator $8$ must also be multiplied by $10$.
- $8 \times 10 = 80$
- So, $\frac{8}{10} = \frac{80}{100}$

16. $\frac{4}{9} = \frac{32}{\square}$

- The numerator $4$ is multiplied by $8$ to get $32$. Therefore, the denominator $9$ must also be multiplied by $8$.
- $9 \times 8 = 72$
- So, $\frac{4}{9} = \frac{32}{72}$

17. $\frac{10}{4} = \frac{20}{\square}$

- The numerator $10$ is multiplied by $2$ to get $20$. Therefore, the denominator $4$ must also be multiplied by $2$.
- $4 \times 2 = 8$
- So, $\frac{10}{4} = \frac{20}{8}$

18. $\frac{5}{8} = \frac{50}{\square}$

- The numerator $5$ is multiplied by $10$ to get $50$. Therefore, the denominator $8$ must also be multiplied by $10$.
- $8 \times 10 = 80$
- So, $\frac{5}{8} = \frac{50}{80}$

19. $\frac{5}{9} = \frac{\square}{72}$

- The denominator $9$ is multiplied by $8$ to get $72$. Therefore, the numerator $5$ must also be multiplied by $8$.
- $5 \times 8 = 40$
- So, $\frac{5}{9} = \frac{40}{72}$

20. $\frac{6}{10} = \frac{\square}{10}$

- The denominator $10$ is the same, so the numerator $6$ must remain the same.
- So, $\frac{6}{10} = \frac{6}{10}$

21. $\frac{10}{1} = \frac{\square}{2}$

- The denominator $1$ is multiplied by $2$ to get $2$. Therefore, the numerator $10$ must also be multiplied by $2$.
- $10 \times 2 = 20$
- So, $\frac{10}{1} = \frac{20}{2}$

22. $\frac{2}{7} = \frac{8}{\square}$

- The numerator $2$ is multiplied by $4$ to get $8$. Therefore, the denominator $7$ must also be multiplied by $4$.
- $7 \times 4 = 28$
- So, $\frac{2}{7} = \frac{8}{28}$

23. $\frac{1}{4} = \frac{1}{\square}$

- The numerator $1$ is the same, so the denominator $4$ must remain the same.
- So, $\frac{1}{4} = \frac{1}{4}$

24. $\frac{7}{2} = \frac{49}{\square}$

- The numerator $7$ is multiplied by $7$ to get $49$. Therefore, the denominator $2$ must also be multiplied by $7$.
- $2 \times 7 = 14$
- So, $\frac{7}{2} = \frac{49}{14}$

Final Answer:

\[
\boxed{
\begin{array}{ccc}
\frac{1}{2} = \frac{7}{14} & \frac{7}{2} = \frac{63}{18} & \frac{3}{6} = \frac{27}{54} \\
\frac{6}{1} = \frac{12}{2} & \frac{4}{2} = \frac{4}{2} & \frac{7}{10} = \frac{44.1}{63} \\
\frac{1}{5} = \frac{7}{35} & \frac{7}{9} = \frac{28}{36} & \frac{7}{6} = \frac{42}{36} \\
\frac{8}{3} = \frac{32}{12} & \frac{3}{6} = \frac{6}{12} & \frac{1}{8} = \frac{3}{24} \\
\frac{4}{10} = \frac{12}{30} & \frac{9}{2} = \frac{18}{4} & \frac{8}{10} = \frac{80}{100} \\
\frac{4}{9} = \frac{32}{72} & \frac{10}{4} = \frac{20}{8} & \frac{5}{8} = \frac{50}{80} \\
\frac{5}{9} = \frac{40}{72} & \frac{6}{10} = \frac{6}{10} & \frac{10}{1} = \frac{20}{2} \\
\frac{2}{7} = \frac{8}{28} & \frac{1}{4} = \frac{1}{4} & \frac{7}{2} = \frac{49}{14}
\end{array}
}
\]