Question

exercise 2 (answers on page 41)
find the number that belongs in the space by building or reducing equivalent fractions.

1. $\frac{1}{2}=\frac{5}{10}$
2. $\frac{2}{3}=\frac{}{15}$
3. $\frac{5}{6}=\frac{}{12}$
4. $\frac{3}{4}=\frac{}{12}$
5. $\frac{2}{5}=\frac{}{20}$
6. $\frac{5}{7}=\frac{}{21}$
7. $\frac{3}{6}=\frac{}{2}$
8. $\frac{6}{8}=\frac{}{4}$
9. $\frac{8}{10}=\frac{}{5}$
10. $\frac{12}{24}=\frac{}{2}$
11. $\frac{5}{30}=\frac{}{6}$
12. $\frac{7}{14}=\frac{}{2}$
13. $\frac{2}{7}=\frac{}{35}$
14. $\frac{7}{42}=\frac{}{6}$
15. $\frac{10}{15}=\frac{}{3}$
16. $\frac{1}{8}=\frac{}{24}$
17. $\frac{1}{3}=\frac{}{24}$
18. $\frac{20}{22}=\frac{}{11}$
19. $\frac{21}{42}=\frac{}{2}$
20. $\frac{17}{51}=\frac{}{3}$
21. $\frac{10}{30}=\frac{}{3}$

Explanation:

Step1: Find scale factor (denominator)

For each problem, calculate the scale factor by dividing the new denominator by the original denominator, or vice versa for reducing.

Step2: Scale numerator/denominator

Multiply or divide the original numerator/denominator by the scale factor to find the missing value.

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1) $\frac{1}{2}=\frac{5}{10}$

Step1: Find scale factor

$\frac{10}{2}=5$

Step2: Scale numerator

$1\times5=5$

2) $\frac{2}{3}=\frac{?}{15}$

Step1: Find scale factor

$\frac{15}{3}=5$

Step2: Scale numerator

$2\times5=10$

3) $\frac{5}{6}=\frac{?}{12}$

Step1: Find scale factor

$\frac{12}{6}=2$

Step2: Scale numerator

$5\times2=10$

4) $\frac{3}{4}=\frac{?}{12}$

Step1: Find scale factor

$\frac{12}{4}=3$

Step2: Scale numerator

$3\times3=9$

5) $\frac{2}{5}=\frac{?}{20}$

Step1: Find scale factor

$\frac{20}{5}=4$

Step2: Scale numerator

$2\times4=8$

6) $\frac{5}{7}=\frac{?}{21}$

Step1: Find scale factor

$\frac{21}{7}=3$

Step2: Scale numerator

$5\times3=15$

7) $\frac{3}{6}=\frac{?}{2}$

Step1: Find scale factor

$\frac{6}{2}=3$

Step2: Scale numerator

$\frac{3}{3}=1$

8) $\frac{6}{8}=\frac{?}{4}$

Step1: Find scale factor

$\frac{8}{4}=2$

Step2: Scale numerator

$\frac{6}{2}=3$

9) $\frac{8}{10}=\frac{?}{5}$

Step1: Find scale factor

$\frac{10}{5}=2$

Step2: Scale numerator

$\frac{8}{2}=4$

10) $\frac{12}{24}=\frac{?}{2}$

Step1: Find scale factor

$\frac{24}{2}=12$

Step2: Scale numerator

$\frac{12}{12}=1$

11) $\frac{5}{30}=\frac{?}{6}$

Step1: Find scale factor

$\frac{30}{6}=5$

Step2: Scale numerator

$\frac{5}{5}=1$

12) $\frac{7}{14}=\frac{?}{2}$

Step1: Find scale factor

$\frac{14}{2}=7$

Step2: Scale numerator

$\frac{7}{7}=1$

13) $\frac{2}{7}=\frac{?}{35}$

Step1: Find scale factor

$\frac{35}{7}=5$

Step2: Scale numerator

$2\times5=10$

14) $\frac{7}{42}=\frac{?}{6}$

Step1: Find scale factor

$\frac{42}{6}=7$

Step2: Scale numerator

$\frac{7}{7}=1$

15) $\frac{10}{15}=\frac{?}{3}$

Step1: Find scale factor

$\frac{15}{3}=5$

Step2: Scale numerator

$\frac{10}{5}=2$

16) $\frac{1}{8}=\frac{?}{24}$

Step1: Find scale factor

$\frac{24}{8}=3$

Step2: Scale numerator

$1\times3=3$

17) $\frac{1}{3}=\frac{?}{24}$

Step1: Find scale factor

$\frac{24}{3}=8$

Step2: Scale numerator

$1\times8=8$

18) $\frac{20}{22}=\frac{?}{11}$

Step1: Find scale factor

$\frac{22}{11}=2$

Step2: Scale numerator

$\frac{20}{2}=10$

19) $\frac{21}{42}=\frac{?}{2}$

Step1: Find scale factor

$\frac{42}{2}=21$

Step2: Scale numerator

$\frac{21}{21}=1$

20) $\frac{17}{51}=\frac{?}{3}$

Step1: Find scale factor

$\frac{51}{3}=17$

Step2: Scale numerator

$\frac{17}{17}=1$

21) $\frac{10}{30}=\frac{?}{3}$

Step1: Find scale factor

$\frac{30}{3}=10$

Step2: Scale numerator

$\frac{10}{10}=1$

Answer:

1. $5$
2. $10$
3. $10$
4. $9$
5. $8$
6. $15$
7. $1$
8. $3$
9. $4$
10. $1$
11. $1$
12. $1$
13. $10$
14. $1$
15. $2$
16. $3$
17. $8$
18. $10$
19. $1$
20. $1$
21. $1$