Question

for each of the following pairs of fractions, circle the greater fraction.
a) $\frac{4}{15}$, $\frac{2}{5}$
b) $\frac{5}{6}$, $\frac{2}{3}$
c) $\frac{2}{3}$, $\frac{11}{18}$
d) $\frac{5}{7}$, $\frac{11}{14}$
e) $\frac{2}{5}$, $\frac{3}{10}$
f) $\frac{3}{4}$, $\frac{9}{16}$
g) $\frac{7}{9}$, $\frac{7}{12}$
h) $\frac{5}{8}$, $\frac{5}{6}$

Explanation:

Step1: Find common denominator for $\frac{4}{15}$ and $\frac{2}{5}$

The common - denominator of 15 and 5 is 15. $\frac{2}{5}=\frac{2\times3}{5\times3}=\frac{6}{15}$. Since $\frac{4}{15}<\frac{6}{15}$, $\frac{2}{5}$ is greater.

Step2: Find common denominator for $\frac{5}{6}$ and $\frac{2}{3}$

The common - denominator of 6 and 3 is 6. $\frac{2}{3}=\frac{2\times2}{3\times2}=\frac{4}{6}$. Since $\frac{5}{6}>\frac{4}{6}$, $\frac{5}{6}$ is greater.

Step3: Find common denominator for $\frac{2}{3}$ and $\frac{11}{18}$

The common - denominator of 3 and 18 is 18. $\frac{2}{3}=\frac{2\times6}{3\times6}=\frac{12}{18}$. Since $\frac{12}{18}>\frac{11}{18}$, $\frac{2}{3}$ is greater.

Step4: Find common denominator for $\frac{5}{7}$ and $\frac{11}{14}$

The common - denominator of 7 and 14 is 14. $\frac{5}{7}=\frac{5\times2}{7\times2}=\frac{10}{14}$. Since $\frac{10}{14}<\frac{11}{14}$, $\frac{11}{14}$ is greater.

Step5: Find common denominator for $\frac{2}{5}$ and $\frac{3}{10}$

The common - denominator of 5 and 10 is 10. $\frac{2}{5}=\frac{2\times2}{5\times2}=\frac{4}{10}$. Since $\frac{4}{10}>\frac{3}{10}$, $\frac{2}{5}$ is greater.

Step6: Find common denominator for $\frac{3}{4}$ and $\frac{9}{16}$

The common - denominator of 4 and 16 is 16. $\frac{3}{4}=\frac{3\times4}{4\times4}=\frac{12}{16}$. Since $\frac{12}{16}>\frac{9}{16}$, $\frac{3}{4}$ is greater.

Step7: Find common denominator for $\frac{7}{9}$ and $\frac{7}{12}$

The common - denominator of 9 and 12 is 36. $\frac{7}{9}=\frac{7\times4}{9\times4}=\frac{28}{36}$, $\frac{7}{12}=\frac{7\times3}{12\times3}=\frac{21}{36}$. Since $\frac{28}{36}>\frac{21}{36}$, $\frac{7}{9}$ is greater.

Step8: Find common denominator for $\frac{5}{8}$ and $\frac{5}{6}$

The common - denominator of 8 and 6 is 24. $\frac{5}{8}=\frac{5\times3}{8\times3}=\frac{15}{24}$, $\frac{5}{6}=\frac{5\times4}{6\times4}=\frac{20}{24}$. Since $\frac{15}{24}<\frac{20}{24}$, $\frac{5}{6}$ is greater.

Answer:

a. $\frac{2}{5}$
b. $\frac{5}{6}$
c. $\frac{2}{3}$
d. $\frac{11}{14}$
e. $\frac{2}{5}$
f. $\frac{3}{4}$
g. $\frac{7}{9}$
h. $\frac{5}{6}$