Question

generate equivalent fractions to get like units. then, subtract.
a. (\frac{3}{4} - \frac{3}{10} =)
b. (3\frac{1}{2} - 1\frac{1}{3} =)

Explanation:

Step1: Find LCD of 4 and 10

The least common denominator (LCD) of 4 and 10 is 20.

Step2: Convert to equivalent fractions

$\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$, $\frac{3}{10} = \frac{3 \times 2}{10 \times 2} = \frac{6}{20}$

Step3: Subtract the fractions

$\frac{15}{20} - \frac{6}{20} = \frac{15 - 6}{20} = \frac{9}{20}$

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Step1: Convert mixed numbers to improper fractions

$3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2}$, $1\frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3}$

Step2: Find LCD of 2 and 3

The least common denominator (LCD) of 2 and 3 is 6.

Step3: Convert to equivalent fractions

$\frac{7}{2} = \frac{7 \times 3}{2 \times 3} = \frac{21}{6}$, $\frac{4}{3} = \frac{4 \times 2}{3 \times 2} = \frac{8}{6}$

Step4: Subtract the fractions

$\frac{21}{6} - \frac{8}{6} = \frac{21 - 8}{6} = \frac{13}{6}$

Step5: Convert to mixed number (optional)

$\frac{13}{6} = 2\frac{1}{6}$

Answer:

a. $\frac{9}{20}$
b. $\frac{13}{6}$ or $2\frac{1}{6}$