Solve the following fraction problems: 1) 4/5 ÷ 3/10, 2) 1/2 − 3/4, 3) 4 5/6 − 1/3

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to your homework problems.

1) $\frac{4}{5} \div \frac{3}{10}$

To divide by a fraction, multiply by its reciprocal.
$\frac{4}{5} \div \frac{3}{10} = \frac{4}{5} \times \frac{10}{3}$
Multiply the numerators and the denominators.
$\frac{4 \times 10}{5 \times 3} = \frac{40}{15}$
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5.
$\frac{40 \div 5}{15 \div 5} = \frac{8}{3}$
The answer is $\boxed{\frac{8}{3}}$ .

2) $\frac{1}{2} - \frac{3}{4}$
Find a common denominator for the fractions.
The least common multiple of 2 and 4 is 4.
$\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$
Subtract the fractions with the common denominator.
$\frac{2}{4} - \frac{3}{4} = \frac{2 - 3}{4}$
Perform the subtraction in the numerator.
$\frac{2 - 3}{4} = \frac{-1}{4}$
The answer is $\boxed{-\frac{1}{4}}$ .

3) $4\frac{5}{6} - \frac{1}{3}$
Convert the mixed number to an improper fraction.
$4\frac{5}{6} = \frac{(4 \times 6) + 5}{6} = \frac{24 + 5}{6} = \frac{29}{6}$
Find a common denominator for $\frac{29}{6}$ and $\frac{1}{3}$ .
The least common multiple of 6 and 3 is 6.
$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$
Subtract the fractions with the common denominator.
$\frac{29}{6} - \frac{2}{6} = \frac{29 - 2}{6}$
Perform the subtraction in the numerator.
$\frac{29 - 2}{6} = \frac{27}{6}$
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3.
$\frac{27 \div 3}{6 \div 3} = \frac{9}{2}$
The answer is $\boxed{\frac{9}{2}}$ .

Solve the following fraction problems: 1) 4/5 ÷ 3/10, 2) 1/2 - 3/4, 3) 4 5/6 - 1/3