Question

set 3 divide fractions by whole numbers
divide. show your work for problems 1–6.
1 $\frac{2}{3} \div 4$
2 $\frac{8}{10} \div 10$
3 $\frac{9}{2} \div 3$
4 $\frac{3}{5} \div 2$
5 $\frac{5}{6} \div 6$
6 $\frac{4}{2} \div 2$

Explanation:

Problem 1: $\boldsymbol{\frac{2}{3} \div 4}$

Step1: Recall fraction division rule

To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number. The reciprocal of 4 is $\frac{1}{4}$. So, $\frac{2}{3} \div 4=\frac{2}{3} \times \frac{1}{4}$.

Step2: Multiply the numerators and denominators

Multiply the numerators: $2\times1 = 2$. Multiply the denominators: $3\times4 = 12$. So we get $\frac{2}{12}$.

Step3: Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor, which is 2. $\frac{2\div2}{12\div2}=\frac{1}{6}$.

Step1: Apply fraction division rule

The reciprocal of 10 is $\frac{1}{10}$. So, $\frac{8}{10} \div 10=\frac{8}{10} \times \frac{1}{10}$.

Step2: Multiply numerators and denominators

Numerators: $8\times1 = 8$. Denominators: $10\times10 = 100$. We have $\frac{8}{100}$.

Step3: Simplify the fraction

The GCD of 8 and 100 is 4. $\frac{8\div4}{100\div4}=\frac{2}{25}$.

Step1: Use fraction division rule

Reciprocal of 3 is $\frac{1}{3}$. So, $\frac{9}{2} \div 3=\frac{9}{2} \times \frac{1}{3}$.

Step2: Multiply and simplify

Multiply numerators: $9\times1 = 9$. Multiply denominators: $2\times3 = 6$. We get $\frac{9}{6}$. Simplify by dividing numerator and denominator by 3: $\frac{9\div3}{6\div3}=\frac{3}{2}$.

Answer:

$\frac{1}{6}$

Problem 2: $\boldsymbol{\frac{8}{10} \div 10}$