Question

1. multiply or divide. leave your answer as a simplified fraction.

a) $\frac{3}{4} \div 8$

b) $\frac{5}{6} * 2\frac{3}{10}$

c) $\frac{1}{\frac{8}{11}}$

Explanation:

Part a) Step1: Recall fraction division rule

To divide a fraction by a whole number, we multiply the fraction by the reciprocal of the whole number. The reciprocal of 8 is $\frac{1}{8}$. So, $\frac{3}{4} \div 8=\frac{3}{4} \times \frac{1}{8}$.

Part a) Step2: Multiply the fractions

Multiply the numerators and denominators: $\frac{3\times1}{4\times8}=\frac{3}{32}$.

Part b) Step1: Convert mixed number to improper fraction

The mixed number $2\frac{3}{10}$ can be converted to an improper fraction. Multiply the whole number (2) by the denominator (10) and add the numerator (3): $2\times10 + 3 = 23$, so $2\frac{3}{10}=\frac{23}{10}$.

Part b) Step2: Multiply the fractions

Now, multiply $\frac{5}{6}$ and $\frac{23}{10}$. We can simplify before multiplying by canceling common factors. 5 and 10 have a common factor of 5. So, $\frac{5\div5}{6} \times \frac{23}{10\div5}=\frac{1}{6} \times \frac{23}{2}$. Then multiply numerators and denominators: $\frac{1\times23}{6\times2}=\frac{23}{12}$.

Part c) Step1: Recall fraction division rule (assuming it's $\frac{1}{8} \div \frac{11}{12}$)

To divide two fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of $\frac{11}{12}$ is $\frac{12}{11}$. So, $\frac{1}{8} \div \frac{11}{12}=\frac{1}{8} \times \frac{12}{11}$.

Part c) Step2: Simplify and multiply

Simplify the fractions before multiplying. 12 and 8 have a common factor of 4. So, $\frac{1}{8\div4} \times \frac{12\div4}{11}=\frac{1}{2} \times \frac{3}{11}$. Then multiply numerators and denominators: $\frac{1\times3}{2\times11}=\frac{3}{22}$.

Answer:

a) $\boldsymbol{\frac{3}{32}}$
b) $\boldsymbol{\frac{23}{12}}$ (or $1\frac{11}{12}$)
c) $\boldsymbol{\frac{3}{22}}$ (assuming the problem for c is $\frac{1}{8} \div \frac{11}{12}$)