Dividing fractions: Unit test
Divide. Write the quotient in lowest terms.

Ask by Huff Hills. in the United States

Jan 24,2025

Question

Dividing fractions: Unit test Divide. Write the quotient in lowest terms. $$ 8 \div 1 \frac{4}{5}=\square $$

UpStudy AI · Accepted Answer

To divide the fraction $$ 8 $$ by the mixed number $$ 1 \frac{4}{5} $$, we will follow these steps:

1. **Convert the mixed number to an improper fraction.**
   - The mixed number $$ 1 \frac{4}{5} $$ can be converted as follows:
     $$
     1 \frac{4}{5} = 1 + \frac{4}{5} = \frac{5}{5} + \frac{4}{5} = \frac{9}{5}
     $$

2. **Rewrite the division as multiplication by the reciprocal.**
   - Dividing by a fraction is the same as multiplying by its reciprocal:
     $$
     8 \div \frac{9}{5} = 8 \times \frac{5}{9}
     $$

3. **Convert the whole number $$ 8 $$ to a fraction.**
   - We can express $$ 8 $$ as $$ \frac{8}{1} $$:
     $$
     \frac{8}{1} \times \frac{5}{9}
     $$

4. **Multiply the fractions.**
   - Multiply the numerators and the denominators:
     $$
     \frac{8 \times 5}{1 \times 9} = \frac{40}{9}
     $$

5. **Simplify the fraction if necessary.**
   - The fraction $$ \frac{40}{9} $$ is already in its lowest terms since $$ 40 $$ and $$ 9 $$ have no common factors other than $$ 1 $$.

Thus, the quotient in lowest terms is:
$$
\frac{40}{9}
$$

So, the final answer is:
$$
\boxed{\frac{40}{9}}
$$
The quotient is $$ \frac{40}{9} $$.

Dividing fractions: Unit test
Divide. Write the quotient in lowest terms.

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