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Problem 5

# $$\frac{4}{5} \div \frac{3}{10}$$

Expert verified
$$\frac{4}{5} \div \frac{3}{10} = \frac{4}{5} \times \frac{10}{3} = \frac{40}{15} = \frac{8}{3}$$
See the step by step solution

## Step 1: Reciprocal of the second fraction

The reciprocal of a fraction is found by swapping the numerator and the denominator. So, the reciprocal of $$\frac{3}{10}$$ is $$\frac{10}{3}$$.

## Step 2: Change division to multiplication

Now, we change the division problem into a multiplication problem. Instead of dividing by the second fraction, we will multiply by its reciprocal: $$\frac{4}{5} \div \frac{3}{10} = \frac{4}{5} \times \frac{10}{3}$$

## Step 3: Multiply numerators and denominators

Next, we multiply the numerators together and the denominators together: $$(4 \times 10) \div (5 \times 3)$$

## Step 4: Perform the multiplication

Now, perform the multiplication: $$\frac{40}{15}$$

## Step 5: Simplify if possible

Finally, let's see if we can simplify the resulting fraction. The greatest common divisor of 40 and 15 is 5. Divide both the numerator and the denominator by 5: $$\frac{40 \div 5}{15 \div 5} = \frac{8}{3}$$

So, $$\frac{4}{5} \div \frac{3}{10} = \frac{8}{3}$$.

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