Question

dividing whole numbers by non-unit fractions: use the drawing tool on the sketch to find how many groups of three - fourths are in 5 wholes. then enter your quotient (answer) in the box below the sketch. $5\div\frac{3}{4}$

Explanation:

Step1: Recall division of fractions rule

To divide a whole number by a fraction, we multiply the whole number by the reciprocal of the fraction. The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$. So, $5\div\frac{3}{4}=5\times\frac{4}{3}$.

Step2: Multiply the numbers

Calculate $5\times\frac{4}{3}=\frac{5\times4}{3}=\frac{20}{3}$. Convert $\frac{20}{3}$ to a mixed number, which is $6\frac{2}{3}$. But since we are looking for the number of groups, we can also think in terms of how many times $\frac{3}{4}$ fits into 5. Each whole has $\frac{4}{3}$ groups of $\frac{3}{4}$ (since $1\div\frac{3}{4}=\frac{4}{3}$). So for 5 wholes, it's $5\times\frac{4}{3}=\frac{20}{3}\approx6.67$. But if we consider the number of full groups, but the problem says "how many groups of three - fourths are in 5 wholes", using the division of fractions formula, the exact value is $\frac{20}{3}$ or $6\frac{2}{3}$.

Answer:

$\frac{20}{3}$ (or $6\frac{2}{3}$)