Question

1. how many groups of \\(\frac{5}{6}\\) are in each of the following quantities? show your thinking.\

a \\(\frac{2}{3}\\)\
b \\(1\frac{1}{2}\\)\
c \\(4\frac{1}{6}\\)\

1. how many groups of \\(1\frac{3}{4}\\) are in each of the following quantities? show your thinking

Explanation:

Part 1a

Step1: Recall division of fractions

To find how many groups of $\frac{5}{6}$ are in $\frac{2}{3}$, we divide $\frac{2}{3}$ by $\frac{5}{6}$. The rule for dividing fractions is to multiply the first fraction by the reciprocal of the second fraction. So, $\frac{2}{3} \div \frac{5}{6} = \frac{2}{3} \times \frac{6}{5}$.

Step2: Multiply the fractions

Multiply the numerators: $2 \times 6 = 12$. Multiply the denominators: $3 \times 5 = 15$. So we have $\frac{12}{15}$, which simplifies to $\frac{4}{5}$ by dividing numerator and denominator by 3.

Step1: Convert mixed number to improper fraction

First, convert $1\frac{1}{2}$ to an improper fraction. $1\frac{1}{2} = \frac{3}{2}$. Now, divide $\frac{3}{2}$ by $\frac{5}{6}$, which is $\frac{3}{2} \times \frac{6}{5}$.

Step2: Multiply and simplify

Multiply numerators: $3 \times 6 = 18$. Multiply denominators: $2 \times 5 = 10$. So we get $\frac{18}{10}$, which simplifies to $\frac{9}{5}$ or $1\frac{4}{5}$ by dividing numerator and denominator by 2.

Step1: Convert mixed number to improper fraction

Convert $4\frac{1}{6}$ to an improper fraction. $4\frac{1}{6} = \frac{25}{6}$. Now, divide $\frac{25}{6}$ by $\frac{5}{6}$, which is $\frac{25}{6} \times \frac{6}{5}$.

Step2: Multiply and simplify

The 6 in the numerator and denominator cancels out. Then we have $\frac{25}{5} = 5$.

Answer:

$\frac{4}{5}$

Part 1b