Questions: i-Ready Divide Fractions: Fractional Quotients - Quiz - Level F Think about the division expression 2 1/5 ÷ 3/5. Do you expect the quotient to be less than 1 or greater than 1 ? Why? The fraction 3/5 fits into 2 1/5 more than 1 time. That means the quotient is ? 1.

$i-Ready Divide Fractions: Fractional Quotients - Quiz - Level F Think about the division expression 2 1/5 ÷ 3/5. Do you expect the quotient to be less than 1 or greater than 1 ? Why? The fraction 3/5 fits into 2 1/5 more than 1 time. That means the quotient is ? 1.$

Transcript text: i-Ready Divide Fractions: Fractional Quotients - Quiz - Level F Think about the division expression $2 \frac{1}{5} \div \frac{3}{5}$. Do you expect the quotient to be less than 1 or greater than 1 ? Why? The fraction $\frac{3}{5}$ fits into $2 \frac{1}{5}$ more than 1 time. That means the quotient is $\square$ ? 1.

Solution

Solution Steps

Step 1: Convert the mixed number to an improper fraction

The mixed number $2 \frac{1}{5}$ can be converted to an improper fraction as follows: \[ 2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5}. \]

Step 2: Rewrite the division as multiplication by the reciprocal

The division expression $2 \frac{1}{5} \div \frac{3}{5}$ can be rewritten as: \[ \frac{11}{5} \div \frac{3}{5} = \frac{11}{5} \times \frac{5}{3}. \]

Step 3: Simplify the multiplication

Multiply the numerators and denominators: \[ \frac{11}{5} \times \frac{5}{3} = \frac{11 \times 5}{5 \times 3} = \frac{55}{15}. \] Simplify the fraction by dividing the numerator and denominator by 5: \[ \frac{55}{15} = \frac{11}{3}. \]

Step 4: Determine if the quotient is greater than 1

The fraction $\frac{11}{3}$ is approximately $3.6667$, which is greater than 1. Therefore, the quotient is greater than 1.