Question

What is the product of 1 5/7×3 2/3

Answer 1

MIXED NUMBERS

To multiply mixed numbers, we can follow these steps:

1. Convert each mixed number into an improper fraction.
2. Multiply the two fractions.
3. Simplify the resulting fraction, if necessary.
4. Convert the simplified fraction back into a mixed number, if desired.

Let's start:

Step 1: Convert mixed numbers to improper fractions:

`\large\qquad\Rrightarrow\begin{aligned}\rm 1 (5)/(7) = (7)/(7) + (5)/(7) = (12)/(7)\end{aligned}`

`\large\qquad\Rrightarrow\begin{aligned}\rm 3 (2)/(3) = (9)/(3) + (2)/(3) = (11)/(3)\end{aligned}`

Step 2: Multiply the fractions:

`\large\quad\Rrightarrow\begin{aligned}\rm(12)/(7) * (11)/(3) = (12 * 11)/(7 * 3) = (132)/(21)\end{aligned}`

Step 3: Simplify the resulting fraction:

`\large\qquad\Rrightarrow\begin{aligned}\rm (132)/(21) = (132 / 3)/(21 / 3) = (44)/(7)\end{aligned}`

Step 4: Convert the simplified fraction back to a mixed number:

To convert 44/7 to a mixed number, we divide the numerator 44 by the denominator 7. The quotient is 6, and the remainder is 2. So, the mixed number is 6 2/7.

Hence, the product is:

`\qquad\qquad\quad\Large\Rrightarrow\begin{aligned}\rm 6\:(\:\:2\:\:)/(7)\end{aligned}`