Solve Fraction Division: 4/6 ÷ 3/7 Step-by-Step

Video Solution

Solution Steps

00:00 Solve

00:03 Instead of division, we'll use multiplication by the reciprocal

00:07 We'll flip between the numerator and denominator of the fraction

00:14 Make sure to multiply numerator by numerator and denominator by denominator

00:17 Calculate the products

00:25 Break down 28 into 18 plus 10

00:31 Break down the fraction into a whole number and remainder

00:38 Any number divided by itself always equals 1

00:42 Reduce the fraction as much as possible

00:45 Make sure to divide both numerator and denominator

00:48 Calculate the quotients

00:52 Convert to a mixed number

00:55 And this is the solution to the problem

Step-by-Step Solution

To solve the fraction division problem $\frac{4}{6} : \frac{3}{7}$ , follow these steps:

Simplify by finding the greatest common divisor (GCD) of 4 and 6, which is 2. Divide both the numerator and denominator by 2:

$\frac{4}{6} = \frac{4/2}{6/2} = \frac{2}{3}$

The reciprocal of $\frac{3}{7}$ is $\frac{7}{3}$ .

Step 3: Multiply the simplified first fraction by the reciprocal of the second.

$\frac{2}{3} \times \frac{7}{3} = \frac{2 \times 7}{3 \times 3} = \frac{14}{9}$

Divide 14 by 9, which gives a quotient of 1 and a remainder of 5:

$\frac{14}{9} = 1\frac{5}{9}$

Therefore, the solution to the problem is $1\frac{5}{9}$ .