Solve Fraction Division: 8/9 ÷ 2/3 Step-by-Step

Question

Complete the following exercise:

89:23=? \frac{8}{9}:\frac{2}{3}=\text{?}

Video Solution

Step-by-Step Solution

To solve the fraction division 89÷23 \frac{8}{9} \div \frac{2}{3} , follow these steps:

  • Step 1: Identify the given fractions 89 \frac{8}{9} and 23 \frac{2}{3} .
  • Step 2: Find the reciprocal of the second fraction. The reciprocal of 23 \frac{2}{3} is 32 \frac{3}{2} .
  • Step 3: Multiply the first fraction by the reciprocal of the second fraction: 89×32 \frac{8}{9} \times \frac{3}{2} .
  • Step 4: Perform the multiplication: multiply the numerators together and the denominators together.

Let's compute the multiplication:

89×32=8×39×2=2418 \frac{8}{9} \times \frac{3}{2} = \frac{8 \times 3}{9 \times 2} = \frac{24}{18}

Step 5: Simplify the resulting fraction 2418 \frac{24}{18} .

To simplify, find the greatest common divisor (GCD) of 24 and 18, which is 6. Divide both the numerator and the denominator by 6:

2418=24÷618÷6=43 \frac{24}{18} = \frac{24 \div 6}{18 \div 6} = \frac{4}{3}

Step 6: If necessary, convert the improper fraction to a mixed number.

Since 43 \frac{4}{3} is an improper fraction, it can be converted to a mixed number:

43=113 \frac{4}{3} = 1 \frac{1}{3}

Therefore, the solution to the problem 89:23 \frac{8}{9} : \frac{2}{3} is 113 1 \frac{1}{3} .

Answer

113 1\frac{1}{3}