Divide these two fractions: [tex]$\frac{4}{3} \div \frac{7}{8}=?$[/tex]
Answer (1)
To divide fractions, multiply by the reciprocal: 3 4 ÷ 8 7 = 3 4 × 7 8 .
Multiply the numerators: 4 × 8 = 32 .
Multiply the denominators: 3 × 7 = 21 .
The result is 21 32 .
Explanation
Understanding the Problem We are asked to divide two fractions: 3 4 and 8 7 . The division operation is represented as 3 4 ÷ 8 7 .
Dividing Fractions To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 8 7 is 7 8 . Therefore, the division problem becomes a multiplication problem: 3 4 ÷ 8 7 = 3 4 × 7 8 .
Multiplying Numerators and Denominators Now, we multiply the numerators together and the denominators together: Numerators: 4 × 8 = 32 Denominators: 3 × 7 = 21 So, the result is 21 32 .
Simplifying the Fraction The fraction 21 32 is in its simplest form because the greatest common divisor (GCD) of 32 and 21 is 1. Therefore, the final answer is 21 32 .
Examples
In cooking, if a recipe calls for 3 4 cups of flour and you only have a 8 7 cup measuring tool, dividing 3 4 by 8 7 tells you how many times you need to fill the 8 7 cup to get the required amount of flour. This ensures accurate proportions in your recipe, maintaining the desired taste and texture of the dish. Understanding fraction division is crucial for scaling recipes up or down and for precise measurements in various fields.
