Calculate [tex]$\frac{3}{8} \times \frac{2}{5}$[/tex]
Give your answer in its simplest form.
Answer (2)
The product of 8 3 and 5 2 is 20 3 after simplifying the fraction. The multiplication involved the numerators and denominators, followed by dividing by the greatest common divisor. Thus, the final answer is 20 3 .
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Multiply the numerators and denominators: 8 3 × 5 2 = 8 × 5 3 × 2 = 40 6 .
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 2: 40 6 = 40 ÷ 2 6 ÷ 2 = 20 3 .
The simplified fraction is 20 3 .
The final answer is 20 3 .
Explanation
Understanding the Problem We are asked to calculate the product of two fractions, 8 3 and 5 2 , and express the answer in its simplest form.
Multiplying the Fractions To multiply fractions, we multiply the numerators together and the denominators together: 8 3 × 5 2 = 8 × 5 3 × 2 = 40 6
Simplifying the Fraction Now we need to simplify the fraction 40 6 . Both the numerator and the denominator are divisible by 2. Dividing both by 2, we get: 40 ÷ 2 6 ÷ 2 = 20 3 The fraction 20 3 is in its simplest form because 3 and 20 have no common factors other than 1.
Final Answer Therefore, the product of 8 3 and 5 2 in its simplest form is 20 3 .
Examples
In baking, if a recipe calls for 8 3 of a cup of flour and you only want to make 5 2 of the recipe, you would multiply 8 3 × 5 2 to find out how much flour you need. The result, 20 3 of a cup, tells you the exact amount of flour to use for the smaller batch. This type of calculation is useful for scaling recipes up or down.
