Multiply these two fractions: [tex]$\frac{2}{7} \times \frac{3}{8}=?$[/tex]
Answer (1)
Multiply the numerators: 2 × 3 = 6 .
Multiply the denominators: 7 × 8 = 56 .
Form the fraction: 56 6 .
Simplify the fraction: 56 6 = 28 3 .
The final answer is 28 3 .
Explanation
Understanding the Problem We are asked to multiply two fractions, 7 2 and 8 3 . To do this, we multiply the numerators together and the denominators together.
Multiplying Numerators First, we multiply the numerators: 2 × 3 = 6 .
Multiplying Denominators Next, we multiply the denominators: 7 × 8 = 56 .
Forming the Fraction So, the product of the two fractions is 56 6 . Now we need to simplify this fraction. Both the numerator and the denominator are even, so we can divide both by 2.
Simplifying the Fraction Dividing the numerator by 2, we get 6 ÷ 2 = 3 . Dividing the denominator by 2, we get 56 ÷ 2 = 28 . Therefore, the simplified fraction is 28 3 .
Final Answer The fraction 28 3 is in its simplest form because 3 is a prime number and does not divide 28. Thus, the final answer is 28 3 .
Examples
Fractions are used in everyday life, such as when baking a cake. If a recipe calls for 7 2 of a cup of flour and you want to make 8 3 of the recipe, you would multiply the fractions to find out how much flour you need. In this case, you would need 28 3 of a cup of flour.
