Find the product. [tex]\frac{7}{9} \times \frac{3}{21}[/tex]
Enter your simplified answer.
Answer (2)
Multiply the numerators and denominators: 9 7 × 21 3 = 9 × 21 7 × 3 .
Factor the denominator: 3 × 3 × 3 × 7 7 × 3 .
Cancel common factors: 3 × 3 × 3 × 7 7 × 3 = 3 × 3 1 .
Simplify the fraction: 9 1 .
Explanation
Understanding the Problem We are asked to find the product of two fractions, 9 7 and 21 3 , and simplify the result.
Multiplying the Fractions To multiply fractions, we multiply the numerators together and the denominators together: 9 7 × 21 3 = 9 × 21 7 × 3
Factoring the Denominator Now, let's simplify the fraction. We can write 9 as 3 × 3 and 21 as 3 × 7 . So we have: 9 × 21 7 × 3 = 3 × 3 × 3 × 7 7 × 3
Simplifying the Fraction We can cancel the common factors of 7 and 3 from the numerator and the denominator: 3 × 3 × 3 × 7 7 × 3 = 3 × 3 × 3 × 7 7 × 3 = 3 × 3 × 3 1 = 9 1 Oops! I made a mistake in the previous step. It should be: 3 × 3 × 3 × 7 7 × 3 = 3 × 3 × 3 × 7 7 × 3 = 3 × 3 1 = 9 1
Final Answer Therefore, the simplified product of the two fractions is 9 1 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 3 1 cup of flour and you want to make half of the recipe, you would need to calculate 2 1 × 3 1 = 6 1 cup of flour. Understanding how to multiply and simplify fractions is essential for accurate measurements and successful cooking.
The product of the fractions 9 7 and 21 3 is calculated by multiplying the numerators and denominators, resulting in 189 21 . Simplifying this fraction gives us the final answer of 9 1 .
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