Work out [tex]\frac{6}{7} \times \frac{5}{2}[/tex]
Give your answer as a fraction in its lowest terms.
Answer (2)
The product of 7 6 and 2 5 is 7 15 after multiplying the numerators and denominators and simplifying the fraction to its lowest terms. The simplification process includes finding the greatest common divisor and dividing the numerator and denominator by it.
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Multiply the numerators and denominators: 7 6 × 2 5 = 7 × 2 6 × 5 = 14 30 .
Find the greatest common divisor (GCD) of 30 and 14, which is 2.
Divide both the numerator and the denominator by the GCD: 14 ÷ 2 30 ÷ 2 = 7 15 .
The simplified fraction is 7 15 .
Explanation
Problem Analysis We are asked to multiply two fractions, 7 6 and 2 5 , and express the result in its lowest terms. This means we need to find the product of the fractions and then simplify the resulting fraction so that the numerator and denominator have no common factors other than 1.
Multiplying the Fractions To multiply two fractions, we multiply the numerators together and the denominators together. So, we have: 7 6 × 2 5 = 7 × 2 6 × 5 = 14 30
Simplifying the Fraction Now we need to simplify the fraction 14 30 to its lowest terms. To do this, we find the greatest common divisor (GCD) of the numerator and the denominator and divide both by the GCD.
Finding the Greatest Common Divisor (GCD) The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The factors of 14 are 1, 2, 7, and 14. The greatest common divisor of 30 and 14 is 2.
Dividing by the GCD Now, we divide both the numerator and the denominator by their GCD, which is 2: 14 30 = 14 ÷ 2 30 ÷ 2 = 7 15
Final Answer The fraction 7 15 is now in its lowest terms, as 15 and 7 have no common factors other than 1.
Conclusion Therefore, 7 6 × 2 5 = 7 15 .
Examples
In cooking, you might need to adjust recipe quantities. For example, if a recipe calls for 7 6 of a cup of flour and you only want to make 2 5 of the recipe, you would multiply these fractions to find out how much flour you need. The calculation 7 6 × 2 5 = 7 15 tells you that you need 7 15 cups of flour, which is a little more than 2 cups.
