Find the multiplicative inverse of – 5/8 × – 3/7 . how to do this sum
The Correct Answer and Explanation is:
To find the multiplicative inverse of the product of −58×−37-\frac{5}{8} \times -\frac{3}{7}−85×−73, follow these steps:
Step 1: Multiply the fractions
First, we need to multiply the two fractions. Multiply the numerators and the denominators:−58×−37=(−5)×(−3)8×7=1556\frac{-5}{8} \times \frac{-3}{7} = \frac{(-5) \times (-3)}{8 \times 7} = \frac{15}{56}8−5×7−3=8×7(−5)×(−3)=5615
So, the result of −58×−37-\frac{5}{8} \times -\frac{3}{7}−85×−73 is 1556\frac{15}{56}5615.
Step 2: Find the multiplicative inverse
The multiplicative inverse of a fraction is obtained by swapping its numerator and denominator. The multiplicative inverse of 1556\frac{15}{56}5615 is:5615\frac{56}{15}1556
Explanation
The multiplicative inverse is a concept that refers to the reciprocal of a number. For fractions, the multiplicative inverse is found by swapping the numerator and the denominator. When you multiply a number by its multiplicative inverse, the result is 1, because:ab×ba=1\frac{a}{b} \times \frac{b}{a} = 1ba×ab=1
In this case, after multiplying the fractions −58-\frac{5}{8}−85 and −37-\frac{3}{7}−73, you get a positive fraction 1556\frac{15}{56}5615, and the multiplicative inverse of this fraction is 5615\frac{56}{15}1556.
In summary, the multiplicative inverse of −58×−37-\frac{5}{8} \times -\frac{3}{7}−85×−73 is 5615\frac{56}{15}1556.
