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 expression (−58)×(−37)(- \frac{5}{8}) \times (- \frac{3}{7})(−85)×(−73), we need to follow these steps:
Step 1: Multiply the fractions
Start by multiplying the two fractions.(−58)×(−37)=−5×−38×7=1556\left( – \frac{5}{8} \right) \times \left( – \frac{3}{7} \right) = \frac{-5 \times -3}{8 \times 7} = \frac{15}{56}(−85)×(−73)=8×7−5×−3=5615
Notice that the negatives cancel out, leaving you with a positive result.
Step 2: Find the multiplicative inverse
The multiplicative inverse of a number is the reciprocal of that number. For any fraction, the reciprocal is obtained by swapping the numerator and denominator.
For 1556\frac{15}{56}5615, its multiplicative inverse would be:Multiplicative Inverse of 1556=5615\text{Multiplicative Inverse of } \frac{15}{56} = \frac{56}{15}Multiplicative Inverse of 5615=1556
Explanation:
To understand this better, remember that the multiplicative inverse of a fraction ab\frac{a}{b}ba is ba\frac{b}{a}ab. This is because multiplying a number by its inverse always results in 1:ab×ba=1\frac{a}{b} \times \frac{b}{a} = 1ba×ab=1
In our case, multiplying 1556\frac{15}{56}5615 by its inverse 5615\frac{56}{15}1556 would give us:1556×5615=1\frac{15}{56} \times \frac{56}{15} = 15615×1556=1
Thus, the multiplicative inverse of (−58)×(−37)=1556(- \frac{5}{8}) \times (- \frac{3}{7}) = \frac{15}{56}(−85)×(−73)=5615 is 5615\frac{56}{15}1556.
This process helps in finding the reciprocal when you’re working with fractions, and it’s a fundamental concept in solving equations involving fractions or performing operations like division.
