Explain why solving (2/5)c = (8/9) by multiplying both sides by (5/2) is the same as solving it by dividing both sides by (2/5)

It's known as keep change and flip. Keep the first fraction, change the division sign into a multiplication sign, and flip the decimal to its reciprocal (switch the numerator and denominator). This is used when dividing fractions. We can even check to see if they have to same output.
2/5 × 5/2 = 1
8/9 × 5/2 = 40/18
2/5 ÷ 2/5 = 1
8/9 ÷ 2/5 = 40/18
Tell me if this helps, I can explain more if needed.

here is answer

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