Question

Explain why you can find 5÷1/3 by multiplying 5 by 3.

Answer 1

Dividing by a fraction is the same as multiplying the reciprocal of the fraction. What is the reciprocal of a fraction? It's essentially the same fraction, just the numerator and denominator switching places (flipping the fraction upside down). Knowing this, the following is true:

$5/\frac{1}{3} = 5*\frac{3}{1}$

We also need to know that whenever the denominator of a fraction is 1, the fraction is equal to the numerator itself. Knowing this, the following is also true:

$\frac{3}{1}=3$

Applying this to the first concept, we can say that:

$5*\frac{3}{1} = 5*3$

I hope this helps!