Question

Without doing the math, determine which is greater, 40. 1/4 or 40÷ 1/4. Explain your reasoning.

Answer 1

40 ÷ $\frac{1}{4}$ is greater

multiplying a whole number by a fraction  reduces the size of the whole number

dividing a whole number by a fraction increases the size of the number

Answer 2

When you divide by a fraction, in this case 40 divided by 1 over 4, you multiply by the reciprocal of what you're dividing by, so:

$\frac{40}{1}$ ÷ $\frac{1}{4}$

turns into...

$\frac{40}{1}$ · $\frac{4}{1}$, or 40 * 4, which equals 160.

With this knowledge, whenever given a set of numbers like you were given, we know that 40 ÷ $\frac{1}{4}$ must be the larger, and 40 · $\frac{1}{4}$ must be the smaller.

Therefore, 40 ÷ $\frac{1}{4}$ is the greater number.

Hope this helps! :)