Question

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

Answer 1

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:

`(40)/(1)` ÷
`(1)/(4)`

turns into...

`(40)/(1)` ·
`(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 ÷
`(1)/(4)` must be the larger, and 40 ·
`(1)/(4)` must be the smaller.

Therefore, 40 ÷
`(1)/(4)` is the greater number.

Hope this helps! :)

Answer 2

40 ÷
`(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