# HELP!! Algebra

posted by KG

A student claims that division always makes things smaller so 5 / (1/2) cannot 10 because 10 is greater than the number 5 she started with. How do you respond?

I don't understand this question at all!!

1. Steve

the smaller the divisor, the larger the quotient.

12/6 = 2
12/4 = 3
12/3 = 4
12/2 = 6
12/1 = 12
12/(1/2) = 24
because there are 24 halves in 12 wholes.

When dividing by a number less than 1, the quotient is larger than the dividend.

Again, if a slice of pie is 1/6 of the pie, then 1/(1/6) = 6. There are 6 slices, each of which is smaller than the whole pie.

In general, when dividing by a fraction, just multiply by the reciprocal.

(2/3)/(4/7) = 2/3 * 7/4 = 14/12

In fact, you use that rule all the time, without thinking about it

3/6 = 3/(6/1) = 3 * (1/6)

2. Anonymous

Ow

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