# ISEE Middle Level Quantitative : How to divide fractions

## Example Questions

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### Example Question #11 : Fractions

is a positive number, and . Which is the greater quantity?

(a) The reciprocal of

(b) The reciprocal of

(a) is the greater quantity

(a) and (b) are equal

(b) is the greater quantity

It is impossible to determine which quantity is the greater from the information given

(a) is the greater quantity

Explanation:

.

The reciprocal of  is therefore  - that is,  times the reciprocal of . The reciprocal of a positive number must be positive, and , so

The reciprocal of  is the greater number.

### Example Question #12 : Fractions

is a positive number. Which is the greater quantity?

(a) The reciprocal of

(b) The reciprocal of

(b) is the greater quantity

(a) and (b) are equal

(a) is the greater quantity

It is impossible to determine which is greater from the information given

It is impossible to determine which is greater from the information given

Explanation:

We examine two scenarios to demonstrate that the given information is insufficient.

Case 1:

The reciprocal of this is .

The reciprocal of this is

, so  has the greater reciprocal.

Case 2: .

The reciprocal of this is .

The reciprocal of this is .

, so  has the greater reciprocal.

### Example Question #13 : Fractions

is a negative number. Which is the greater quantity?

(a) The reciprocal of

(b) The reciprocal of

It is impossible to determine which is greater from the information given

(a) is the greater quantity

(a) and (b) are equal

(b) is the greater quantity

(b) is the greater quantity

Explanation:

is negative, so we will let , making  positive. It follows that .

The reciprocal of  is ;

the reciprocal of  is .

and  are both positive; , so , and . Therefore, the reciprocal of  is the greater quantity.

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