ISEE Middle Level Quantitative : How to divide fractions

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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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 

Possible Answers:

(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

Correct answer:

(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 

Possible Answers:

(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

Correct answer:

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 

Possible Answers:

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

Correct answer:

(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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