Which of the following fractions can be expressed as the difference of the reciprocals of two consecutive integers?

Answer Choices

Correct answer marked below

1/60

1/65

1/70

1/72

Correct

4/84

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Explanation

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Official Explanation

Official

To determine which fraction can be represented as the difference of the reciprocals of two consecutive integers, let’s denote two consecutive integers as x and x+1.

The reciprocals of these integers are 1/x and 1/(x+1). The difference between these two fractions is given by: 1/x - 1/(x+1). To perform this subtraction, we need a common denominator, which leads us to: 1/x - 1/(x+1) = (x+1)/(x(x+1)) - x/(x(x+1)) = 1/(x(x+1)). This shows that the resulting fraction has a numerator of 1 and a denominator that is the product of two consecutive integers.

Now, let’s analyze the answer choices:

A. 1/60 - 60 cannot be expressed as the product of two consecutive integers. ELIMINATE.…

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Comments

MishalFeb 26, 2025

this helped me

SergioNov 29, 2024

thankss

What this question tests

What it tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Common trap

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.