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# 4/5 - 4/7 or 4/7-2/5

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4/5 - 4/7 or 4/7-2/5 [#permalink]  24 Aug 2018, 23:59
Expert's post
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Question Stats:

80% (00:36) correct 20% (00:24) wrong based on 65 sessions
 Quantity A Quantity B $$\frac{4}{5} - \frac{4}{7}$$ $$\frac{4}{7}-\frac{2}{5}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

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[Reveal] Spoiler: OA

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Re: 4/5 - 4/7 or 4/7-2/5 [#permalink]  26 Aug 2018, 08:12
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Carcass wrote:
 Quantity A Quantity B $$\frac{4}{5} - \frac{4}{7}$$ $$\frac{4}{7}-\frac{2}{5}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E

QTY A = $$\frac{4}{5} - \frac{4}{7}$$ =$$\frac{{28 - 20}}{35}= \frac{8}{35}$$

QTY B = $$\frac{4}{7}-\frac{2}{5}$$ = $$\frac{{20 - 14}}{35}=\frac{6}{35}$$

Therefore QTY A > QTY B
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Re: 4/5 - 4/7 or 4/7-2/5 [#permalink]  27 Aug 2018, 05:57
1
KUDOS
Expert's post
Carcass wrote:
 Quantity A Quantity B $$\frac{4}{5} - \frac{4}{7}$$ $$\frac{4}{7}-\frac{2}{5}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E

Another approach is to use matching operations to get the fractions with the same denominators on the same side (the steps below can be performed in your head)

Given:
Quantity A: 4/5 - 4/7
Quantity B: 4/7 - 2/5

Add 4/7 to both quantities to get:
Quantity A: 4/5
Quantity B: 4/7 + 4/7 - 2/5

Add 2/5 to both quantities to get:
Quantity A: 4/5 + 2/5
Quantity B: 4/7 + 4/7

Simplify:
Quantity A: 6/5 = 1 1/5
Quantity B: 8/7 = 1 1/7

Subtract 1 from both quantities to get:
Quantity A: 1/5
Quantity B: 1/7

Since the denominator in Quantity A is smaller than the denominator in Quantity B, 1/5 must be greater than 1/7

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Re: 4/5 - 4/7 or 4/7-2/5   [#permalink] 27 Aug 2018, 05:57
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# 4/5 - 4/7 or 4/7-2/5

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