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555-605 Level|   Arithmetic|   Fractions and Ratios|            
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jlgdr
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(0.025*(15/2)*48)/(5*0.0024*(3/4)) 17 Sep 2013, 10:03
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E
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Difficulty:

25% (medium)

Question Stats:

80% (01:48) correct 20% (02:06) wrong based on 1697 sessions

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\(\frac{0.025*(7.5)*48)}{5*0.0024*(3/4))}\)

(A) 0.1
(B) 0.2
(C) 100
(D) 200
(E) 1,000
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E
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(0.025*(15/2)*48)/(5*0.0024*(3/4)) 19 Sep 2013, 04:11
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number of decimel points is same in Numerator and Denomintor. It's like there is no decimel involved
equation becomes (25*75*48*4)/(5*3*24)
= 5*25*2*4
= 125*8 (would stop solving here)
= 1000
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(0.025*(15/2)*48)/(5*0.0024*(3/4)) 18 Sep 2013, 08:43
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(0.025*(15/2)*48)/(5*0.0024*(3/4))

1) 0,025/ 5 = 5*(0,005)/5 =0,005
2) 15/2 =7,5 and 3/4 =0,75 thus: 7,5/0,75 = 10
3) 48/0,0024 = 48/0,0024 =20.000 (0,0024*10.000*2)

0,005*10*20.000= 0,05*20.000=1000
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(0.025*(15/2)*48)/(5*0.0024*(3/4)) 21 Apr 2022, 10:45
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Quote:
\(\frac{0.025 \times 7.5 \times 48}{5 \times 0.0024 \times \frac{3}{4}}=\)

(A) 0.1
(B) 0.2
(C) 100
(D) 200
(E) 1,000
Show more

Let's first convert \(\frac{3}{4}\) to \(0.75\), its decimal equivalent, to get: \(\frac{0.025 \times 7.5 \times 48}{5 \times 0.0024 \times 0.75}=\)

Key property: \(\frac{ABC}{DEF} = \frac{A}{D} \times \frac{B}{E} \times \frac{C}{F} \)

Strategy: I'm going to use this property to split the original fraction into the product of 3 individual fractions.
There are a few different ways I can split up the fraction. For example, I could pair up 0.025 and 5 to get 0.025/5, but that seems like a pain to calculate.
Similarity, I could pair up 48 and 0.0024 to get 48/0.0024, but that also seems like a pain.
Instead, I'm going to use the fact that the answer choices are extremely spread apart in order to pair up values that I can easily approximate.

So, we get: \(\frac{0.025}{0.0024} \times \frac{7.5}{0.75} \times \frac{48}{5}\)

Let's evaluate (or approximate) each fraction individually.

\(\frac{0.025}{0.0024} ≈ \frac{0.025}{0.0025} ≈ \frac{(1000)(0.025)}{(1000)(0.0025)} ≈ \frac{250}{25} ≈ 10\) [multiplying numerator and denominator by 1000 resulted in a fraction with integer values only, which made it easier to calculate]

\(\frac{7.5}{0.75} = \frac{(100)(7.5)}{(100)(0.75)} = \frac{750}{75} = 10\)

\(\frac{48}{5} ≈ \frac{50}{5} ≈ 10\)

Substitute values to get: \(\frac{0.025}{0.0024} \times \frac{7.5}{0.75} \times \frac{48}{5} ≈ 10 \times 10 \times 10 ≈ 1000\)

Answer: E
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(0.025*(15/2)*48)/(5*0.0024*(3/4)) 05 Aug 2024, 12:04
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