According to the chart above, the income of Beta Corporation in 2000 was what fraction of Alpha Corporation’s income in 2004? A. 0.88 / 13 B. 1.74 / 13 C. 2 / 7 D. 2 / 5.8 E. 2.9 / 0.87
(D) As shown in the chart, Beta Corporation's 2004 income is $1.74 billion. The chart shows that this is a 13% decrease from Beta’s income in 2000. To solve for Beta Corporation's income in 2000, set the 2000 value as n, and set up the following equation: (100% – 13%)n = $1.74 billion .87n = $1.74 billion. Divide both sides by 0.87 to get n = $2 billion.
The question asks what percent of Alpha Corporation's 2004 income was Beta Corporation's 2000 income, namely: 2/5.8. Algebraically, this is 2 = x(5.8). x = 2/5.8. The correct answer is choice (D). ----------- Is there an easy wasy to divide by decimals? I approached this question correctly but made an error in the math of muliplying 0.87 by 1.74.
The best and most reliable method is long division. You can look it up in math prep. guide or any school book.
The shortcut I'd like to point out is to get rid of decimals right away. 1.74 / 0.87 = 174 / 87 And then you use the long division method.
When we get rid of decimals, we use the fact that if we multiply the numerator and denominator by the same number (except 0), the fraction will remain the same. To get rid of decimals we can multiply by 10 several times.
You also can use the fact that multiplication of a decimal number by 10 yields moving the dot one digit to the right. And multiplication of an integer by 10 yields extra digit 0 to the right.
I advise to at least have the integer in the denominator. Having an integer in the numerator might be useful as well.
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