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Percents
A percent is another way to describe a part of a whole (which means that percents are also another way to talk about fractions or decimals). Percent literally means “of 100” in Latin, so when you attend school 25 percent of the time, that means you only go to school 25/ 100 of the time (or .25).
You would probably fail all your classes if your attendance percentage was that low, so don’t get any ideas from our example. Instead, take a look at this question: 3 is what percent of 15?
This question presents you with a whole, 15, and then asks you to determine how much of that whole 3 represents in percentage form. Since a percent is “of 100,” to solve the question you have to set the fraction 3/ 15 equal to x⁄100:
15 x = 3 × 100 = 300
x= 20
Converting Percents into Fractions or Decimals
You should be skilled at converting percents into fractions and decimals, because these problems will definitely come up on the Math IC test.
Percents relate to decimal numbers very simply and directly. A percent is a decimal number with the decimal point moved two decimal places to the left.
For example:50 % of 12 = .50 × 12 = 6
12 % of 120 = .12 × 120 = 14.4
To convert from a decimal number to a percent, move the decimal point two places to the right:
.07 × 1100 = 7 % of 1100 = 77 .97 × 13 = 97 % of 13 = 12.61
On an even more simplistic level, we can just say that 50% = .5 or 22.346% = .22346. Percentages greater than 100 exist, too. 235% = 2.35, for example.
To convert from a percent to a fraction, take the percentage number and place it as the numerator over the denominator 100. 58 percent is the same as 58/ 100
To convert from a fraction back to a percent, the easiest method is to convert the fraction into a decimal first and then change the resultant decimal into a percent.
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Explanations
1.D
This question tests your understanding of order of operations, exponents, and logarithms.
We’ll solve it step by step. The numerator simplifies to
The denominator is 5, because 25 = 32. So the answer is 40⁄5 = 8.
2.E
The product of two negative numbers must be positive, and the product of an even number and any other number is even: therefore, (a × b) must be even and positive. The square of an even number is even and positive, so c2 is even and positive. Since two positive even numbers will sum to a positive even number, (a × b) + c2 must be positive and even. When you add one to this value, the end result is odd and positive. 9 is the only answer choice that is odd and positive.
3.B
Find the prime factorizations of 24 and 42 to find their LCM and GCF.
24 = 23 × 3 42 = 2 × 3 × 7
The LCM of the two numbers is 23 × 3 × 7 = 168, and the GCF of the two numbers is 2 × 3 = 6. Now you just need to find the absolute value of the difference between the LCM and the GCF: |168 – 6| = |162| = 162.
4.C
Fractions are equivalent to each other if the numerator and denominator of one fraction can be multiplied by the same scalar, and the result is the other fraction. After reducing the first two fractions, you should have realized that they were both equivalent to
3/7. As soon as you got to the third one and found that it was already in reduced form and not equal to 3 /7, you could have stopped. If you checked the last two, you found that they, too, are equal to 3/7. 5.B
To answer this problem, use scientific notation. When you type 533 into your calculator, it is approximately 1.16 × 1023. This means that the decimal point has been moved over 23 decimal places, so there must be 23 + 1 = 24 digits in the full number.
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Decimals
Decimals are just another way to express fractions. After all, to produce a decimal, you simply divide the numerator of a fraction by the denominator. For example, 1/2 = 1 ÷ 2 = .5.
Comparing Decimals
Like fractions, comparing decimals can be a bit deceptive. As a general rule, when comparing two decimals such as .3 with .003, the decimal with more leading zeroes is the smaller one. But if asked to compare .003 with .0009, you might be tempted to overlook the additional zero, and because 9 is the larger integer, choose .0009 as the larger decimal. That would be wrong. Use caution to avoid such mistakes. It might help to line up the decimal points of the two decimals:
.0009 is clearly smaller than .0030 Similarly,
.000900 is smaller than .000925
Converting Decimals to Fractions
Knowing how to convert decimals into fractions and fractions into decimals are useful skills. Sometimes you’ll produce a decimal while solving a question, and then you’ll have to choose from fractions for test choices. Other times, it may just be easier to work with fractions. Whatever the case, both conversions can be done easily.
To convert a decimal number to a fraction:
- Remove the decimal point and make the decimal number the numerator.
- Let the denominator be the number 1 followed by as many zeroes as there are decimal places in the decimal number.
- Reduce the fraction.
Let’s convert .3875 into a fraction. First, we eliminate the decimal point and make 3875 the numerator:
Since .3875 has four digits after the decimal point, we put four zeroes in the denominator:
Then, by finding the GCF of 3875 and 10,000, which is 125, we can reduce the fraction:
To convert from fractions back to decimals is a cinch. Simply carry out the necessary division on your calculator, such as for 3/5:
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