Numbers and percents
Mathematics, Grade 8
Numbers and percents
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Study Guide Numbers and percents Mathematics, Grade 8
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NUMBERS AND PERCENTS Numbers and percents refer to the relationship between fractions, decimals, and percents. • A percent is a term that describes a decimal in terms of one hundred. Percent means per hundred. • Percents, fractions and decimals all can equal each other, as in the case of 10%, 0.1 and 1/10. • Fractions and decimals can easily be changed into percent. • There are three cases of percent. o In the first, a percentage of a number is taken. o In the second, a number is given as ? percent of another number. o In the third case, a number is given as a percentage of ? number. • To solve for the three cases of percent, the Percent Equation can be used. The percent equation refers to the proportion, a/b = p/100, or 'a is p percent of b'. By filling in the given information, the missing number can be found. How to use numbers and percents To change a fraction to a decimal or percent, the fraction must be put into terms of 100 if possible. • For example, 3/4 changes into 75/100. Once it is in this form, it is changed into the decimal, .75 and the percent, 75%. If the fraction cannot be put into terms of 100 easily, then divide the fraction to get into decimal form. • For example, 16/27, when divided is .5925. Take the decimal form and move the decimal point two places to the right to find the percent. So .5925 becomes 59.25%. With decimals, move the decimal point two places to the right to get the percent. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Using the first of the three cases of percent, a percentage of a number is taken. • For example, what is 16% of 45? To find the answer, use the percent equation: Ex. x/45 = 16/100 → 100x = (45)(16) → 100x = 720 → x = 7.2 Using the second case of percent, the percent is missing. Again the percent equation can be used. • For example, if Ken got 78 out of 120 question correct on a test, what percent would that be? Ex. 78/120 = x/100 → (78)(100) = 120x → 7800 = 120x → x = 65 Using the third case of percent, the number that is being multiplied by the percent is missing. • For example, 16% or 22 people said they did not like their job; how many people were asked if they liked their job? Ex. 22/x = 16/100 → 2200 = 16x → 137.5 ≈ 138 Try This! 1. What is the fraction, 3/8, as a percent? 2. What is the decimal, .825, as a percent? 3. What is 65% as a decimal? 4. What is 44% as a fraction? 5. What is 25% of 82? 6. Five is what percent of 75? 7. Sixteen is 54% of what number? 8. If Roger got 33 questions correct out of 39 questions, what percent would that be? 9. If Dan fixes 64% or 7 of the cars at his shop, how many cars total did he need to fix? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
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