1. FRACTIONAL AND DECIMAL EQUIVALENTS OF PERCENTS

Transcription

1 Percent 7. FRACTIONAL AND DECIMAL EQUIVALENTS OF PERCENTS Percent means out of 00. If you understand this concept, it then becomes very easy to change a percent to an equivalent decimal or fraction. % means out of 00 or, which is equal to.0 00.% means. out of 00 or., which is equivalent to or.0 c c% means c out of 00 or 00, which is equivalent to c or.0c 00 % means out of 00 or, which is equivalent to or.00 To change a percent to a decimal, therefore, we must move the decimal point two places to the left, as we are dividing by 00. 6%.6.%.00.%.0 To change a decimal to a percent, we must reverse the above steps. We multiply by 00, which has the effect of moving the decimal point two places to the right, and insert the percent sign..7 7%.0.%.00.% To change a percent to a fraction, we remove the percent sign and divide by 00. This has the effect of putting the percent over 00 and then simplifying the resulting fraction. % % 00 0.% To change a fraction to a percent, we must reverse the above steps. We multiply by 00 and insert the percent sign % 0% / 7 00 % % 7 % /

2 7 Chapter Some fractions do not convert easily, as the denominator does not divide into 00. Such fractions must be changed to decimals first by dividing the numerator by the denominator. Then convert the decimal to a percent as explained on the previous page. Divide to two places only, unless it clearly comes out even in one or two additional places ) % ). 000.% Certain fractional and decimal equivalents of common percents occur frequently enough so that they should be memorized. Learning the values in the following table will make your work with percent problems much easier. PERCENT DECIMAL FRACTION 0%. %. 7%.7 0%. 0 0%. 0 70% % %. 66 %.66 6 %.6 6 %. 6 0%. 0%. 60%.6 0%. %. 7 %.7 6 %.6 7 %.7 7

3 Percent 7 Exercise Work out each problem. Circle the letter that appears before your answer.. % may be written as a decimal as (A). (B). (C).0 (D).00 (E).0. Write as a fraction in simplest form: %. (A) 0 (B) 7 0 (C) 7 0 (D) 9 0 (E) 7. Write.6 as a percent. (A).6% (B).6% (C).06% (D) 6% (E) 60%. Write as an equivalent percent. (A) % (B).6% (C) % (D).% (E). %. Write % as a decimal. (A). (B).00 (C).0 (D) 0.0 (E).0

4 7 Chapter. FINDING A PERCENT OF A NUMBER Most percentage problems can be solved by using the proportion % 00 part whole. Although this method will work, it often yields unnecessarily large numbers that make for difficult computation. As we look at different types of percent problems, we will compare methods of solution. In finding a percent of a number, it is usually easier to change the percent to an equivalent decimal or fraction and multiply by the given number. Find % of. x 00 00x 6 x 6. Decimal Method Change % to. and multiply Find % of. Decimal Method Fraction Method x 00 00x 00 x Change % to Which method do you think is the easiest? When the fractional equivalent of the required percent is among those given in the previous chart, the fraction method is by far the least time-consuming. It really pays to memorize those fractional equivalents.

5 Percent 7 Exercise Work out each problem. Circle the letter that appears before your answer.. What is 0% of 0? (A).6 (B).6 (C) 6 (D) 60 (E) 600. What is % of 67? (A) (B). (C). (D). (E).. Find 6 % of 0. (A) 0 (B) (C) 00 (D) 6 (E). What is % of 0? (A) (B). (C).0 (D).00 (E).000. Find r% of s. (A) 00s r (B) rs 00 (C) 00r s (D) r 00s (E) s 00r

6 76 Chapter. FINDING A NUMBER WHEN A PERCENT OF IT IS GIVEN This type of problem may be solved using the proportion method, although this may again result in the unnecessary use of time. It is often easier to translate the words of such a problem into an algebraic statement, using decimal or fractional equivalents for the percents involved. Then it will become evident that we divide the given number by the given percent to solve. 7 is % of what number? 7 00 x x 700 x 0 0 is 66 % of what number? Equation Method 7. 0x 700 x 0 x Equation Method x 66 x x 00 0 x x x 00x 000 x 0 x 60 Just think of the amount of time you will save and the extra problems you will get to do if you know that 66 % is and use the equation method. Are you convinced that the common fraction equivalents in the previously given chart should be memorized?

7 Percent 77 Exercise Work out each problem. Circle the letter that appears before your answer.. 7 is % of what number? (A) 6 (B) 60 (C) 600 (D) 6. (E).6. 0 is % of what number? (A) 0 (B) 00 (C) 6 (D) 60 (E) % of what number is 7? (A) 7 (B) 0 (C) 90 (D) 0. (E) 6. m is p% of what number? (A) (B) (C) (D) (E) mp 00 00p m m 00p p 00m 00m p. 0% of what number is r? (A) (B) (C) (D) (E) r r 0r r 00r

8 7 Chapter. TO FIND WHAT PERCENT ONE NUMBER IS OF ANOTHER This type of problem may also be solved using the proportion method. However, this may again result in the use of an unnecessary amount of time. It is often easier to put the part over the whole, simplify the resulting fraction, and multiply by is what percent of 00? x x 000 x % is what percent of 7? x x Fraction Method % Fraction Method % Time consuming long division is needed to find x 6 %. If you have memorized the fractional equivalents of common percents, this method requires only a few seconds. What percent of 7 is 6? x x 600 x % 9 Fraction Method %

9 Percent 79 Exercise Work out each problem. Circle the letter that appears before your answer.. is what percent of 0?. (A) 0 (B) (C) (D). (E) 0 of 6 is what percent of (A) (B) 0 (C) 0 (D) (E). What percent of 96 is? (A) 6 (B) of 60?. What percent of is? (A) (B) 0 (C) 00 (D) (E) 0. What percent of y is x? (A) x y (B) x 00y (C) xy 00 (D) 00x y (E) 00y x (C) 7 (D) (E)

10 0 Chapter. PERCENTS GREATER THAN 00 When the percentage involved in a problem is greater than 00, the same methods apply. Remember that 00% ; 00% ; 00% and so forth. Therefore 0% will be equal to 00% + 0% or. Let us look at one example of each previously discussed problem, using percents greater than 00. Find 7% of 60 Decimal Method Fraction Method 7 x x 000 x 0 0 is % of what number? Decimal Method Fraction Method 0 00 x x 000 x 6 0 is what percent of 0? x x 000 x % 0. x 000 x x 6 Fraction Method 0 0 % 0 x 0 x 0 x x 6

11 Percent Exercise Work out each problem. Circle the letter that appears before your answer.. 6 is 0% of what number? (A) (B) (C) 6 (D) (E). What is 00% of 6? (A) (B) (C) (D) (E). What percent of 90 is 0? (A) is 00% of what number? (A) 0 (B) 000 (C) 00 (D) 70 (E) 00. To multiply a number by 7 %, the number should be multiplied by (A) 7. (B) 70 (C).7 (D).7 (E).7 (B) (C) (D) 0 (E)