V

PERCENTAGE

86. Meaning of Percentage. We have already learned that, several hundred years before the invention of decimals, merchants found it convenient to count by the hundred. In this system, or .4, becomes 10%. A per cent is therefore merely the numerator of a fraction having 100 as its denominator. Similarly, 2, or .12, which reduces to 10%, is called 12 per cent and is written 12%. Again,

12

As percentage is a part of common business language, it should be understood thoroughly by all.

87. Changing a Common Fraction or a Decimal to a Per Cent. First change the common fraction or decimal to a common fraction with a denominator 100, then write the numerator alone with the per cent sign after it. Thus,

88. Changing a Per Cent to a Common Fraction or to a Decimal. Write the per cent as the numerator of a common fraction with 100 as the denominator.

its lowest terms or to a decimal. Thus,

Then reduce this to

EXERCISES

Fill in the blank spaces in the columns given below. Carry out mentally as many as possible.

41. A nickel is what per cent of a dollar? of a halfdollar? of a quarter? of a dime? of 20 ¢? of 40 ¢? of 30 ¢?

42. What per cent of a yard is 9 in. ? 1 ft.? 18 in. ?

43.

What per cent of a foot is 3 in.? 6 in.? 8 in.? 2 in.? 15 in. ?

89. Finding a Per Cent of a Number.-20% of 450 is the same as or 2 of 450. Why? In finding a per cent of a number the per cent must first be reduced either to a common fraction or to a decimal. It is simpler to change the per cent to a decimal except when the equivalent fraction is a simple aliquot part of 100, as in the list here given.

Find 45.2% of 352.

then find .452 of 352. Find 163 % of 624.

First change 45.2 % to 452 and Hence, what is 45.2 % of 352 ?

First notice that 163 % is the com

mon fraction. Then find of 624. What is this? Hence, what is 163 % of 624?

Finding n, which is R per cent of N, is stated by the equation,

n = R % X N.
R%

The number n is sometimes called percentage.

EXERCISES

How?

1. Change each per cent in the list above to a common fraction; to a decimal. When is it better to use the common fraction than the decimal form in solving problems containing a per cent?

Use pencil and paper as little as possible.

20. In 1918 the government increased freight rates 25 %. What would be the increase in a freight bill which before had been $ 35.36? $106.32? $ 85.46? $124.08?

21. The new freight, F, is what per cent of the old freight, f? State this as an equation.

22.

From the equation in Ex. 21 find ƒ in terms of F. Hence, the old freight is what per cent of the new freight? 23. A manual on home architecture states that in a wellproportioned living-room the width should be 75 % of the length. State W in terms of L by an equation. Find L in terms of W.

24. What should be the width of a living-room that is 16 ft. long? 18 ft. long? 22 ft. long? 25 ft. long?

25. In a well-lighted room the window-space is at least 18% of the floor-space. How large should the window-space be in a room 9 by 10 ft.? 10 by 12 ft. ? 15 by 21 ft. ? 26. Apply the test in Ex. 25 to your schoolroom.

27.

About 23% of the total population of the United States is of school age. Find the number of school-children in the following states with the populations stated:

28. The milk from a certain cow contains 3.5 % butter fat. How many pounds of butter fat in 416 lb. milk?

29. Cork weighs 24 % as much as an equal volume of water. If a cubic foot of water weighs 62.5 lb., what will be the weight of a cubic foot of cork?

30. The government estimates that 7% of the money spent for food is wasted. At this rate how much is wasted per year in a home where the monthly expenditure for food is $ 26? $ 25? $ 35? $75?

31. In a certain junior high school 96 % of the pupils invested in Thrift Stamps and Baby Bonds. What per cent of the school did not invest in Thrift Stamps or Baby Bonds? At this rate how many of the estimated 23,000,000 schoolchildren in this country own Thrift Stamps or Baby Bonds?

32. About 65 % of the current necessary to run an electric toaster is wasted. What per cent is used? State by an equation that c units of current are used of C units paid for. How much current of 30 ¢ paid for is used?

33. Solve the above equation for C. How much must be paid for the current to get 40¢ of usable current?

34. Solve the equation on page 50 for N.

90. Finding a Number that is a Certain Per Cent of Another Number.-We have just been finding the product of two numbers, one of which was a per cent expressed as a common fraction or as a decimal. We have here the reverse problem: namely, to find the number which, multiplied by the per cent, produces the given product number. This is at once seen from the equation,

Twenty-five per cent of what number equals 315?

.25, n = 315, and the number, N, is found