1. In a package containing 500 sheets of paper, 3 out of each hundred, or 3 per cent, were imperfect. How many sheets were imperfect? 2. In his collection of 200 foreign stamps, John found that 4 out of each 100 stamps, or 4%, were Italian stamps. How many Italian stamps did he have? 3. Margaret is making a collection of postal cards of famous places in America. She has in all 300 postal cards. Of this number 5% show pictures of Yellowstone Park. How many of her postal cards show pictures of Yellowstone Park. In finding a given per cent of a number, the answer is often spoken of as a percentage.1 4. Find 2 per cent of 300 books. What is the percentage? 5. What is the percentage when 3 per cent of $400 is found? When 2% of 700 miles is found? 6. What is the percentage when 5% of 400 men is taken? A convenient way of finding a percentage of a number mentally is to point off two places in the number to show what one per cent equals, and then to multiply by the given number of per cent. To find 5% of 400 men, 1% is thought of as 4 (4.00) men, and 5% as 5 times 4 men, or -men. 1 The number of which the percentage is a part is called the base. Unless the use of this term is desired by the teacher, it may be omitted as unnecessary. FINDING A PERCENTAGE 217 7. A young man earned $500 and saved 8% of it. What was the percentage saved? 8. A farmer had $600 in a bank. He took out 4% of it. What was the percentage taken out? Name the percentages found by taking: A school containing 400 children had its membership increased 5 per cent. What was the new membership? 1. A village containing 800 people increased in population 2%. What was its new population? 2. A library containing 500 volumes was increased 10%. How many books did it then contain? 3. Increase 200, 4 per cent; 300, 2 per cent;.400, 2 per cent. 4. What is the amount when $600 is increased 3%? When $500 is increased 5%? When $900 is increased 2%? III Out of my savings amounting to $300, I spend 4%. How much money have I left? [Without pencil.] 1. What is the attendance at school when, out of a membership of 500 pupils, 2% are absent? 2. A boy had 300 marbles. He lost 5% of them. How many did he have left? 3. How much is left after 5% is taken from $200? After 3% is taken from $300? After 2% is taken from $600? In solving problems in percentage, it is often convenient to express different fractional parts as per cents, and different per cents as fractional parts. With the help of this diagram, a number of the most common equivalents can be found. [Without pencil.] 1. The diagram contains 100 small squares. One of these squares is what part of the diagram? What per cent of it? 2. One half of the diagram equals how many hundredths of it? What per cent of it? 3. One fourth of the diagram equals how many hundredths of it? What per cent? 4. Three fourths of the diagram equals how many hundredths of it? What per cent? FRACTIONAL PARTS AND EQUIVALENT PER CENTS 219 6. Express as a fraction: 25%; 50%; 75%. 7. A boy has saved 50% of the amount necessary to buy a printing press. What part of the money needed has he saved? 8. A girl's father helped her to buy a writing desk by paying 25% of the cost. What part was left for her to pay? What per cent? 9. Study the diagram and find the per cents that stand for other fractional parts, such, for example, as and 1. II (1) What per cent of a quantity is of it? Since in one whole there is 108, or 100%, in of a quantity there is of 100%, or 40%. (2) What fractional part of a number equals 70% of it? 1. With the help of the first solution above, tell how to find the per cent that equals a given fractional part. 2. With the help of the second solution, tell how to find the fractional part that equals a given per cent. 3. Express as a per cent: [Without pencil.] 9 ;o; 10; §; §; t. 4. One tenth of a man's salary was used for rent. What per cent was used? 5. Three fifths of a boy's earnings was put into a savings bank. What per cent was put in? 6. Express as a fractional part: 10%, 20%, 40%, 80%, 90%. 7. In an arithmetic test, a boy solved 80% of his problems correctly. What part did he solve correctly? 8. What part of the work in a test is correctly done when a mark of 90% is received? III [Without pencil.] 1. What per cent of a quantity is equal to of it? 2. Practice counting from cent. Begin in this way: = 3. Learn these equivalents: } = 121%. 3 = 371%. to §, expressing each part as a per 121%; , or 1, = 25%. 4. What per cent of a quantity is equal to of it? To? To ? 5. Count from to, expressing each part as a per cent. 6. Learn these equivalents: // = 331%. 3 = 66%. = 163%. 8 = 831%. Use the following exercises daily until they are mastered: Out of his earnings amounting to $1750 a year, a man saves 20%. How much money does he save? SOLUTION USING A COMMON FRACTION SOLUTION USING A DECIMAL = .20. $1750 .20 = $350.00 |