Oral.

REVIEW AND SUMMARY

127

1. What are the names of the first four places in a whole number?

2. What is the name of the fifth place? The sixth?

3. How many periods are there in a number of 6 places? 4. What is the name of the seventh place in a whole number? What is the name of the third period?

Write:

5. Three million, two hundred seventy thousand, sixtyfive.

6. Twenty-five million, ninety thousand, one hundred twenty.

7. Eighty-seven million, eighty-seven thousand, fortynine.

8. Twenty million, forty thousand, one hundred forty. 9. What is a ratio? Give several examples.

10. What other questions mean the same as: "What is the ratio of 9 to 27?"

II. A man invested $500 and received an income of $25. What is the ratio of the income to the investment?

12. Illustrate what is meant by average. Name two kinds of problems in which it has been used.

13. Four cars together carry 240,676 lb. of granite; what is the average number of pounds which one car carries?

14. In 1884 the export from the United States of iron and steel and articles manufactured from them amounted to $21,900,000; in 1900 the value of the same exports was $121,900,000. What was the difference between the values of the exports for the two years given?

15. The price of wheat was: Monday, $.67; Tuesday, $.683; Wednesday, $.661; Thursday, $.67§; Friday, $.673; Saturday, $.667. Find the average price for the week.

PERCENTAGE

Rate Per Hundred

I. Find the cost of 600 coats at $492 per hundred.

2. Find the cost of 350 chairs at $112 per hundred.

$492

6

$112 31

3. A boy is permitted to fish in a pond on condition that he gives the owner 30 per hundred of the fish caught. He caught 120 fish. How many did he give the owner?

=

SUGGESTION: 30 of the hundred equal parts of the fish caught =10% of 120 = ?

4. Fractions with the denominator 100 are extensively used in practical and business arithmetic.

?

?

?

# = 180.

32. Write as an ordinary fraction 5 hundredths. Reduce

it to its lowest terms.

33. Write as an ordinary fraction 12 hundredths. Then cancel 12 from both terms.

26. 4.

30. 11.

27.1.

31. 12.

MEANING OF PER CENT

129

1. Of 600 pupils in a school 2 per hundred were absent; how many were absent?

2. A contractor bought 12,000 bricks; 28 per hundred were defective; how many defective bricks were there in the lot?

3. An army consists of 6,500 men; of these 11 per hundred are officers, the rest privates; how many officers are there?

4. Two thousand persons wished to attend a political meeting, but the hall would accommodate only 47 per hundred of them; find the capacity of the hall.

5. A defeated candidate received 35 per hundred of the 8,620 votes cast; how many did he receive?

In expressions like the above, per cent is commonly used instead of per hundred. Per cent is derived from the Latin per centum meaning per hundred.

Thus, 6 per cent (6%) means 6 per hundred. The symbol % is read per cent.

6. Read Exercises 1-5, using per cent whenever per hundred occurs. This does not change the meaning.

7. How many strawberry-plants are there in a square outlined in the picture? Those marked with circles are dead.

If there are as many dead in each hundred plants, how many per cent of the plants in the field are dead? How many per cent are alive?

130

MEANING OF PER CENT

1. Helen colored some water with cochineal. With a measuring-glass she took 80 parts of the red water and 20 parts of clear water and poured them into a glass. How many per cent of the solution were taken from the clear water?

80

60

40

20

2. Wesley colored some water with bluing and some with cochineal. He measured 40 parts of red water and 60 parts of blue water and mixed them together. How many per cent of the solution were taken from the red water? How many from the blue?

3. If convenient, make a solution using 30% of red water and 70% of clear water; one using 75% of red water and 25% of blue; also other solutions.

4. Draw a square and divide it into 10 equal rectangles. Divide each rectangle into 10 equal squares.

small squares are there in the figure?

How many

5. Shade 1% of the squares in the figure of Exercise 4. Shade 5% of them; 10%; 25%; 50%; 75%; 80%.

6. Draw a circle and shade 25% of it; 50% of it; 75%.

7. Draw a rectangle whose breadth is 20% of its length;

one whose breadth is 75% of its length.

The percentage of salt in the bodies of water named is:

8. In the bodies of water named, how many pounds of salt are there in each 100 pounds of water?

9. Find the amount of salt in 1,700 pounds of water from each.

10. Make and solve 5 other problems using the facts of the table.

PROBLEMS-WALK BUILDING

131

The picture shows a section of 1 yard of cement walk. In building such a walk a space is excavated the width of the proposed walk and half filled with coarse gravel. Then, of the rest is filled with concrete (cement and fine gravel), and the rest with cement and sand. The dotted lines in the figure are used simply to show the number of hundredths in each part.

How many

1. How many rows of squares are there in the section? How many squares are there in each row? squares are there in the whole section? How many are there in of it? In 1 of it?

2. What part of the material used in building a cement walk is coarse gravel? How many parts in 100 parts are coarse gravel? How many per cent?

3. What part of the material used in building such a walk is concrete? How many parts in 100 parts are concrete? How many per cent?

4. What part of the material used is cement and sand? How many parts per hundred? How many per cent?

5. 20% of anything are how many hundredths of it? What part of it? What percentage of anything is of it? of it? of it?

of it? How many are: 6. 20% of 200? 9. 25% of 500?