20. Which of the following are exactly divisible by 2? by 3? by 5? by 9? by 10? 45, 61, 360, 207, 783, 53, 540, 117, 102, 107, 37, 97, 201, 855, 732, 380, 4320, 105? 21. A number that is exactly divisible by 9 is exactly divisible by 3. Why?

22. All multiples of even numbers are even numbers. Why?

23. The number denoted by the two right-hand figures of 216 is 16. Will 4 exactly divide 16? 200? 216?

24. Write a number of three or more places in which the number denoted by the two right-hand figures is some multiple of 4. Is the number exactly divisible by 4?

A number is exactly divisible by 4 if the number denoted by its two right-hand figures is exactly divisible by 4.

25. Which of the following are exactly divisible by 4: 112, 202, 420, 532, 514 ?

26. Centennial years that are divisible by 400 (1200, 1600, etc.) and other years divisible by 4 are leap years. Which of the following will be leap years: 1910, 1912, 1908, 1926, 1924, 1960, 1990, 2000, 2100?

27. Write 10 numbers that are exactly divisible by 3.

113. The three pairs of factors of 24. are 2 and 12, 3 and 8, 4 and 6. Name all the pairs of factors of each of the following, naming no factor larger than 20:

PART II

FRACTIONS

114. 1. Draw a line 4 inches long.

two equal parts. What is each part called?

Divide it into

2. If 6 pupils are separated into three equal groups, what part of the pupils will each group contain?

3. Draw a line. Divide it into eight equal parts.

ᄒ

ᄒ

C

ᄒ

ᄒ

D

E

to to to to to to to to to to to to to to

4. A represents the line undivided.

B represents

the line as divided into two equal parts. What does C represent? D? E? What name is given to each part of the line in B? in C? in D? in E? In each case, how many of the parts does it take to equal the entire line?

5. The length of the line is represented in turn by 1, 2, 4, 8, and 18. of the line === of the line. 16 of the line ==

§, *

6.

7.

of the line.

of the line + of the line =

the line of the line of the line.

8. What is the sum of of the line and of the line? What is the difference between of the line and of the line?of the line and of the line?

9. of the line is longer than line is longer than of the line. than of the line.

10. Using 8 objects, show that same as of 8 objects, and that of as g of 8 objects.

196

of the

of the line.
of the line is longer

of 8 objects is the 8 objects is the same

of a circle is equal

11. Show by dividing circles that to of a circle; that of a circle is equal to g of a circle; that of a circle plus of a circle is equal to of a circle; that of a circle is equal to 1 of a circle.

12. Show by dividing rectangles that,,,, and of a rectangle are equivalent parts.

13. Using objects, show that of 12 objects is the same as 8 of 12 objects; that of 12 objects is the same as of 12 objects.

14. Show by folding paper that === ; that =2=3=12 = 3 = 3

115. Ratio.

A

B

C

1. Line A is what part of line B? what part of line C? 2. If B is called 1, what is A? C? If Cis called 1, what is A? B? If Cis called 6, what is A? B?

3. If A is called 3, what is B? C? If A is called 4, what is B? C?

4. The ratio of line A to line B is 1. What is the ratio of line A to line C? of line B to line A? of line B to line C? of line C to line B? of line C to line A?

A B

C

D

E

116. 1. The surface A is what part of the surface B? of C? of D? of E?

2. The ratio of A to B is; of A to Cis; of A to D is; of A to E is.

3. The surface B is what part of the surface C? of D? The ratio of B to C is ; of B to D is

of E?

of B to E is

4. What is the ratio of C to E? If C represents 40 A, what does E represent?

5. What is the ratio of B to A? of C to A? of D to A? of E to A? of C to B? of E to C? of D to B? of E to B?

6. The ratio of C to D is, or; of D to Cis, or 3.

7. What is the ratio of D to E? of E to D? of E to C? 8. If A represents 10 acres, what does B represent? C? D? E?

9. If B represents 40 acres, what does A represent? C? D? E?

10. If the cost of the land represented by B is $100, what is the cost of the land represented by A? C? D? E?

11. If the area represented by E is 640 acres, what is the area represented by C? B? A? D?

12. Draw two lines such that the ratio of one to the other is; 2; 5.

13. Draw oblongs such that the ratio of one to the other is ; ; ; 3; §.

1

117. 1. The unit of 3 is 1; of 3 da. is 1 da.; of 3 mi. is 1 mi.

2. The unit 1 mi. may be regarded as composed of equal parts, as of 2 half miles, of 4 quarter miles, of 8 eighth miles, etc. If the unit 1 mi. is regarded as composed of 4 equal parts, each part is expressed as mi.; 3 such parts are expressed as mi. A unit may be regarded as composed of 2 or more equal parts.

3. A fraction is one or more of the equal parts of a unit, as,, etc.

4. In the fraction, 4 is the denominator. It shows the number of equal parts into which the unit has been divided. It names the equal parts. 3 is the numerator. It shows the number of the equal parts of the unit that have been taken to make the fraction . denotes 3 of the 4 equal parts of the unit 1.

5. When a unit is divided into two or more equal parts, each of these parts becomes in

turn a unit.

2' 3'

Such

1, etc., are fracWhat is the unit of yd., yr.?

6. Draw a line 1 ft. long. Divide it into 4 equal parts. Show the part that is expressed by ft.; by ft.; by

ft. The ratio of 1 part of the line to the whole line is What is the ratio of 2 parts of the line to the whole line? of 3 parts? What is the ratio of the line to 1 part? to 2 parts? to 3 parts?

7. Draw a line 8 in. long. Let it represent 1 mi. Show the part that represents mi.; mi.; & mi. Show the part whose ratio to the whole line is,,, Show the part to which the ratio of the whole. line is 2; 8; 4; ; ; .