MULTIPLES

45. Oral.

A multiple of a number is another number that exactly contains it.

9 and 30 are multiples of 3. 10, 20, and 45 are multiples of 5.

A common multiple of two or more numbers is a number that exactly contains each of them.

15, 30, and 75 are common multiples of 3 and 5.

The least common multiple of two or more numbers is the smallest number that exactly contains each of them.

15 is the least common multiple of 3 and 5.

L. C. M. stands for least common multiple.

1. What number is a common multiple of 3 and 7?

2. What number is a common multiple of 2, 3, and 5?

3. What number is the least common multiple of 5 and 7?

Name the least common multiple of:

3. Divide 8 × 10 by 4 × 10, or 80 by 40.

4. Divide 8 by 4. Do we get the same answer if we leave the 10 out of both dividend and divisor?

This rejecting of equal factors from both dividend and divisor is called cancelation.

If we reject the same factor or factors from both dividend and divisor, we do not change the value of the quotient.

48. Written.

Divide 4×7 by 3 × 7.

What factor has been canceled from both dividend and divisor? What is the quotient?

Divide 16 x 3 by 2 × 27.

18 × 3

2 × 27 9

The factor 2 may be canceled from 16 in the dividend and 2 in the divisor. The factor 3 may be canceled from 3 in the dividend and 27 in the divisor. The quotient is §.

49. Oral.

FRACTIONS

Draw a line 1 inch long and divide it into halves. Divide another inch line into fourths; another into eighths.

1. How many halves of an inch are there in an inch? How many fourths? How many eighths? How many tenths? How many twelfths? How many twentieths?

2. What do we call one of the four equal parts of a unit? One of the eight equal parts? One of the ten equal parts?

3. What do we call 3 of the four equal parts of a unit? 3 of the eight equal parts? 7 of the ten equal parts?

4. How many thirds of an orange are there in 2 oranges? In 5 oranges? In 7 oranges? In 12 oranges?

5. How many fourths are there in 2 oranges? How many eighths? How many tenths? How many twelfths?

6. How many fourths of a lemon are there in half a lemon? In one and one half lemons? In two and one half lemons? 7. What is of 15? % of 15? of 40? of 16? 30 ?

of

of an orange or of an orange? or org?

1 of 1 ? 1 of 1 ? 1 of 1? 1 of 1?

10. Is there any difference between 1 of 2 pineapples and of 1 pineapple?

11. What is of 24? of 32?% of 50? of 30? of 40?

50. Oral.

A fraction is one or more of the equal parts of anything.

A fraction is also an expression of division. means 1÷4, or 1 whole thing divided into 4 equal parts. means 93, or 9 divided into 3 equal parts.

The number below the line is the denominator. It shows into how many equal parts the whole is divided.

The number above the line is the numerator. It shows how many parts are thought of.

means that the whole is divided into 4 equal parts, and 3 of these parts are thought of.

The numerator and denominator are the terms of a fraction. A proper fraction is a fraction whose numerator is less than its denominator; as,,, . Its value is less than 1.

11

8

An improper fraction is a fraction whose numerator is equal to or greater than its denominator; as, §, §, 13. Its value equals 1, or is greater than 1.

12

A mixed number is a whole number and a fraction written together; as, 51, 63, 463.

In the following list name (1) all the proper fractions; (2) all the improper fractions; and (3) all the mixed numbers:

1. Nine twentieths; six and six sevenths; fourteen fifteenths.

2. Thirteen seventeenths; twenty-three hundredths.