2. When is changed to 12ths, the denominator is made 4 times as large. We know this because 3 is contained in 12 four times. The numerator must also be made 4 times as large, so it is multiplied by 4.

3

3. Change to 12ths: 1, 3, 4, 4, 5, ¿, 1.
4. Change to 18ths: 1, 1, 3, 5, 1, 1, §.
5. Change to 24ths: 3, 4, 5, 1, 12, §, 12.
6. Change to 20ths:,,, o, &, 1, 16.
7. Change to 36ths: 4, 2, 5, 12, 1, 3, J.
8. Change to 30ths:,, 10, 15, §, f.

287. Written Exercises.

3

Change to 12ths and add:

MODEL A:

3

Add the fractions in Exercises 3-8, Sec. 286.

12

288. Written Exercises.

1. Find the sum of 85, 63, and 63.

Change the fractions to 12ths and add the sum of

the fractions to the sum of the whole numbers.

dividing the numerator and denominator by 4. This does not change the value of the fraction.

2. Remember: If the numerator and the denominator of a fraction are divided by the same number, the value of the fraction is not changed.

3. The fraction is not in its lowest terms because both the numerator and the denominator may be divided by a number that will change them to smaller numbers without changing the value of the fraction. What is the number?

MEASURES

290. 1. The exact measures of 12 ft. are: 1 ft., 2 ft., 3 ft., 4 ft., 6 ft., and 12 ft.

2. The exact measures of 18 ft. are: 1 ft., 2 ft., 3 ft., 6 ft., 9 ft., and 18 ft.

3. 2 ft., 3 ft., and 6 ft. are each exact measures of 12 ft. and 18 ft. They are common measures of 12 ft. and 18 ft.

4. 6 ft. is the greatest measure that is common to 12 ft. and 18 ft. It is the greatest common measure of 12 ft. and 18 ft.

291. Find the exact measures of:

7. What is meant by the greatest common measure of two or more quantities?

This is generally known as the greatest common divisor, or greatest common factor of the quantities.

294. Oral Exercises.

Change to whole or mixed numbers:

FACTORS AND MULTIPLES

297. Oral Exercises.

1. Numbers that are exactly divisible by 2 are

even numbers.

2. Name the even numbers to 30. Numbers that are exactly divisible by 2 end in what figures?

3. Numbers that are not exactly divisible by 2 are odd numbers.

4. Name the odd numbers to 30.

5. Some numbers cannot be divided by any whole numbers except themselves and 1 without leaving a remainder. These are called prime numbers. The following are prime numbers: 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. These can be divided only by themselves and 1 without leaving a remainder.

6. A factor of a number is one of two or more numbers which multiplied together will make the number. 6 and 5 are each factors of 30. 2, 3, 4, and 6 are each factors of 12.

7. A common factor is a common unit of measure. 6 is a common factor of 12 and of 36, because both of these numbers are exactly divisible by 6. Name the common factors of 24 and 36.

To reduce a fraction to its lowest terms, divide both numerator and denominator by their common factors.