20. Find the totals in the following list of the naval forces of the United States in 1917:

21. Find the totals in the following list showing the extent of a recent Naval Appropriation Bill:

CHAPTER III

FRACTIONS AND FACTORS

A Fraction is an expression denoting one or more equal parts of a unit. It is an indicated division, usually written in the form.

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

It

The number above the line is called the numerator. shows how many parts have been taken to form the fraction.

The numerator and denominator are called the terms of the fraction.

A proper fraction is one whose numerator is less than its denominator. Thus, 4, 3, and are proper fractions.

An improper fraction is one whose numerator is equal to, or greater than, its denominator. Thus, 4, §, and 22 are improper fractions.

A mixed number is a whole number with a fraction. Thus, 13, 2, and 34 are mixed numbers.

Rule.

Mixed Numbers Expressed as Fractions

To express a mixed number as a fraction, multiply the whole number by the denominator, add the numerator, and write the result over the denominator.

EXAMPLE. Express 3g as a fraction.

8x3+5= 29, the numerator of the fraction required.

Rule. To express an improper fraction as a whole or mixed number, divide the numerator by the denominator.

EXAMPLE. Express 22 as a whole or mixed number.

34 7)22

ORAL DRILL

Express as whole or mixed numbers the following fractions:

Express as whole or mixed numbers the following fractions:

The Greatest Common Divisor of two or more numbers is the greatest number that is exactly contained in all of them. It is also called the highest common factor.

Thus, 12 is the greatest common divisor of 24 and 36. Greatest Common Divisor is commonly abbreviated G. C. D. or H. C. F.

The principal use of greatest common divisor is its application in reducing fractions to their lowest terms.

Prime Numbers. If numbers have no common factor other than 1, they are said to be prime to each other.

The greatest common divisor of two or more numbers can frequently be found by inspection, but when this is impossible, observe the following rule.

Rule.(1) Separate the numbers into prime factors, and (2) find the product of the prime factors common to the numbers.

EXAMPLE. Find the G. C. D. of 54, 72, and 108.

A Factor of a number is a number which is exactly contained in that number. Thus, 2, 3, 4, and 6 are all factors of 12.