A fraction represents parts of a whole. The top number of a fraction, called the numerator, indicates how many equal-sized parts are present. The bottom number of a fraction, called the denominator, indicates how many equal-sized parts make a whole.

Fractions have several forms:

properfraction: the numerator is less than the denominator

improperfraction: the numerator is greater than or equal to the denominator

mixed number: the combination of a whole number and a fraction

Improper fractions can be converted to mixed numbers by dividing. (In fact, the fraction bar is also a division symbol.)

\(\frac{14}{3}=14÷3=4=4\frac{2}{3}\)

To convert a mixed number to a fraction, multiply the whole number by the denominator of the fraction, and add the numerator. The result becomes the numerator of the improper fraction; the denominator remains the same.

To multiply fractions, multiply numerators and multiply denominators. Reduce the product to lowest terms. To divide fractions, multiply the first fraction by the reciprocal of the second fraction. When multiplying and dividing mixed numbers, the mixed numbers must be converted to improper fractions.

The reciprocal of a fraction is just the fraction with the top and bottom numbers switched.

Adding or subtracting fractions requires a common denominator. To find a common denominator, multiply the denominators of the fractions. Then, add the numerators and keep the denominator the same to find the sum.

\(\frac{a}{b}+\frac{c}{b}=\frac{a\ +\ c}{b}\)

\(\frac{a}{b}−\frac{c}{b}=\frac{a\ −\ c}{b}\)

Decimals

In the base-10 system, each digit (the numeric symbols 0 – 9) in a number is worth ten times as much as the number to the right of it. For example, in the number 321 each digit has a different value based on its position: 321 = 300 + 20 + 1. The value of each place is called place value.

Place Value Chart

1,000,000

10^{6}

millions

100,000

10^{5}

hundred thousands

10,000

10^{4}

ten thousands

1,000

10^{3}

thousands

100

10^{2}

hundreds

10

10^{1}

tens

1

10^{0}

ones

.

decimal

1/10

10^{-1}

tenths

1/100

10^{-2}

hundredths

To convert a decimal number to a fraction, write the digits in the numerator and write the place value of the final digit in the denominator. Reduce to lowest terms, if necessary.