RATIOS

A ratio is a proportional relationship of one value to another, e.g., the ratio of gas to oil in chain saw mix. Ratios can be written either as a fraction, 1/2, or in ratio notation, 1:2. The value of a ratio is the division of the first number by the second number. For example, consider the ratio 1:40 . This ratio is read as "1 to 40". Any fraction, for instance, 1/20, can also be written as a ratio: 1:20

SUBTRACTING FRACTIONS

Similar to adding fractions, fractions must have a common denominator (the bottom numbers must be the same) before being subtracted.

There are three steps to subtracting fractions:

ADDING FRACTIONS

There are three steps to adding fractions:

DIVIDING FRACTIONS

Division of fractions involves using the reciprocal (flipped form) of the second fraction. The reciprocal of a number is such that the product of a number and its reciprocal is 1.

MULTIPLYING FRACTIONS

A whole number and a fraction, or two or more fractions, can be multiplied together. Whole numbers and fractions must be changed to all fractions, with no whole numbers, in order to multiply.

There are three steps to multiplying fractions:

SIMPLIFYING FRACTIONS

Simplifying a fraction is writing a number in its most basic form. Sometimes fractions involve very large numbers in both the numerator (top number) and in the denominator (bottom number). As a general rule, it is easier to work with simpler fractions. So, always simplify.

There are three basic rules for simplifying fractions:

FRACTIONS: BITS AND PIECES

Fractions are used often, for instance when adding leftover pails of foam or mixing gas and oil for chain saw fuel.

ORDER OF OPERATION

Some math problems are a mixture of addition, subtraction, division, and multiplication. An operation to be performed might be true for one item but not another, so parentheses are used () for clarification.

There is a specific order to follow when making calculations.

The order in which operations are performed is:

POWERS AND EXPONENTS

When a number is multiplied by itself several times, instead of writing each repetition of the multiplication, it is easier to use exponential notation. For example, 12 × 12 × 12 × 12 × 12 × 12 would be 12 multiplied to itself 6 times or 12⁶. The number being multiplied is called the base and the number of times it is multiplied by itself is called the exponent. In the above case, the base is 12 and the exponent is 6. When a number has an exponent of 2, it is said to be squared.

DECIMAL NUMBERS

How a number is read depends on where the decimal point is placed. The figure below is similar to the chart for large numbers in Section 1.1. The decimal point comes after the ones position. The numbers to the right of the decimals represent tenths (0.1), hundreds (0.01), thousands (0.001), and so on down to infinitesimally small numbers.

All whole numbers (called integers) have a decimal point at the end. For instance, 10 = 10., 24 = 24., and 17,801 = 17,801 = 17,801.0.