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.
 

DIVISION: DIVIDING INTO SMALLER PARTS

Division is used to split groups up into smaller sections. Suppose there are 24 pairs of gloves in the storage locker and you want to distribute them evenly among 8 crewpeople. How many pairs of gloves would each crewperson receive. Dividing 24 by 8 yields 3; each crewperson would receive 3 pairs of gloves. Some words and symbols often seen in division are divided by, into, the symbol "÷",and the symbol "/".

MULTIPLICATION: A SHORTCUT TO REPEATED ADDITION

Multiplication is a simpler way of doing repeated addition. Suppose Ron can do 30 push-ups in one minute. If he maintained a steady pace, how many push-ups could he do in five minutes? You could add 30 + 30 + 30 + 30 + 30, or you could multiply 30 × 5 to arrive at the answer of 150 push-ups. Some words and symbols used in multiplication are times, the product of, the "×" sign, or a dot like "•". Sometimes numbers that are being multiplied will be put in parentheses (30)(5)=150. 

SUBTRACTION: COMPUTING A DIFFERENCE

Subtraction is used in two types of situations. The first is "How much is left?" and the second is "How much more is needed?" Some words used in subtraction are "minus", "take away", "less", and "difference".

Example 1 - How many are left? 
 

ADDITION: ADDING TO A SUM OR TOTAL

Addition is used when combining items, or putting items together to obtain a total. It helps answer questions such as "How many?" "How much?" or "How far?" Let's look at different ways that addition can be used. Some words used often to refer to addition are "plus", "and", "the sum of", "total", or "added to".

Example 1 - Pedro's crew has 4 pulaskis. Jane's crew has 6 pulaskis. How many pulaskis do they have together?

HOW TO READ LARGE NUMBERS

Numbers are separated into groups: ones, tens, hundreds, thousands, millions, and so on. Each group contains three subgroups: ones, tens, and hundreds. When writing or reading a large number, begin at the left with the largest group, and proceed to the right. For instance, 7,482 is read as seven thousand, four hundred, eighty-two. The following chart can help in reading large numbers.