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# Basic Number and Integer Word Problems Study Guide

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## Introduction to Basic Number and Integer Word Problems

Mathematics is the supreme judge; from its decisions there is no appeal.

—TOBIAS DANTZIG (1884–1956)

This section will focus on counting and the other basic operations in math, and will apply them to solving math word problems.

Let's begin our study of basic number and integer word problems with a review of the number sets and the rules for the four basic math operations.

Rational Numbers: any number that can be expressed as , where b is not equal to zero, and a and b are both integers.

This is the set that includes any number that can be written as a fraction, such as 5 = and , and it also includes all repeating and terminating decimals, like 0.5 and 1.3.

Integers: {…–2, –1, 0, 1, 2 …}

This is the set of whole numbers and their opposites. There are no fractions or decimals in this set.

Whole Numbers: {0, 1, 2, 3, 4 …}

This set contains no fractions or decimals, and no negative values.

Natural (Counting) Numbers: {1, 2, 3, 4, 5 …}

This is the set of whole numbers without zero.

The questions in this section will focus on the natural numbers, whole numbers, and integers. Lesson 7 will concentrate on the set of rational numbers in fraction form, and Lesson 8 will cover word problems with decimals.

## Integers

Integers are the set of whole numbers and their opposites, and there are no fractions or decimals contained in this set. There are rules that can be applied when performing operations with integers, and we use the concept of absolute value when applying these rules of arithmetic.

The absolute value of a number is the distance the number is away from zero on a number line. It is a positive value no matter if you are counting from the right or from the left.

Absolute value is announced by using vertical bars on either side of the number. To find the absolute value of a number, count the number of units it is away from zero on a number line.

For example, the absolute value of 4, written as | 4 |, is equal to 4. The absolute value of –5, written as | –5 |, is equal to 5. Each of these examples is shown on the number line that follows.

 Tip: Think of the absolute value of a number as the value of the number without any sign. The absolute value of a number is always positive.

1. If the signs are the same, add the absolute values and keep the sign.
2.  Examples: 2 + 3 = 5 –2 + –4 = –6 –10 + –20 = –30
3. If the signs are different, subtract the absolute value of one number from the absolute value of the other and take the sign of the number with the larger absolute value.
4.  Examples: –2 + 4 = 2 5 + –11 = –6 –21 + 30 = 9

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