Integer Word Problems

An integer is defined as a number that can be written without a fractional component. For example, 11, 8, 0, and −1908 are integers whereas √5, Π are not integers. The set of integers consists of zero, the positive natural numbers, and their additive inverses. Integers are closed under the operations of addition and multiplication.

We use integers in our day-to-day life like measuring temperature, sea level, and speed limit. Translating verbal descriptions into expressions is an essential initial step in solving word problems. Deposits are normally represented by a positive sign and withdrawals are denoted by a negative sign. Negative numbers are used in weather forecasting to show the temperature of a region. Solving these integers word problems will help us relate the concept with practical applications.

Adding Integers
1. Rearrange the terms so that integers with the same sign are next to each other.
2. Add integers with like signs together.
3. Subtract the absolute values of integers with different signs.
4. The sign of the solution will be the sign of the larger integer.

Subtracting Integers
1. Rewrite the problem by changing the second term to its additive inverse.
2. Add the values.

Multiplying Integers
1. Multiply the absolute values of the integers.
2. If the two factors have the same sign, the product is positive.
3. If the two factors have different signs, the product is negative.

Dividing Integers
1. Divide the absolute values of the integers.
2. If the two integers have the same sign, the quotient is positive.
3. If the two integers have different signs, the quotient is negative.

The price of one share of stock fell 4 dollars each day for 8 days. How much value did one share of the stock lose?

The stock price fell, so it is represented by -4. This happened for 8 days.
-4 x 8 = -32
The stock’s value dropped by $32.