Basic Number and Integer Word Problems Study Guide

Subtracting Integers

Change the subtraction to addition and change the sign of the number following the subtraction to its opposite. Then, follow the rules for addition.

Examples:	–4 – 5	9 – (–6)	–14 – (–11)
	–4 + –5	9 + 6	–14 + 11
	–9	15	–3

Multiplying and Dividing Integers

1. If there is an even number of negative signs, perform the operation as usual and make the answer positive.

Examples:

–8 × –6 = 48

–20 ÷ –4 = 5

–2 × –3 × –4 × –1 = 24

2. If there is an odd number of negative signs, perform the operation as usual and make the answer negative.

Examples:

–2 × 5 = –10

40 ÷ –8 = –5

–10 × –2 × –4 = –80

Integer Word Problem Practice

Now that the rules for each of the operations with these number sets have been reviewed, it is time to move on to word problems that involve these operations. The sample questions that follow will use the steps to solving word problems introduced in the previous section to break down each question into smaller pieces.

Example 1

Jason is eating at a restaurant and orders a hamburger and a side of sliced apples. There are 12 slices of apple in the portion. If there are 5 calories in each apple slice and 230 calories in the hamburger, what is the total number of calories of his meal?

Read and understand the question. This question asks for the total number of calories in a meal. The number of calories in the hamburger and the number of calories in each piece of apple is given. The number of slices, 12, is also given.

Make a plan. The fact that you are finding the total number of calories in this case tells you to use addition. Find the total number of calories by adding the number of calories in the hamburger with the total number of calories in the apple slices. Find the total number of calories in the apple slices first by multiplying the number of calories in one slice by 12.

Carry out the plan. Find the total calories in the apple slices by multiplying 12 by 5.

12 × 5 = 60

There are 60 calories in the side of apple slices. Now, add this amount with the number of calories in the hamburger: 60 + 230 = 290. There are a total of 290 calories in the meal.

Check your answer. Check the solution to this problem by working backward. Start with the solution of 290 calories and subtract the number of calories in the hamburger:

290 – 230 = 60

This amount should be the total number of calories in the side of apple slices. Divide this number by 5 calories in each slice: 60 ÷ 5 = 12 slices, which was given in the question. This solution is checking.

Example 2

On four plays, a football team has a gain of 8 yards, a loss of 10 yards, a gain of 2 yards, and then a loss of 20 yards. If they began on the 50-yard line, what yard line were they on at the end of the four plays?

Read and understand the question. This question deals with the gain and loss of yards of a football team. Each gain is a positive number and should be added; each loss is a negative number and should be subtracted. The starting place of the team is given, and you are looking for the yard line at the end of the plays.

Make a plan. Begin with the number 50. This represents the 50-yard line, or halfway across the football field. Use the rules of adding and subtracting integers to find the yard line on which the team ends the plays.

Carry out the plan. Start with the number 50 to represent the 50-yard line and add a gain of 8 yards: 50 + 8 = 58. Then, subtract a loss of 10 yards: 58 – 10 = 48. This represents the 48-yard line of the original team. Now, add a gain of 2 yards: 48 + 2 = 50. Then, subtract a loss of 20 yards: 50 – 20 = 30. The team is on their own 30-yard line at the end of the four plays.

Check your answer. Check your answer by working backward and use inverse operations. Begin with the solution of the 30-yard line. Add 20 yards, subtract 2 yards, add 10 yards, and subtract 8 yards: 30 + 20 – 2 + 10 – 8 = 50. Since this is where the team started before the plays, this answer is checking.

Example 3

Gretchen is working on the problem –30 divided by –6 at her desk at school. What should she write for the correct answer?

Read and understand the question. This question is looking for the result after a division problem. The two numbers in the problem are both negative.

Make a plan. Use the rules for dividing integers to complete this question.

Carry out the plan. Divide –30 ÷ –6 = 5. There is an even number of negatives in the problem, so the answer is positive.

Check your answer. Check your answer by doing the inverse operations. Multiply 5 by –6 and the result is –30. This question is checking.

Find practice problems and solutions for these concepts at Basic Number and Integer Word Problems Practice Questions.