ABE Math Tutorials/Whole numbers/Word problems

Word problems

Introduction

So far, all of our math work has been just "arithmetic". But most of the GED test involves word problems. Many people say : "I just can't do word problems ." In fact, working with word problems requires only 2 main skills:

Types

• Reading ability: Word problems involve words. To know what to do in a word problem, you first have to be able to understand what the question is asking you. If you are already a good reader, you will have an advantage with word problems (and with all the GED tests, for that matter!) How can you become a good reader? Research has shown that the best way to improve your reading ability is with practice. Just read. Read for at least 15 minutes every day: read a newspaper, a magazine article, or a good story.

• Basic arithmetic skills: Once you understand what the question is asking you to do, you have to choose the right operation (add, subtract, multiply, or divide) and then do the arithmetic.

Let's start with an example:

Examples

• One weekend, Susan's family had a garage sale. They made $64 on Saturday, and $102 on Sunday. How much money did they make in all from the garage sale?

The first thing we have to do in this problem is to figure out which operation to use. The question itself gives a clue: it says "how much money ... in all". The "in all" suggests that we're going to have to add. And, in fact, all we have to do is to add the two numbers together :

64 + 102 = 166. They made $166 in all. Let's try another one:

• Mark bought 250 bricks to make a patio. However, the patio only required 208 bricks. How many bricks did Mark have left over?

First, let's figure out which operation to use. It helps if you can picture what is happening here: Mark buys 250 bricks, uses 208 of them, and you're asked to figure out how many are left. It's clear that we're going to have to subtract to get the answer:

250 - 208 = 42 He will have 42 bricks left over. Let's try another one:

Activity

Ken, Maria, Sara and Manuel got together to buy a lottery ticket. Their ticket was lucky, and they won $100,000. If the prize money was shared evenly, how much did each person get?Which operation will we use for this question? Once again, you have to imagine what is going on here. We have $100,000 in prize money, which has to be divided up so that each of the 4 people involved will get an equal share. It's clear that we'll have to use division:

100,000 ÷ 4 = 25,000 Each person will get $25,000 Ready for one more?

Self Assessment

To earn some extra money, Karen stuffs envelopes for a marketing company. Once she has each envelope stuffed, she puts it into a mailing box. She can fit 240 envelopes into each box. At the end of the day, she has filled 4 boxes with envelopes. How many envelopes has she stuffed?Once again, you have to picture what is going on in order to figure out what to do here. We are told that Karen has 4 boxes filled with envelopes at the end of the day. Each box holds 240 envelopes. Can you see that this is a multiplication problem?

4 x 240 = 960. She has stuffed 960 envelopes at the end of the day.

Ready to try a few on your own? (You may use your calculator if you wish. But if you need the arithmetic practice, please do the work "long hand".)

Assignment

1. Shannon pays $435 a month in rent for her apartment. How much rent will she pay in a year? 2. Eli made a downpayment of $3000 on a car. The total cost of the car is $11,500. How much does he have left to pay? 3. The Northern Upholstery Company upholstered 52 couches in January, 58 couches in February, and 103 couches in March. How many couches did they upholster in all during this three-month period? 4. Lorraine got a phone bill for $248. The phone company told her that she could pay it off in 4 monthly installments. How much will she have to pay on the bill each month?

To check your answers, click here.

The word problems that we have been working on so far are called "one step problems" -- they each require only one operation to find the answer. Other problems are more complicated. Let's look at a problem:

Discussion

One weekend, Susan's family had a garage sale with Marika's family. Together they made $64 on Saturday, and $102 on Sunday. They decided to share the money they earned equally. How much money did each family receive from the garage sale? Can you see that this problem starts out like the very first problem we tried? To do that problem, we added up the amounts that the yard sale earned each day to get the total for the weekend. But now we have to "split" that total between the two families -- we will have to divide after we add. This kind of problem is called a "two step problem".

So first we'll add: 

64 + 102 = $166 ....and now we'll divide:

166 ÷ 2 = $83 Each family will receive $83 from the yard sale. Ready for another? See if you can figure out which operations you need to use in this question:

Case Study

Mark had 30 bricks stored in his shed. He bought a box of 250 bricks to make a patio. However, the patio only required 208 bricks. How many bricks will Mark have left over when he is finished the patio?

Again, you may recognize that this problem starts out like one of the first ones we tried. Try to picture what is happening: Mark starts out with 30 bricks, buys 250 more, then uses 208. So first we can add:

30 + 250 = 280 bricks ... and then we'll subtract the number of bricks he used in the patio: 280 - 208 = 72 bricks left over.

If you're ready for the Word Problems homework, click here.