Word Problems with Decimals

Problem-Solving Strategy

The 4-Step Approach

Read carefully, identify the operation, set up the math, and check if your answer makes sense!

1 Read and Understand

Read the problem twice. Identify what you know and what you need to find. Circle or underline the numbers.

2 Choose the Operation

Look for keywords that tell you which operation to use. Are you combining, comparing, splitting, or grouping?

3 Set Up and Solve

Write out the math problem. Use the decimal rules you learned. Show your work!

4 Check Your Answer

Does the answer make sense? Is it reasonable? Did you include the right units (dollars, meters, etc.)?

Keywords to Look For

These words often tell you which operation to use:

Addition Keywords

total sum altogether combined in all plus more than

Subtraction Keywords

difference left over remaining change less than fewer how much more

Multiplication Keywords

times each per every product of total cost

Division Keywords

split shared equally per each quotient how many in each average

Careful! Some words like "per" and "each" can signal either multiplication or division depending on the context. Always think about what the problem is really asking!

Worked Example

Problem: Maria bought 3 notebooks at $2.75 each and a pen for $1.50. How much did she spend in total?

1

Understand: We need to find the total cost of 3 notebooks plus 1 pen.
Known: notebooks cost $2.75 each, pen costs $1.50

2

Operation: Multiplication (3 notebooks at $2.75 each) then Addition (add the pen)

3

Solve:
Cost of notebooks: 3 x $2.75 = $8.25
Total: $8.25 + $1.50 = $9.75

4

Check: $9.75 is reasonable for 3 notebooks and a pen. Estimate: 3 x $3 + $1.50 = $10.50 (close!)
Answer: Maria spent $9.75

Practice Problems

Money Problem 1

Jake has $20.00. He buys a sandwich for $6.75 and a drink for $2.50. How much money does he have left?

Shopping Problem 2

A store sells apples for $1.25 per pound. Emma buys 4.5 pounds of apples. How much does she pay?

Measurement Problem 3

A ribbon is 15.6 meters long. It needs to be cut into 6 equal pieces. How long is each piece?

Science Problem 4

In a science experiment, a plant grew 1.25 cm on Monday, 0.75 cm on Tuesday, and 1.50 cm on Wednesday. What was the total growth over the three days?

Money Problem 5

Gas costs $3.45 per gallon. Mr. Chen puts 12 gallons in his car. How much does he pay?

Measurement Problem 6

Sofia ran 2.75 km on Saturday and 3.25 km on Sunday. How much farther did she run on Sunday than Saturday?

Shopping Problem 7

A package of cookies costs $3.60. If the package contains 12 cookies, what is the cost per cookie?

Science Problem 8

A container holds 2.5 liters of water. If you pour in another 0.75 liters, then remove 1.25 liters, how much water is in the container?

Money Problem 9

A movie ticket costs $8.50 for adults and $5.25 for children. A family of 2 adults and 3 children goes to the movies. What is the total cost?

Measurement Problem 10

A carpenter has a board that is 8.4 meters long. She cuts off 2.75 meters for one project. How much of the board is left?

Check Your Understanding

Understanding Check 1

Which operation would you use to solve this problem?

"A recipe calls for 2.5 cups of flour. If you want to make 3 batches, how much flour do you need?"

Understanding Check 2

Which operation would you use to solve this problem?

"You have $15.75 and want to split it equally among 3 friends. How much does each friend get?"

What We Learned

1

Read Carefully

Understand what the problem is asking before you start calculating

2

Find Keywords

Look for words that signal which operation to use

3

Show Your Work

Write out the steps - it helps catch mistakes

4

Check Reasonableness

Ask: Does my answer make sense in the real world?

SAT/ACT Connection: Word problems are a major part of standardized tests. The strategies you learn here - reading carefully, identifying operations, and checking your work - will help you succeed on these tests!

Next Steps

Practice creating your own word problems using decimals
Look for decimal situations in your daily life (shopping, cooking, sports)
Try multi-step problems that use more than one operation
Move on to learn about Common Mistakes to avoid!