In our everyday lives, we often face problems that cannot be solved with just one step. When you plan a birthday party, buy supplies for a school project, or figure out how much time you need to finish your homework, you usually need to think through several steps. In math, we call these multi-step word problems. These problems ask you to use more than one operation-like addition, subtraction, multiplication, or division-to find the answer. Learning to solve multi-step problems helps you break big challenges into smaller, easier pieces.
A multi-step word problem is a problem that requires you to do two or more calculations to find the final answer. Unlike simple one-step problems where you just add or multiply once, multi-step problems ask you to combine different operations in the right order.
Think of it like following a recipe. You can't just mix all the ingredients at once. First, you measure the flour, then you add the eggs, then you mix them together. Each step depends on the one before it.
Here are the key features of multi-step word problems:
When you face a multi-step problem, it helps to follow a clear plan. Here is a four-step plan that works for most problems:
Read the problem at least twice. The first time, read it to understand what is happening. The second time, look for specific information:
Decide which operations you need to use and in what order. Ask yourself:
It can help to write down each step you plan to take in words before you start calculating.
Work through your plan one step at a time. Write down the answer to each step clearly. Use that answer in the next step. Show all your work so you can check it later.
After you finish, ask yourself: Does my answer make sense? Is it reasonable? You can check by estimating or by working backward from your answer.
Many multi-step problems combine addition and subtraction. You might need to add two amounts together first, then subtract another amount. Or you might subtract first and then add.
Example: Maria had 45 stickers in her collection.
Her friend gave her 23 more stickers on Monday.
On Tuesday, Maria gave 18 stickers to her brother.How many stickers does Maria have now?
Solution:
First, I need to find how many stickers Maria had after her friend gave her more stickers.
Stickers after Monday = 45 + 23 = 68 stickers
Next, I subtract the stickers she gave to her brother.
Stickers now = 68 - 18 = 50 stickers
Maria has 50 stickers now.
Example: A library had 312 books on the shelves.
On Monday, 87 books were checked out.
On Tuesday, 45 books were returned.How many books are on the shelves now?
Solution:
First, I find how many books remained after Monday.
Books after Monday = 312 - 87 = 225 books
Next, I add the books that were returned on Tuesday.
Books now = 225 + 45 = 270 books
The library has 270 books on the shelves now.
Sometimes you need to multiply first to find a total amount, and then add or subtract. These problems often involve groups of items or repeated amounts.
Example: A baker made 8 trays of cookies.
Each tray has 12 cookies.
The baker sold 35 cookies in the morning.How many cookies does the baker have left?
Solution:
First, I need to find the total number of cookies the baker made.
Total cookies = 8 × 12 = 96 cookies
Next, I subtract the cookies that were sold.
Cookies left = 96 - 35 = 61 cookies
The baker has 61 cookies left.
Example: Jake bought 4 packs of trading cards.
Each pack contains 15 cards.
He already had 28 cards at home.How many trading cards does Jake have altogether?
Solution:
First, I find how many cards Jake bought.
Cards bought = 4 × 15 = 60 cards
Next, I add the cards he already had.
Total cards = 60 + 28 = 88 cards
Jake has 88 trading cards altogether.
Division problems often involve splitting a total into equal groups or finding how many groups you can make. In multi-step problems, you might divide first and then use that answer in another operation.
Example: A school has 96 students going on a field trip.
The students will ride in vans.
Each van holds 8 students.
Each van costs 45 dollars to rent.How much will it cost to rent all the vans needed?
Solution:
First, I need to find how many vans are needed.
Number of vans = 96 ÷ 8 = 12 vans
Next, I multiply the number of vans by the cost of each van.
Total cost = 12 × 45 = 540 dollars
It will cost 540 dollars to rent all the vans.
Money problems are very common in multi-step word problems. These problems might involve buying multiple items, receiving change, or comparing costs. Remember to keep track of dollars and cents carefully.
Example: Emma went to the store with 50 dollars.
She bought 3 books for 7 dollars each.
She also bought a pen for 2 dollars.How much money does Emma have left?
Solution:
First, I find how much Emma spent on books.
Cost of books = 3 × 7 = 21 dollars
Next, I find the total amount Emma spent.
Total spent = 21 + 2 = 23 dollars
Now I subtract the total spent from the money she started with.
Money left = 50 - 23 = 27 dollars
Emma has 27 dollars left.
Example: A toy store is having a sale.
Robot toys cost 12 dollars each.
Car toys cost 8 dollars each.
Marcus bought 2 robots and 3 cars.How much did Marcus spend in total?
Solution:
First, I find how much Marcus spent on robots.
Cost of robots = 2 × 12 = 24 dollars
Next, I find how much Marcus spent on cars.
Cost of cars = 3 × 8 = 24 dollars
Now I add both amounts to find the total.
Total spent = 24 + 24 = 48 dollars
Marcus spent 48 dollars in total.
Some multi-step problems ask you to compare two amounts. You might need to find each amount separately and then compare them by finding the difference or deciding which is greater.
Example: Sarah collected 8 bags of apples.
Each bag has 15 apples.
Tom collected 95 apples.Who collected more apples and by how many?
Solution:
First, I find how many apples Sarah collected.
Sarah's apples = 8 × 15 = 120 apples
Tom collected 95 apples, which is given in the problem.
Now I compare by finding the difference.
Difference = 120 - 95 = 25 apples
Sarah collected more apples. She collected 25 more apples than Tom.
Multi-step problems can also involve time, such as figuring out schedules or durations. You might need to add or subtract time amounts.
Example: A movie starts at 2:15 PM.
The movie is 105 minutes long.
After the movie, the family spends 30 minutes having a snack.What time will they finish the snack?
Solution:
First, I find the total time spent on the movie and snack.
Total time = 105 + 30 = 135 minutes
Next, I convert 135 minutes to hours and minutes.
135 minutes = 2 hours and 15 minutes
Now I add this time to the starting time of 2:15 PM.
2:15 PM + 2 hours = 4:15 PM
4:15 PM + 15 minutes = 4:30 PM
They will finish the snack at 4:30 PM.
Many multi-step problems have what we call hidden questions. A hidden question is a question that is not directly asked but must be answered before you can solve the main problem.
Think of hidden questions like stepping stones across a stream. You can't jump directly to the other side. You need to step on the stones in between to get there safely.
To find hidden questions, ask yourself: "What do I need to know first before I can answer the main question?"
Let's look at an example and identify the hidden question:
Example: A farmer has 6 fields.
Each field has 24 rows of corn.
Each row has 18 corn plants.How many corn plants does the farmer have in total?
Solution:
The hidden question is: How many corn plants are in one field?
First, I find how many plants are in one field.
Plants per field = 24 × 18 = 432 plants
Next, I multiply by the number of fields.
Total plants = 6 × 432 = 2,592 plants
The farmer has 2,592 corn plants in total.
There are several strategies that can help you solve multi-step word problems more easily:
Drawing helps you see what is happening in the problem. You can draw simple shapes, boxes, or lines to represent the numbers and operations.
When a problem has several pieces of information, organize them in a list or table. This helps you keep track of what you know and what you need to find.
A number sentence is an equation that shows the mathematical operation. Writing number sentences for each step helps you organize your thinking.
For example, if a problem says "There were 56 birds, then 23 more came, then 15 flew away," you can write:
Before solving, make a rough estimate of what the answer should be. Round the numbers to make them easier to work with. After you solve, check if your exact answer is close to your estimate.
Example: A school cafeteria serves lunch to 4 grades.
Each grade has 78 students.
Today, 19 students brought lunch from home.How many students need to buy lunch in the cafeteria?
Solution:
First, I estimate: 4 × 78 is about 4 × 80 = 320. Then 320 - 19 is about 320 - 20 = 300. My answer should be close to 300.
Now I solve exactly. First, I find the total number of students.
Total students = 4 × 78 = 312 students
Next, I subtract the students who brought lunch from home.
Students buying lunch = 312 - 19 = 293 students
My answer of 293 is close to my estimate of 300, so it makes sense.
293 students need to buy lunch in the cafeteria.
When solving multi-step word problems, watch out for these common mistakes:
Certain words in problems give you clues about which operation to use. However, be careful-keywords are helpful hints, but you still need to think about what the problem is asking.
| Operation | Common Keywords |
|---|---|
| Addition | total, altogether, sum, combined, in all, plus, more than (when adding) |
| Subtraction | difference, left, remaining, fewer, less than, minus, how many more |
| Multiplication | times, product, each, every, per, groups of, twice |
| Division | share, split, quotient, each (when dividing), per (when finding unit rate), average |
Remember that in multi-step problems, you will use more than one operation, so look for multiple keywords.
Multi-step word problems may seem challenging at first, but they become easier with practice. The most important skills are:
Every time you solve a multi-step problem, you are building your problem-solving skills. These skills will help you not just in math class, but whenever you face a challenge that needs careful thinking and planning.
Example: A pet store has 7 fish tanks.
Each tank has 16 goldfish and 9 guppies.
The store sold 28 fish today.How many fish does the pet store have now?
Solution:
First, I find how many fish are in each tank.
Fish per tank = 16 + 9 = 25 fish
Next, I find the total number of fish in all tanks.
Total fish at start = 7 × 25 = 175 fish
Now I subtract the fish that were sold.
Fish now = 175 - 28 = 147 fish
The pet store has 147 fish now.
With patience and practice, you will become confident at solving even the most complex multi-step word problems. Remember to work carefully, show all your steps, and always check your answer!