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Multi-Step
Word Problems

Break big questions into small steps using the four operations: add, subtract, multiply, and divide.

ISEE Lower Level Quantitative Reasoning

What Is a Multi-Step Problem?

A multi-step word problem asks more than one question to get the final answer. You cannot solve it with just one calculation. Instead, you do several smaller steps in the right order.

The Four Operations

Every multi-step problem is built from these four basic operations. Knowing which one to use is the key skill.

Add \( + \)
Combine groups or find a total.
Subtract \( - \)
Take away or find the difference.
Multiply \( \times \)
Equal groups added many times.
Divide \( \div \)
Share equally or make equal groups.

One Problem, Many Steps

Full Problem "How many pencils are left?" Step 1: Multiply
\( 3 \times 6 = 18 \)
Step 2: Subtract
\( 18 - 5 = 13 \)
Final Answer 13 pencils

The Golden Rule of Order

If a question asks "how many are left," you must first know how many you started with. So you compute the total before you take any away.

Multiply & Divide Before Add & Subtract

When you write the steps as one number sentence, do the multiplying and dividing first, then add or subtract.

A quick memory trick: "My Dear Aunt Sally" reminds you to Multiply, Divide, Add, then Subtract.

One-Step vs. Multi-Step

One-Step
"Ana has 12 stickers and gets 8 more. How many now?" Just \( 12 + 8 = 20 \). One calculation finishes it.
Multi-Step
"Ana has 12 stickers, gets 8 more, then shares them with 4 friends equally." Add, then divide: \( 20 \div 4 = 5 \).

A 4-Step Game Plan

1
Read carefully. Find what the question is really asking for.
2
List the numbers and circle the action words (each, total, left, share).
3
Plan the steps in order and pick the operation for each one.
4
Solve and check. Does the answer make sense for the question?

Reading the Clue Words

Operation Clue Words
Addtotal, in all, sum, altogether, more
Subtractleft, fewer, difference, how many more
Multiplyeach, per, groups of, times, double
Divideshare equally, split, each gets, per group

Worked Example 1

Problem: A bakery makes 4 trays of muffins. Each tray holds 8 muffins. They sell 19 muffins. How many muffins are left?

Step 1: Total made
\( 4 \times 8 = 32 \)
→ Step 2: Take away sold
\( 32 - 19 = 13 \)

Worked Example 2

Problem: Liam saves $6 each week for 5 weeks. He spends $14 on a book, then shares the rest equally between 2 friends. How much does each friend get?

1
Multiply: \( 6 \times 5 = 30 \) dollars saved.
2
Subtract: \( 30 - 14 = 16 \) dollars left.
3
Divide: \( 16 \div 2 = 8 \) dollars each.

Worked Example 3

Problem: A class has 28 students. They split into 4 equal teams. Each team needs 3 markers. How many markers are needed in all?

Step 1: Team size
\( 28 \div 4 = 7 \)
→ Step 2: Markers total
\( 4 \times 3 = 12 \)

Common Mistakes

✕ Stopping Early
Answering after one step when the question needs two or three.
✕ Wrong Order
Subtracting before finding the total, so the numbers don't match.
✕ Using Extra Numbers
Using a number that isn't needed for the question being asked.

Quick Summary

Step What To Do
ReadFind what the question asks for
PlanList numbers, pick operations in order
SolveMultiply/divide first, then add/subtract
CheckMake sure the answer makes sense

Question 1 of 5

A store has 5 boxes with 9 apples each. They sell 22 apples. How many apples are left?

Question 2 of 5

Sam has $20. He buys 3 toys that cost $4 each. How much money does he have left?

Question 3 of 5

There are 24 cookies shared equally among 6 plates. Then 2 more cookies are added to each plate. How many cookies are on each plate?

Question 4 of 5

Mia reads 8 pages a day for 5 days, then 12 pages a day for 3 days. How many pages in all?

Question 5 of 5

A teacher has 30 pencils. She gives 6 to each of 4 students. How many pencils does she have left?

You've Got the Steps!

One small step at a time turns any big problem into an easy one. Keep practicing!