How to Solve Multi-Step Arithmetic Word Problems

In the real world, math problems usually take more than one step to figure out. Multi-step arithmetic word problems are word problems that require you to use two or more operations (addition, subtraction, multiplication, or division) to find the final answer.

The main challenge is deciding which operations to use and in what order to use them.

4 Steps to Solve Multi-Step Problems

Whenever you face a word problem with a lot of information, use these four steps to break it down:

1. Understand the problem: Read carefully. What do you know? What are you trying to find out?
2. Make a plan: Decide which steps you need to take and what math operations ($+$, $-$, $\times$, $\div$) to use.
3. Solve step-by-step: Do the math one piece at a time. Write down what your answer means after each step.
4. Check your work: Does your final answer make sense?

Let's look at a few common examples.

Example 1: Finding the Total

Problem: A store sold $24$ boxes of $12$ pencils and $15$ boxes of $8$ pens. How many items were sold in total?

• Step 1: Find the total number of pencils. Since there are $24$ boxes and each has $12$ pencils, we multiply: $24 \times 12 = 288$ The store sold $288$ pencils.
• Step 2: Find the total number of pens. Since there are $15$ boxes and each has $8$ pens, we multiply: $15 \times 8 = 120$ The store sold $120$ pens.
• Step 3: Find the total items. Add the pencils and pens together: $288 + 120 = 408$ Answer: $408$ items were sold in total.

Example 2: Calculating Change

Problem: Maria has \50$. She buys$3$books at$$8$ each. How much change does she get?

• Step 1: Find the total cost of the books. She buys $3$ books that cost \8each. We multiply: $$3 \times 8 = 24$$ The books cost$24$ in total.
• Step 2: Find the change. Subtract the total cost from the money she started with: $50 - 24 = 26$ Answer: Maria gets \26$ in change.

Example 3: Multiple Operations

Problem: A school orders $24$ boxes of pencils with $12$ in each box. They give $5$ pencils to each of their $48$ students. How many pencils are left over?

• Step 1: Find the total pencils ordered. $24 \times 12 = 288 \text{ pencils ordered}$
• Step 2: Find the total pencils given away. They give $5$ pencils to $48$ students. We multiply: $48 \times 5 = 240 \text{ pencils given away}$
• Step 3: Find how many are left. Subtract the pencils given away from the pencils ordered: $288 - 240 = 48$ Answer: There are $48$ pencils left.

Tips for Success

• Look for clue words: Words like "total" usually mean addition or multiplication. Words like "left" or "change" usually mean subtraction. "Each" often hints at multiplication or division.
• Label your numbers: As you do each step, write down a quick label (like "$240$ pencils given away"). This stops you from getting confused about what your numbers mean in the middle of a problem!