Solving Multi-Step Word Problems

In the real world, math problems rarely take just one step to solve. Often, you need to use a combination of addition, subtraction, multiplication, and division to find the final answer. These are called multi-step word problems.

The 4-Step Problem-Solving Method

To tackle these problems without getting confused, follow these four simple steps:

1. Understand: Read the problem carefully. What information is given? What are you trying to find?
2. Plan: Decide which operations ($+$, $-$, $\times$, $\div$) you need to use and in what order.
3. Solve: Do the math step-by-step.
4. Check: Look back at your answer. Does it make sense in the context of the story?

Let's look at some examples!

Example 1: Calculating Total Pay

Problem: Jake earns \8$per hour for$6$hours on weekdays and$$12$per hour for$4$ hours on weekends. What is his total weekly pay?

Step 1: Understand We need to find Jake's total pay for the whole week. We know his weekday rate and hours, and his weekend rate and hours.

Step 2: Plan First, multiply to find the weekday pay. Next, multiply to find the weekend pay. Finally, add the two amounts together to find the total.

Step 3: Solve

• Weekday pay: $8 \times 6 = 48$
• Weekend pay: $12 \times 4 = 48$
• Total pay: $48 + 48 = 96$

Step 4: Check Jake earns \48$during the week and$$48$on the weekend.$$48 + $48 = $96$. The math is correct! Jake's total weekly pay is **$$96$**.

Example 2: Dealing with Remainders

Problem: A school orders $235$ pencils. The pencils come in boxes of $12$. How many boxes are needed so that the school gets at least $235$ pencils?

Step 1: Understand We need $235$ pencils. They only come in groups (boxes) of $12$. We need to find the total number of boxes to buy.

Step 2: Plan First, divide the total number of pencils by the number of pencils per box. Then, look at the remainder to see if we need to add an extra box to get enough pencils.

Step 3: Solve Divide $235$ by $12$: $235 \div 12 = 19 \text{ R } 7$

This means $19$ boxes will give us $19 \times 12 = 228$ pencils. We still need $7$ more pencils to reach our goal of $235$. Therefore, we must order one more box. $19 + 1 = 20$

Step 4: Check If we order $20$ boxes, we get $20 \times 12 = 240$ pencils. This is enough to cover the $235$ pencils needed. The school needs $20$ boxes.

Tips for Success

• Look for keywords: Words like total, altogether, difference, each, and per can give you clues about which operations to use.
• Write down your steps: Don't try to keep all the numbers in your head. Write down the answer to each step so you can easily use it in the next one.