Lesson 5: Solve Multi-Step Problems

Property

To find a total ($T$) in a multi-step problem, you may first need to find an unknown part ($Q_{\text{unknown}}$) by relating it to a known part ($Q_{\text{known}}$).
Step 1: Find the unknown part: $Q_{\text{unknown}} = Q_{\text{known}} + \text{difference}$
Step 2: Find the total: $T = Q_{\text{known}} + Q_{\text{unknown}}$

Examples

Property

To solve a two-step problem, first answer the hidden question to find an intermediate value. Then, use that value to perform the second step and solve the main problem.

Examples

Property

To solve complex problems, break them down into a series of smaller calculations. Often, you will need to perform multiplication or division first to find a subtotal, followed by addition or subtraction to find the final answer.

Examples

• Three friends buy 4 movie tickets for 15 dollars each and a large popcorn for 9 dollars. They use a 6 dollar coupon and split the final cost evenly. How much does each friend pay?

Step 1 (Multiply): $4 \times 15 = 60$ dollars for tickets.
Step 2 (Add): $60 + 9 = 69$ dollars for tickets and popcorn.
Step 3 (Subtract): $69 - 6 = 63$ dollars after the coupon.
Step 4 (Divide): $63 \div 3 = 21$ dollars per friend.

• A school buys 8 boxes of pencils, with 12 pencils in each box. The school already had 24 pencils. If the pencils are distributed equally among 10 classrooms, how many pencils does each classroom get?

Step 1 (Multiply): $8 \times 12 = 96$ new pencils.
Step 2 (Add): $96 + 24 = 120$ total pencils.
Step 3 (Divide): $120 \div 10 = 12$ pencils per classroom.

Explanation

Some problems require you to use all four basic operations: addition, subtraction, multiplication, and division. To solve these, you must identify the hidden questions and determine the correct order of operations. First, perform any necessary multiplication or division to find intermediate amounts, such as a total cost or quantity. Then, use addition or subtraction to combine or adjust those amounts before performing a final division or other calculation to arrive at the answer.