Multi-step arithmetic word problems drills

Solve multi-step real-world problems requiring several arithmetic operations.

Free, timed SHSAT practice sets on multi-step arithmetic word problems— every question includes a full worked explanation, and there's no account required.

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How to solve multi-step word problems

Break the story into small steps and do them in order. Write down the result of each step before you go to the next one.

  1. Do the multiplications first (3 items at 13.25 dollars each is \(3 \times 13.25 = 39.75\) dollars).
  2. Add up everything spent or used.
  3. Subtract that from the starting amount.
  4. Add anything that comes in later, such as a gift.

Example: Ana has 60 dollars, buys 2 books at 12.50 dollars each, then gets 15 dollars. Spent: \(2 \times 12.50 = 25\). Left: \(60 - 25 = 35\). Now: \(35 + 15 = 50\) dollars.

Traps:

Worked examples

Example 1.
Grace has \(\$90.25\). Grace buys 2 pairs of headphones at \(\$23.75\) each and 1 umbrella at \(\$13.75\) each, then receives \(\$28.00\) as a gift. How much money does Grace have now?
Show answer and explanation
Answer:
A

Spent \(= 2 \times \$23.75 + 1 \times \$13.75 = \$61.25\). Remaining \(= \$90.25 - \$61.25 = \$29.00\). Plus the gift: \(\$29.00 + \$28.00 = \$57.00\). (Forgetting to add the gift gives $29.00. Subtracting each price only once (not multiplying by the number bought) gives $80.75. Subtracting only the first purchase gives $70.75.)

Example 2.
A bakery bakes 11 batches of 24 cookies each. They sell 219 cookies and give away 5 cookies. How many cookies are left?
Show answer and explanation
Answer:
D

Total baked \(= 11 \times 24 = 264\) cookies. Remaining \(= 264 - 219 - 5 = 40\) cookies. (Subtracting only the sold cookies gives 45 cookies. Grouping the subtraction as \(264 - (219 - 5)\) gives 50 cookies. Reporting the cookies that are gone (\(219 + 5\)) gives 224 cookies.)