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Step 5 · Multiplication and first fractions topics

Solve word problems that need two steps, write them as one equation with a letter for the unknown, and check the answer with an estimate.

Two steps, one at a time

Some problems need two calculations. Find the first answer, then use it in the second. Ask yourself: what do I need to know first?

Example: Two steps

Sam buys 3 packs of 6 pencils and gives away 5 pencils. How many pencils does Sam have left?

  1. Step 1: how many pencils were bought? 3 × 6 = 18.
  2. Step 2: take away the ones given away. 18 − 5 = 13.

Answer13 pencils

A bar model helps you see the steps. Draw the parts you know and mark the part you are looking for.

3 packs of 6 make 18. 5 are given away and 13 are left.

Writing it as one equation

You can write both steps as one equation, with a letter for the number you do not know. For Sam's pencils: 3 × 6 − 5 = p. Multiply first, then subtract: p = 13.

Example: Using a letter

24 children split into 4 equal teams. Then 2 more children join each team. How many children are in each team now? Write an equation with t for the answer.

  1. 24 ÷ 4 + 2 = t.
  2. 24 ÷ 4 = 6.
  3. 6 + 2 = 8.

Answert = 8 children

Is the answer sensible?

After solving, check that the answer makes sense. Round the numbers and work it out roughly in your head.

Example: Checking by rounding

A shop had 312 apples, sold 189, then got 205 more. Rafa says there are now 328. Is that sensible?

  1. Round to hundreds: 300 − 200 + 200 = 300.
  2. 328 is close to 300, so it is sensible.
  3. Exactly: 312 − 189 = 123, and 123 + 205 = 328.

AnswerYes, 328 is right.

If the estimate and the answer are far apart, look for the mistake: a missed step, or adding where you should subtract.

Try it yourself

Work each one on paper first, then open the answer to check.

  1. There are 4 boxes of 8 crayons, and 7 crayons are broken. How many crayons are not broken?

    Show answer

    25. 4 × 8 = 32, and 32 − 7 = 25.

  2. Mia has 30 cents. She buys 2 stickers at 9 cents each. How much money is left?

    Show answer

    12 cents. 2 × 9 = 18, and 30 − 18 = 12.

  3. Write an equation with n for: 5 bags of 6 marbles, and 4 more marbles.

    Show answer

    5 × 6 + 4 = n, so n = 34.

  4. A farmer puts 45 eggs in boxes of 5, then sells 3 boxes. How many boxes are left?

    Show answer

    6 boxes. 45 ÷ 5 = 9, and 9 − 3 = 6.

  5. Leo says 198 + 403 is about 900. Is that sensible?

    Show answer

    No. 200 + 400 = 600, so the answer should be about 600. It is 601.

What next?