Solving Story Problems with Decimals

1. A plan for story problems

A story problem is solved in the head before it is solved on paper. Rushing to calculate with the first numbers you see is the biggest cause of wrong answers. Use this plan every time — it is the same plan examiners expect to see in BECE Paper 2 working.

1. 1Read the whole story twice. Underline the numbers and the question.
2. 2Picture it: draw a quick bar model or table if it helps.
3. 3Decide the operation(s) and the order of the steps.
4. 4Estimate the answer with rounded numbers.
5. 5Calculate carefully, keeping decimal points lined up or counted correctly.
6. 6Check against your estimate and answer in a sentence with units.

Here is the curriculum's first example. A group of two hundred and fifteen men and seven hundred and eighty-four women went to watch a musical concert. GH₵25 was collected at the gate from each person. How much was collected altogether? There are two steps. First find the number of people: 215 + 784 = 999. Then the money: 999 × 25. Use compensation: 1,000 × 25 − 1 × 25 = 25,000 − 25 = GH₵24,975.

2. More than, less than: adding and subtracting decimals

"Less than" and "more than" stories often need two steps, and a bar model shows them clearly. In the hook, Mrs Anderson's amount is 2.4 kg less than Mrs Adamu's, so her bar is shorter. The question asks for the amount altogether, so after finding her amount we must add both.

▶ The bar model shows two steps: first find Mrs Anderson's amount, then add both amounts.

So the two women bought 24.8 kg altogether. The learner in the hook only did step 1 and answered the wrong question. When you add or subtract decimals, remember to line up the decimal points and use placeholder zeros, exactly as you learned in the previous lessons.

3. Times as much, shared equally: multiplying and dividing decimals

Multiplying a decimal by a whole number. Ebo weighs 28.6 kg and his father weighs four times as much. Multiply as if there were no decimal point: 286 × 4 = 1,144. The original number had one decimal place, so the answer has one decimal place: 114.4 kg. Check by estimating: 30 × 4 = 120, so 114.4 is sensible. Their total weight is 28.6 + 114.4 = 143 kg.

Dividing a decimal by a whole number. Mrs Armah shares 45.75 m of linen equally among her five children. Divide as normal and keep the decimal point in the quotient exactly above the decimal point in the dividend: 45.75 ÷ 5 = 9.15. The long division below divides 4,575 by 5; since 45.75 has two decimal places, 915 becomes 9.15.

▶ 4,575 ÷ 5 = 915. Because 45.75 has 2 decimal places, put the point back: 45.75 ÷ 5 = 9.15 m each.

4. Problems from a table

Information is often given in a table. Read the row and column labels carefully and pick out only the numbers you need. A school's Management Committee approved this budget for its open day anniversary:

▶ The same budget as a bar chart: robes cost the most and library books the least.

• Painting and choir robes together: 4,580 + 5,340 = GH₵9,920.
• How much more for the pitch than the library: 3,050 − 2,690 = GH₵360.
• If twice the approved amount was spent on prizes: 2 × 4,270 = GH₵8,540.

Worked examples

Try each one yourself first, then open the solution and compare every step.