Multi-step problems and checking estimates | Year 7

01 / LEARN

The idea, step by step

Translate the situation before calculating

Decide which amounts are being joined, removed, scaled or shared. Write a short calculation and use brackets if a total must be found before multiplication or division. Draw a simple bar or list the amounts when the story is difficult to follow.

Use compatible units before combining quantities. Dividing a length in metres by a length in centimetres without conversion gives the wrong count, even if the division itself is accurate.

Interpret the result

Estimate with nearby friendly values to check the size, but keep exact fractions or supplied decimals in the main calculation. Early rounding can build up error. Inverse operations can check the arithmetic.

Think about what a remainder means. A ribbon question may ask for complete pieces, so a fractional piece is not counted. A shopping question asking how many bags are needed may require the count to be rounded up.

A common trap

Round each intermediate result to make the answer more accurate.

Instead: Estimate separately. Keep exact fractions and the supplied decimal values during the actual calculation, then round only when the question or context requires it.

02 / WORKED EXAMPLES

See the thinking

Example 1

Buy enough flour

A recipe uses $\frac{3}{4}$ kg for one batch. You make $2 \frac{1}{2}$ batches. Flour is sold in 1 kg bags. How many bags are needed?

$\frac{3}{4} \times \frac{5}{2} = \frac{15}{8} = 1 \frac{7}{8}$ kg.
This is just below 2 kg, matching an estimate.
One bag is not enough. Two bags provide enough flour.

2 bags

Example 2

Keep within a budget

A group has 30 dollars. Three tickets cost 6.50 dollars each, and snacks cost 4.80 dollars altogether. How much remains?

Tickets cost 3 times 6.50 = 19.50 dollars.
Total spent = 19.50 + 4.80 = 24.30 dollars.
Remaining amount = 30.00 - 24.30 = 5.70 dollars.
An estimate of about 5 dollars supports the size of the answer.

5.70 dollars

Check your understanding

A $1 \frac{1}{2}$ L jug fills cups of $\frac{1}{4}$ L. How many cups are filled?

Show answer

6 cups

$\frac{3}{2} \div \frac{1}{4} = 6$ .

03 / WORKSHEET

Your turn

6 questions · 16 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Join a $\frac{2}{3}$ m strip to a $\frac{5}{6}$ m strip, without overlap. Find the total length.
2 marks
Four pens cost 1.65 dollars each. A notebook costs 3.40 dollars. Find the total cost.
2 marks
Each rice portion uses $\frac{3}{8}$ kg. How many portions can be made from $2 \frac{1}{4}$ kg?
2 marks
A walk is $3 \frac{1}{2}$ km long. You have walked $1 \frac{3}{4}$ km. What fraction of the whole walk remains?
3 marks
A 12.5 m roll is cut into four 2.4 m lengths. Estimate and calculate the length left.
3 marks
A $\frac{4}{5}$ kg bag is shared equally among six people. How much does each receive? Could each receive $\frac{1}{5}$ kg? Explain.
4 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Join a $\frac{2}{3}$ m strip to a $\frac{5}{6}$ m strip, without overlap. Find the total length.
2 marks
$\frac{4}{6} + \frac{5}{6} = \frac{9}{6} = \frac{3}{2}$ .
$1 \frac{1}{2}$ m
Four pens cost 1.65 dollars each. A notebook costs 3.40 dollars. Find the total cost.
2 marks
4 times 1.65 = 6.60; 6.60 + 3.40 = 10.00.
10.00 dollars
Each rice portion uses $\frac{3}{8}$ kg. How many portions can be made from $2 \frac{1}{4}$ kg?
2 marks
$\frac{9}{4} \div \frac{3}{8} = \frac{9}{4} \times \frac{8}{3} = 6$ .
6 portions
A walk is $3 \frac{1}{2}$ km long. You have walked $1 \frac{3}{4}$ km. What fraction of the whole walk remains?
3 marks
Remaining distance is $\frac{7}{2} - \frac{7}{4} = \frac{7}{4}$ km.
$\frac{7}{4} \div \frac{7}{2} = \frac{1}{2}$ .
$\frac{1}{2}$
A 12.5 m roll is cut into four 2.4 m lengths. Estimate and calculate the length left.
3 marks
Four lengths use 9.6 m.
12.5 - 9.6 = 2.9 m.
An estimate near 3 m; exactly 2.9 m.
A $\frac{4}{5}$ kg bag is shared equally among six people. How much does each receive? Could each receive $\frac{1}{5}$ kg? Explain.
4 marks
$\frac{4}{5} \div 6 = \frac{2}{15}$ .
Six shares of $\frac{1}{5}$ kg would need $\frac{6}{5}$ kg, more than the bag contains.
$\frac{2}{15}$ kg each; no.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Equivalent fractions and mixed numbers; ordering rational numbers on number lines; adding/subtracting fractions; multiplying/dividing fractions; four operations with decimals; converting between fractions and decimals; multi-step problems and checking estimates.

Official curriculum source ↗

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