Multi-step problems and checking estimates | Year 7

01 / LEARN

Understand the idea.

Translate the situation before calculating

Before calculating, identify the quantities and decide what each operation represents: joining, removing, scaling or counting groups. Write a calculation in the story's order, using brackets when a combined amount must be found before another operation.

Keep units compatible. A total in metres must be compared with a piece length in metres, not an unconverted number of centimetres. Label intermediate amounts so that a mass, a price and a count cannot be confused.

Interpret the result

Use a separate estimate to predict the answer's size, then keep exact fractions and the supplied decimals in the actual calculation. Early rounding may change a final purchasing decision or lose money in a budget.

Interpret the result in context. A fractional number of required bags usually means buying the next whole bag; a fractional number of possible full pieces means counting only the completed pieces. Check whether the question asks for capacity or demand.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

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?

Worked solution

1
Convert the batch count to an improper fraction.
$2 \frac{1}{2} = \frac{5}{2}$
Improper fractions allow the batch count to multiply the flour needed per batch.
2
Calculate the required mass.
$\begin{aligned} \frac{3}{4} \times \frac{5}{2} & = \frac{15}{8} \\ = 1 \frac{7}{8} kg \end{aligned}$
Scaling the mass per batch by the number of batches gives the total flour needed.
3
Compare with whole-bag capacities.
$1 < \frac{15}{8} < 2$
One 1 kg bag is insufficient, while two supply at least the required mass.
4
State and check the purchase.
$2 - \frac{15}{8} = \frac{1}{8} kg$
Buying two bags leaves one eighth of a kilogram after the recipe, confirming there is enough.

Answer

2 bags

EXAMPLE 02

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?

Worked solution

1
Find the total ticket cost.
$3 \times 6.50 = 19.50 dollars$
There are three equal ticket prices to combine.
2
Include the shared snack cost once.
$19.50 + 4.80 = 24.30 dollars$
The snack amount is already the group’s total, so it is not multiplied by three.
3
Subtract the spending from the budget.
$30.00 - 24.30 = 5.70 dollars$
The money remaining is the initial budget minus all spending.
4
Check the size with an estimate.
$30 - (3 \times 7 + 5) = 4$
Both costs were rounded upward, so the estimated remainder of 4 dollars is lower than the exact remainder of 5.70 dollars.

Answer

5.70 dollars

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

6 cups

Divide the total volume by one cup's volume: $\frac{3}{2} \div \frac{1}{4} = \frac{3}{2} \times 4 = 6$ . Six quarter-litre cups use exactly the jug's one and a half litres.

Keep practising

6 worksheet questions · 16 marks

Open worksheet 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.

Checking saved progress…

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 ↗

In this lesson

Understand the idea.

Translate the situation before calculating

Interpret the result

See the method in action.

Buy enough flour

Convert the batch count to an improper fraction.

Calculate the required mass.

Compare with whole-bag capacities.

State and check the purchase.

Keep within a budget

Find the total ticket cost.

Include the shared snack cost once.

Subtract the spending from the budget.

Check the size with an estimate.

Try it yourself.

Check your understanding

Keep practising