Mathematics • Year 8 • Unit 1 • Lesson 17
Dividing a Quantity in a Given Ratio
Use the unitary method — sum of parts, value of one part, then multiply for each share — to split money, mass and time. One worked example, one guided example with blanks, then eight independent problems including reverse problems.
1. I do — fully worked example
Watch the unitary method in action. Sum the parts, find the value of ONE part, then multiply.
Problem. Three friends share $480 in the ratio 1 : 2 : 3. How much does each receive?
Step 1 — Add the ratio parts (total parts).
1 + 2 + 3 = 6 parts
Reason: this tells us the $480 is being split into 6 equal "parts" (even though the shares are unequal).
Step 2 — Find the value of 1 part.
$480 ÷ 6 = $80 per part
Reason: total ÷ number of parts.
Step 3 — Multiply each ratio number by the 1-part value.
Friend A: 1 × $80 = $80
Friend B: 2 × $80 = $160
Friend C: 3 × $80 = $240
Reason: each share is (ratio number) × (value of 1 part).
Step 4 — Sum check.
$80 + $160 + $240 = $480 ✓
Reason: the shares MUST add back to the original total — if they don't, you have an arithmetic mistake.
Answer: $80, $160, $240.
2. We do — fill in the missing steps
Same shape as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. Split $600 in the ratio 2 : 3. Find each share.
Step 1 — Total parts: 2 + 3 = ______
Step 2 — Value of 1 part:
$600 ÷ ______ = $______
Step 3 — Each share:
First share: 2 × $______ = $______
Second share: 3 × $______ = $______
Step 4 — Sum check:
$______ + $______ = $______ (should be $600) ✓
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation (two-part splits). The middle two are standard (three-part splits). The last two are extension (reverse problems — given one share, find the total).
Foundation — two-part splits
3.1 Split $60 in the ratio 1 : 2. 1 mark
3.2 Split $140 in the ratio 3 : 4. 1 mark
3.3 Split 24 m in the ratio 3 : 5. 1 mark
3.4 Split $300 in the ratio 2 : 3. 1 mark
Standard — three-part splits
3.5 Split $210 in the ratio 2 : 3 : 2. Show your sum check at the end. 2 marks
3.6 A 36 kg bag of dry concrete mix is in the ratio 2 : 3 : 4 (cement : sand : gravel). How much of each? 2 marks
Extension — reverse problems
3.7 Two people share a sum of money in the ratio 4 : 5. The smaller share is $160. (a) Find the value of 1 part. (b) Find the total amount shared. 2 marks
3.8 Two friends split a pizza in the ratio 3 : 2. The smaller share is 4 slices. How many slices in total? 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (faded $600 in 2 : 3)
Step 1: 2 + 3 = 5 parts.
Step 2: $600 ÷ 5 = $120 per part.
Step 3: First = 2 × $120 = $240; Second = 3 × $120 = $360.
Step 4: $240 + $360 = $600 ✓.
3.1 — $60 in 1 : 2
Parts = 3; 1 part = $60 ÷ 3 = $20. Shares: $20 and $40. Check: $20 + $40 = $60 ✓.
3.2 — $140 in 3 : 4
Parts = 7; 1 part = $140 ÷ 7 = $20. Shares: $60 and $80. Check: $60 + $80 = $140 ✓.
3.3 — 24 m in 3 : 5
Parts = 8; 1 part = 24 ÷ 8 = 3 m. Shares: 9 m and 15 m. Check: 9 + 15 = 24 ✓.
3.4 — $300 in 2 : 3
Parts = 5; 1 part = $300 ÷ 5 = $60. Shares: $120 and $180. Check: $120 + $180 = $300 ✓.
3.5 — $210 in 2 : 3 : 2
Parts = 7; 1 part = $210 ÷ 7 = $30. Shares: $60, $90, $60. Check: $60 + $90 + $60 = $210 ✓.
3.6 — 36 kg in 2 : 3 : 4
Parts = 9; 1 part = 36 ÷ 9 = 4 kg. Cement: 8 kg; sand: 12 kg; gravel: 16 kg. Check: 8 + 12 + 16 = 36 ✓.
3.7 — Reverse: 4 : 5, smaller share $160
(a) Smaller share is 4 parts, so 1 part = $160 ÷ 4 = $40.
(b) Total parts = 4 + 5 = 9. Total amount = 9 × $40 = $360. (Or: bigger share = 5 × $40 = $200, total = $160 + $200 = $360.)
3.8 — Reverse: pizza in 3 : 2, smaller = 4 slices
Smaller share is 2 parts = 4 slices, so 1 part = 2 slices. Total parts = 3 + 2 = 5. Total = 5 × 2 = 10 slices.