P6 Algebra Problem Sums ALB5

ALB 5

Part-Whole Model  |  Dividing Into Equal Groups (One-Step)

In ALB 1–4, we found totals or remainders.
In ALB 5, after combining all parts into a total, we divide equally into a fixed number of groups to find how many are in each group. The answer is written as a fraction expression.
✏️  Guided Example
Benjamin had 7 boxes of cookies. Each box contained n cookies. He then bought another 32 cookies. He packed all the cookies equally into 8 jars. How many cookies did each jar contain?
STEP 1
Understanding the Problem

How many boxes of cookies did Benjamin have?

▶ 7

How many cookies were there in each box?

▶ n

How many jars did he pack all the cookies equally into?

▶ 8

What am I trying to find?

▶ The number of cookies each jar contained.

STEP 2
Devising a Plan

▶ Draw a comparison model — first find the total, then divide into 8 equal jars.

Total: 7 × n = 7n 32 Total = 7n + 32 ÷ 8: ? ? ? ? ? ? ? ? 8 equal jars — each jar contains ?
STEP 3
Carrying Out the Plan
(7 × n + 32) ÷ 8
= (7n + 32) ÷ 8
= (7n + 32) / 8
Each jar contained (7n + 32) / 8 cookies.
STEP 4
Looking Back

Check all the steps and calculations.

Total cookies = 7 × n + 32
               = (n+n+n+n+n+n+n) + 32
               = 7n + 32
Each jar = (7n + 32) ÷ 8 ✓
💡 Key Idea: First combine all parts into a total expression, then divide by the number of equal groups. Write the answer as a fraction: (total expression) / number of groups.
ALB 5

Practice – Part-Whole Model (Dividing Into Equal Groups)

Score 0 / 8
📝 Answer both parts of each question, then click Lock In Answers. Write fraction answers as (expression) / number, e.g. (10m + 54) / 9.
1

Penny had 10 boxes of coins. Each box contained m coins. Her mother gave her another 54 coins. She then divided all the coins equally into 9 containers.

💡 Find the total coins first, then divide by 9.
(i)  1 mark
How many coins did Penny have altogether? Give your answer in terms of m.
(ii)  1 mark
How many coins did each container contain? Give your answer in terms of m.
✅ Worked Answer
Total: 10 × m = 10m 54 Total = 10m + 54 ÷ 9: ? ? ? ? ? ? ? ? ? 9 equal containers — each has (10m + 54) / 9 coins
(i)  10 × m + 54 = 10m + 54
(ii) (10m + 54) ÷ 9
Each container had (10m + 54) / 9 coins.
2

A group of 15 pupils had an average height of k cm. A boy of height 128 cm left the group. What was the new average height of the remaining group of pupils?

💡 Total first = 15k. Subtract the boy (128), then divide by 14 remaining pupils.
(i)  1 mark
What was the total height of the remaining 14 pupils? Give your answer in terms of k.
(ii)  1 mark
What was the new average height of the remaining group? Give your answer in terms of k.
✅ Worked Answer
Total: 15 × k = 15k Split: remaining, ? 128 left 15k − 128 ÷14: each = (15k−128)/14
(i)  Total = 15 × k = 15k
     After boy left: 15k − 128
(ii) Pupils left = 15 − 1 = 14
     New average = (15k − 128) ÷ 14
New average height = (15k − 128) / 14 cm
3

Norman had 23 small albums of stamps. Each small album contained an average of y stamps. His father gave him another 64 stamps. He redistributed all the stamps equally into 8 big albums.

💡 Total = 23y + 64, then divide equally into 8 albums.
(i)  1 mark
How many stamps did Norman have altogether? Give your answer in terms of y.
(ii)  1 mark
How many stamps did each big album contain? Give your answer in terms of y.
✅ Worked Answer
Total: 23 × y = 23y 64 Total = 23y + 64 ÷ 8: ? ? ? ? ? ? ? ? 8 big albums — each has (23y + 64) / 8 stamps
(i)  23 × y + 64 = 23y + 64
(ii) (23y + 64) ÷ 8
Each big album had (23y + 64) / 8 stamps.
4

Mrs Lee bought 17 packets of lollipops and 9 boxes of sweets. Each packet contained n lollipops and each box contained 15 sweets. She shared all the candies equally among 20 pupils.

💡 Total = 17n + (9 × 15) = 17n + 135. Then divide by 20.
(i)  1 mark
How many candies were there altogether? Give your answer in terms of n.
(ii)  1 mark
How many candies did each pupil receive? Give your answer in terms of n.
✅ Worked Answer
Total: 17 × n = 17n 9 × 15 = 135 Total = 17n + 135 ÷20: 20 pupils — each gets (17n + 135) / 20 candies
(i)  Sweets = 9 × 15 = 135
     Total = 17n + 135
(ii) (17n + 135) ÷ 20
Each pupil received (17n + 135) / 20 candies.

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