Gap Units Concept (Full Gap: Opposite Change)

Given: Excess and Shortage + Number of Big and Small Units

First

Sue-Anne wanted to buy 5 pens, but needed $2.60 more.

She then decided to buy 2 pens and had $4.15 left.

Find the cost of a pen.

Second

Alex bought some soil for his potted plants.

If he divides the soil equally into 12 pots, he would have 4.3g of soil left.

If he divides the soil equally into 16 pots, he would be short of 3.9g of soil.

How much soil does Alex have?

Given: Excess and Shortage + Big and Small Units

First

Mrs Muthu bought some pens for her pupils. If she gave them 8 pens each, she would have 15 pens left. If she gave them 12 pens each, she would need 25 more pens. How many pens did Mrs Muthu buy?

Big Unit = 12 pens each
Small Unit = 8 pens each
Gap Unit = 12 - 8 = 4 pens each

Gap Amount
= 25 pens more + 15 pens left
= 40 pens

Number of Units
= 40 pens ÷ 4 pens each
= 10 units = 10 pens

Second

Miss Tan has a bag of sweets to distribute to the pupils in her tuition class. If she gives each pupil 5 sweets, she will have 3 sweets left.
If she gives each pupil 7 sweets, she would need another 25 sweets.

a) How many pupils are there in her tuition class?
b) How many sweets does she have in her bag?

a)

Big Unit = 7 sweets each
Small Unit = 5 sweets each
Gap Unit = 7 - 5 = 2 sweets each

Gap Amount
= 3 sweets left + another 25 sweets
= 28 sweets

Number of Units
= 28 sweets ÷ 2 sweets each
= 14 units = 14 pupils

b)

Approach 1: Using Case 1

Number of Sweets
= 14 pupils × 5 sweets each + 3 sweets left
= 73 sweets

Approach 2: Using Case 2

Number of Sweets
= 14 pupils × 7 sweets each - 25 sweets
= 73 sweets

Third

Mrs Ling wanted to give every pupil in her class some stickers.
If she had given each pupil 12 stickers, she would be short of 32 stickers.
If she had given each pupil 9 stickers, she would have 76 stickers left.

a) How many pupils were there in Mrs Ling's class?
b) How many stickers did Mrs Ling have?

Fourth

Some lollipops were given to a group of pupils.

If each pupil received 12 lollipops, there would be a shortage of 5 lollipops.
If each pupil received 11 lollipops, there would be an extra of 4 lollipops.

a) How many pupils were there?
b) How many lollipops were there?

Fifth

A teacher wants to distribute some tokens to every pupil in her class.
If she gives 2 tokens to each pupil, she would have 130 tokens left.
If she gives 6 token to each pupil, she would be short of 10 tokens.
How many pupils are there in her class?

Sixth

Miss Lee had some pencils for her pupils.
If she gave each pupil 7 pencils, she would have 5 pencils too many.
If she gave each pupil 8 pencils, she would need another 2 pencils.
How many pencils did Miss Lee have?

Seventh

Rita and her friends wanted to give a farewell gift to their maths teacher. If each student paid $8, there would be $3 left. However, if each of them paid $7, they would b short of $4.
a) How many students were there?
b) How much was the gift worth?

Eighth
At a tree planting campaign, each student is expected to plant an equal number of trees. If each student planted 5 trees, there will be 11 trees left. If each student planted 7 trees, there will be 3 trees left.
a) How many students take part in the green campaign?
b) How many trees are being planted?

Ninth