Gap Unit Concept (Full Gap: Similar Change, Shortage)

I want to distribute all my goldfish equally into a number of tanks.
If I put 10 goldfish in each tank, I will be short of 30 goldfish.
If I put 8 goldfish in each tank, I will be short of 6 goldfish.

a) How many tanks are there?
b) How many goldfish are there?

Andre wishes to hold a birthday party and distribute some sweets to every friend at his party.
If he gives 9 sweets to each friend, he would be short of 46 sweets.
If he gives 7 sweets to each friends, he would be short of 8 sweets.
How many friends have been invited to attend Andre's party?

Gap Unit Concept (Full Gap: Similar Change, Excess)

Troy had a class party where he gave out 5 cookies to each girl in his class and had 85 cookies left.
If he had decided to give 2 more cookies to each girl, he would have 11 cookies left.
How many girls were there in his class?

Mr Lawrence gave candies to every pupil in his class.
If he gave each pupil 12 candies, he would have 6 candies left.
If he gave each pupil 9 candies, he would have 117 candies left.
How many pupils were there in Mr Lawrence's class?

Mrs Sonneman wanted to donate some money to a children's home.
If she were to give each child $30, she would have $50 left.
If she were to give each child $25, she would have $375 left.
How many children were there in the children's home?

Gap Units Concept (Partial Gap, Combination)

First
A shop owner has a total of 40 bicycles and tricycles for sale. There are 92 wheels altogether. How many tricycles are there?

Maximise: All are Bicycles

40 × 2 = 80 wheels

Gap Amount 
= 92 - 80 = 12

Gap Unit

3 wheels each - 2 wheels each = 1 wheel each

Quantity of Tricycles
= 80 wheels ÷ 1 wheel each
= 80 tricycles


Second
Zachary saw 20 camels and peacocks at the local zoo.
A camel has 4 legs while a peacock has 2.
He decides to count the total number of their legs for a science experiment and found out that they have 46 legs altogether.
How many camels and how many peacocks did he see?

Answer: (4 camels, 16 peacocks)


Third
There was a total of 47 insects and arachnids in a Creepy Crawlies Exhibit at the Science Centre.
It was found that there was a total of 318 legs altogether.
How many arachnids and how many insects were there of an arachnid has 4 pairs of legs while an insect has 3?

Answer: (18 arachnids, 29 insects)


Fourth
Jerome bought 36 shirts for his soccer team.
He paid $12 for each medium-sized shirt and $8 for each small-sized shirt.
He paid $376 for all the shirts.
How many small-sized shirts did Jerome buy?


Fifth
45 big and small containers have a total mass of 265kg.
Each big container has a mass of 7kg.
Each small container has a mass of 5kg.
How many small container are there?


Sixth
The total length of 37 pieces of ribbons and strings 2170cm.
Each piece of ribbon measures 70cm and each piece of string measures 50cm.
How many more pieces of string than ribbon are there?

Seventh
Patricia divided 201kg of corn into 7kg packets and 5kg packets.
She then found out that she had a total of 33 packets.
How many 5kg packets of corn did Patricia pack?


Eighth
The average score of 100 participants at a mathematics inter-school competition was 63.
Given that the average score of the boys was 60 and the average score of the girls was 70, find
i) the number of girls who participated in the competition
ii) the number of boys


Ninth
Tom spent $81 on a total of 24 toy cars and toy planes.

Each toy car cost $3 and each toy planes $4. How many toy cars did Tom buy?

Maximize: All Units are Toy Planes
24 × $4 = $96

Gap Amount
= $96 - $81 = $15

Gap Unit = Big Unit - Small Unit
= $4 - $3 = $1

Quantity of Toy Cars
= Gap Amount ÷ Gap Unit
= $15 ÷ $1 = 15 cars

Tenth


Eleventh
A tutition centre paid $12006 for a total of 256 wooden chairs and metal chairs. A wooden chair costs $69 and a metal chair costs $28.
How many wooden chairs were purchased for the tuition centre?

Twelfth
Lolita packed a total of 1016 baby carrots and potatoes into 57 styrofoam boxes.
These baby carrots and potatoes are packed into separate boxes.
Each hox can hold either 36 baby carrots or 8 potatoes only.

Thirteenth
Meng sold a total of 368 large and small durians at the prices shown below and collected $2760.
How many large durians did Meng sell?

Fourteenth
Weiyang started a savings plan by putting 2 coins in a money box every day.
Each coin was either a 20 cent or 50 cent coin.
His mother also put in a $1 coin in the box every 7 days.
The total value of the coins after 182 days was $133.90

a) How many coins were there altogether?
b) How many of the coins were 50 cent coins?

Average

A group of 150 pupils participated in a Science contest. Their average was 66 marks. The average score for the boys was 70 marks and for the girls, it was 60 marks. How many girls participated in the Science contest?

Total Marks = 150 pupils × 66 marks each = 9900 marks

All Boys Total Marks = 150 boys × 70 marks each = 10 500
Gap Amount = 10 500 - 9900 = 600
Gap Unit = 70 - 60 = 10 marks each

Gap Quantity = 600 marks / 10 marks each = 60 girls

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

Gap Units Concept (Full Gap)

Given: Excess and No Remainder

First

Ismail has some cookies. If he gives each of his friends 5 cookies, there would be no remainder.

If he gives each of them 3 cookies instead, he would have 36 left. How many cookies does Ismail have?

Big Unit = 5 cookies each
Small Unit = 3 cookies each
Gap Unit = 5 - 3 = 2 cookies each

Gap Amount = 36 cookies left

Number of Units
= 36 cookies ÷ 2 cookies each
= 18 units = 18 friends

Number of cookies
= 18 friends × 5 cookies each
= 90 cookies