# Whole Numbers 3

In this article, the learning objectives are:

- Whole Number Strategy – Grouping

## Whole Number Strategy – Grouping

In  Whole Number Strategy – Grouping, we will solve questions by grouping the items in a group and determine the number of groups involved.

#### Question 1:

$3$ apples cost $5$. What is the cost of $9$ apples?

#### Solution:

Number of apples in 1 group $= 3$ apples
Number of groups of apples\begin{align}\\ &= 9 \div 3\\ &= 3 \end{align}

Cost of 1 group of apples $= 5$
Cost of 3 groups of apples\begin{align}\\ &= 3 \times 5\\ &= 15 \end{align}

The cost of $9$ apples is $15$

$15$

#### Question 2:

A fruit seller sold $5$ mangoes for $8$. Marissa bought $25$ mangoes from the fruit seller. How much did she pay?

#### Solution:

Number of mangoes in 1 group $= 5$ mangoes
Number of groups of mangoes\begin{align}\\ &= 25 \div 5\\ &= 5 \end{align}

Cost of 1 group of mangoes $= 8$
Cost of 5 group of mangoes\begin{align}\\ &= 5 \times 8\\ &= 40 \end{align}

She paid $40$.

$40$

#### Question 3:

At a supermarket, every $5$ apples cost $2$ and every $10$ oranges cost $3$. Find the total cost of $10$ apples and $30$ oranges.

#### Solution:

Number of apples in 1 group $= 5$ apples
Number of groups of apples\begin{align}\\ &= 10 \div 5\\ &= 2 \end{align}

Cost of 1 group of apples $= 2$
Cost of 2 groups of apples\begin{align}\\ &= 2 \times 2\\ &= 4 \end{align}
Number of oranges in 1 group $= 10$ oranges
Number of groups of oranges\begin{align}\\ &= 30 \div 10\\ &= 3 \end{align}

Cost of 1 group of oranges $= 3$
Cost of 3 groups of oranges\begin{align}\\ &= 3 \times 3\\ &= 9 \end{align}
Total cost of $10$ apples and $30$ oranges\begin{align}\\ &= 4 + 9\\ &= 13 \end{align}

The total cost of $10$ apples and $30$ oranges is $13$

$13$

#### Question 4:

Ahmad painted $30$ balls using either green or red paint. For every $4$ balls painted green, $2$ balls were painted red. How many balls were painted red?

#### Solution:

There are $4$ green balls and $2$ red balls red in 1 group.
Number of groups of balls\begin{align}\\ &= 30 \div 6\\ &= 5 \end{align}
Number of balls painted red in 1 group $= 2$
Number of red balls in 5 groups\begin{align}\\ &= 5 \times 2\\ &= 10 \end{align}

$10$ balls were painted red.

$10$ balls

#### Question 5:

Yvonne received $3$ free packets of milk for every $5$ packets of biscuits she bought. Given that she received $27$ free packets of milk, how many packets of biscuits did she buy?

#### Solution:

There are $5$ packets of biscuits and $3$ free packets of milk in 1 group.
Number of groups\begin{align}\\ &= 27 \div 3\\ &= 9 \end{align}

Number of packets of biscuits in 1 group $= 5$
Number of packets of biscuits in 9 groups\begin{align}\\ &= 9 \times 5\\ &= 45 \end{align}

She bought $45$ packets of biscuits.

$45$ packets

#### Question 6:

Helen received $3$ bonus stamps for every $5$ she spent in a supermarket. Given that she spent a total of $189$, how many bonus stamps will she get?

#### Number of groups of $5$ in \begin{align}\\ 189 &= 189 \div 5\\ &= 37 \text{ groups R } 4 \end{align}

There are $37$ groups of $5$ and a remainder of $4$

Number of bonus stamps she will get\begin{align}\\ &= 37 \times 3\\ &= 111 \end{align}

She will get $111$ bonus stamps.

$111$ cookies

#### Question 7:

Pauline baked $498$ cookies to sell. She packed the cookies into boxes of 8 and sold each box for $7$. If she sold all the boxes of cookies, how much money did she collect?

#### Solution:

Number of boxes of $8$ cookies\begin{align}\\ &= 498 \div 8\\ &= 62 \text{ groups R 2 cookies} \end{align}

She packed $62$ boxes of $8$ cookies and there are $2$ cookies left.

Amount of money she collected\begin{align}\\ &= 62 \times 7\\ &= 434 \end{align}

She collected $434$

$434$

#### Question 8:

During a sale, notebooks were sold at $5$ for $7$. Given that Janice has $50$, what is the greatest number of notebooks she could buy?

#### Solution:

Number of groups of $7$ in \begin{align}\\ 50 &= 50 \div 7\\ &= 7 \text{ groups R } 1 \end{align}

There are $7$ groups of $7$ and a remainder of $1$.
Greatest number of notebooks she could buy\begin{align}\\ &= 7 \times 5\\ &= 35 \end{align}

The greatest number of notebooks she could buy is $35$

$35$

Question 9:

Tom has $20$. He wants to buy as many pens as he can. A pen costs $2$ while a pack of $5$ pens costs $8$. What is the greatest number of pens he could buy?

#### Solution:

Number of pens in 1 group $= 5$ pens

Cost of 1 group of pens $= 8$

Number of groups of $8$ in \begin{align}\\ 20 &= 20 \div 8\\ &= 2 \text{ groups R } 4 \end{align}

There are 2 groups of $8$ and a remainder of $4$

Number of pens in 2 groups\begin{align}\\ &= 2 \times 5\\ &= 10 \end{align}

Cost of 1 pen $= 2$

Number of pens Tom can buy with the remaining \begin{align}\\ 4 &= 4 \div 2\\ &= 2 \end{align}

Greatest number of pens Tom could buy\begin{align}\\ &= 10 + 2\\ &= 12 \end{align}

The greatest number of pens Tom could buy is $12$

$12$

#### Question 10:

A fruit seller bought $17$ boxes of mangoes. Each box contained $5$ mangoes. He repacked the mangoes into packets of $3$ and sold all the packets at $10$ each. How much money did he collect?

#### Solution:

Total number of mangoes\begin{align}\\ &= 17 \times 5\\ &= 85 \end{align}

Number of packets of $3$ mangoes\begin{align}\\ &= 85 \div 3\\ &= 28 \text{ groups R } 1 \text{ mango} \end{align}

The fruit seller packed $28$ packets of $3$ mangoes and had $1$ mango left.

Cost of 1 packet of mangoes $= 10$

Amount of money he collected from $28$ packets of mangoes\begin{align}\\ &= 28 \times 10\\ &= 280 \end{align}

He collected $280$ from his sale.

$280$

#### Question 11:

The following shows the ongoing promotion for T-shirts at a store.

Terry wants to get $12$ T-shirts. What is the least amount of money he has to pay?

#### Solution:

Number of T-shirts in 1 group\begin{align}\\ &= 2 + 1\\ &= 3 \end{align}
Number of groups of 3 T-shirts\begin{align}\\ &= 12 \div 3\\ &= 4 \end{align}
Cost of 1 group of T-shirts\begin{align}\\ &= 2 \times 45\\ &= 90 \end{align}
Cost of 4 groups of T-shirts\begin{align}\\ &= 4 \times 90\\ &= 360 \end{align}

The least amount he has to pay is $360$

$360$

#### Question 12:

The following shows the ongoing promotion for scarves at a store.

Violet wants to buy $11$ scarves. What is the least amount of money she has to pay?

#### Solution:

Number of scarves in 1 group\begin{align}\\ &= 3 + 1\\ &= 4 \end{align}
Number of groups of 4 scarves\begin{align}\\ &= 11 \div 4\\ &= 2 \text{ groups R } 3 \text{ scarves} \end{align}

To get $11$ scarves, there are 2 groups of $4$ scarves and another $3$ scarves.

Number of free scarf in 1 group $= 1$
Number of free scarves in 2 groups\begin{align}\\ &= 2 \times 1\\ &= 2 \end{align}

Number of scarves paid for\begin{align}\\ &= 11-2\\ &= 9 \end{align}

Total amount of money Violet need to pay\begin{align}\\ &= 9 \times 22.50\\ &= 202.50 \end{align}

Violet needs to pay $202.50$

$202.50$

#### Question 13:

Gary bought doughnuts at Shop A. Aziz spent the same amount of money as Gary at Shop B. How many doughnuts did Aziz buy at Shop B?

#### Solution:

Gary (Shop A):

Number of doughnuts in 1 group $= 3$

Number of groups of doughnuts Gary bought\begin{align}\\ &= 15 \div 3\\ &= 5 \end{align}

Cost of 1 group of doughnuts $= 2$

Cost of 5 groups of doughnuts\begin{align}\\ &= 5 \times 2\\ &= 10 \end{align}

Since Aziz spent the same amount of money as Gary, Aziz spent $10$ on doughnuts at Shop B.

Aziz (Shop B):

Number of groups of $5$ in \begin{align}\\ 10 &= 10 \div 5\\ &= 2 \end{align}

Number of doughnuts in 1 group $= 6$

Number of doughnuts in 2 groups\begin{align}\\ &= 2 \times 6\\ &= 12 \end{align}

Aziz bought doughnuts at Shop B.

12 doughnuts

Continue Learning
Volume Money
Mass Fractions
Addition And Subtraction Whole Numbers 1
Whole Numbers 3 Whole Numbers 6
Bar Graphs Angles
Multiplication and Division Length, Mass And Volume
Length Area and Perimeter
Parallel And Perpendicular Lines

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