Multiplication, Division, Profit and Loss with Money for Primary 4

Money (2)

Performance Objectives

By the end of the lesson, students should be able to:

1. multiply money by a whole number;
2. divide money by a whole number
3. appreciate the need of correct multiplication and division of money in real life transactions;
4. calculate profit and loss
5. relate the four basic operations on money to buying and selling in real life;
6. solve quantitative reasoning problems involving addition and subtraction of money.

Multiplication of Money by Whole Numbers

Multiplication of money is used when finding the total cost of several items that have the same price. It is also used when calculating a total amount that is a certain number of times larger than another amount.

When multiplying money, treat the Naira (₦) and Kobo (k) separately, or convert the entire amount to Kobo, multiply, and then convert back to Naira and Kobo.

Steps for Multiplying Money

The procedure for multiplying money by a whole number involves the following steps:

1. Write the money amount (Naira and Kobo) and the whole number in a vertical format, aligning the Kobo and Naira parts.
2. Multiply the Kobo part by the whole number first.
3. If the Kobo result is 100 or more, convert every 100 Kobo into ₦1 and carry over the Naira amount to the Naira column.
4. Multiply the Naira part by the whole number.
5. Add any carried-over Naira to the result of the Naira multiplication.
6. Write the final answer with the Naira and Kobo symbols.

Worked Examples

Example 1: Multiply ₦15.50 by 3.

Solution:

$$
\begin{array}{r}
₦15.50 \\
\times \quad 3 \\
\hline
₦46.50
\end{array}
$$

Explanation:

1. Multiply the Kobo part: $50 \text{ kobo} \times 3 = 150 \text{ kobo}$.
2. Convert 150 kobo: $150 \text{ kobo} = ₦1 \text{ and } 50 \text{ kobo}$. Write down 50 kobo and carry over ₦1.
3. Multiply the Naira part: $₦15 \times 3 = ₦45$.
4. Add the carried-over Naira: $₦45 + ₦1 = ₦46$.
5. The final answer is ₦46.50.

Example 2: A school buys 7 exercise books, and each book costs ₦80.25. How much did the school spend in total?

Solution:

$$
\begin{array}{r}
₦80.25 \\
\times \quad 7 \\
\hline
₦561.75
\end{array}
$$

Explanation:

1. Multiply the Kobo part: $25 \text{ kobo} \times 7 = 175 \text{ kobo}$.
2. Convert 175 kobo: $175 \text{ kobo} = ₦1 \text{ and } 75 \text{ kobo}$. Write down 75 kobo and carry over ₦1.
3. Multiply the Naira part: $₦80 \times 7 = ₦560$.
4. Add the carried-over Naira: $₦560 + ₦1 = ₦561$.
5. The total amount spent is ₦561.75.

Example 3: Calculate the cost of 12 loaves of bread if one loaf costs ₦350.00.

Solution:

$$
\begin{array}{r}
₦350.00 \\
\times \quad 12 \\
\hline
₦4200.00
\end{array}
$$

Explanation:

1. Multiply $₦350$ by $2$: $₦350 \times 2 = ₦700$.
2. Multiply $₦350$ by $10$: $₦350 \times 10 = ₦3500$.
3. Add the results: $₦700 + ₦3500 = ₦4200$.
4. The total cost is ₦4200.00.

Division of Money by Whole Numbers

Division of money is used when sharing a total amount equally among a number of people or items. It is also used to find the cost of one item when the total cost of several identical items is known.

Steps for Dividing Money

The procedure for dividing money by a whole number involves the following steps:

1. Write the money amount (Naira and Kobo) and the whole number in a division format.
2. Divide the Naira part by the whole number first.
3. If there is a remainder from the Naira division, convert it to Kobo by multiplying it by 100.
4. Add this converted Kobo to the original Kobo part of the money.
5. Divide the total Kobo amount by the whole number.
6. Write the final answer with the Naira and Kobo symbols.

Worked Examples

Example 1: Divide ₦75.60 by 6.

Solution:

$$
\begin{array}{r}
₦12.60 \\
6 \overline{)₦75.60} \\
-6 \downarrow \\
\hline
15 \\
-12 \downarrow \\
\hline
36 \\
-36 \downarrow \\
\hline
00
\end{array}
$$

Explanation:

1. Divide ₦75 by 6: $75 \div 6 = 12$ with a remainder of 3. Write ₦12.
2. Convert the remainder ₦3 to Kobo: $₦3 \times 100 = 300 \text{ kobo}$.
3. Add this to the original 60 kobo: $300 \text{ kobo} + 60 \text{ kobo} = 360 \text{ kobo}$.
4. Divide 360 kobo by 6: $360 \div 6 = 60 \text{ kobo}$.
5. The final answer is ₦12.60.

Example 2: Five friends shared a total bill of ₦1200.75 equally. How much did each friend pay?

Solution:

$$
\begin{array}{r}
₦240.15 \\
5 \overline{)₦1200.75} \\
-10 \downarrow \\
\hline
20 \\
-20 \downarrow \\
\hline
00 \\
-00 \downarrow \\
\hline
07 \\
-05 \downarrow \\
\hline
25 \\
-25 \\
\hline
0
\end{array}
$$

Explanation:

1. Divide ₦1200 by 5: $1200 \div 5 = 240$. Write ₦240.
2. Divide 75 kobo by 5: $75 \div 5 = 15$. Write 15 kobo.
3. Each friend paid ₦240.15.

Example 3: A trader bought 8 bags of rice for ₦96,800.00. What is the cost of one bag of rice?

Solution:

$$
\begin{array}{r}
₦12100.00 \\
8 \overline{)₦96800.00} \\
-8 \downarrow \\
\hline
16 \\
-16 \downarrow \\
\hline
08 \\
-08 \downarrow \\
\hline
00 \\
-00 \downarrow \\
\hline
00
\end{array}
$$

Explanation:

1. Divide ₦96800 by 8: $96800 \div 8 = 12100$.
2. The cost of one bag of rice is ₦12,100.00.

Understanding Profit and Loss

In real-life transactions, especially when buying and selling, people often want to know if they made money or lost money. This is where the ideas of profit and loss are important.

Cost Price (CP)

The cost price (CP) is the amount of money a seller pays to buy an item or to produce it.

Selling Price (SP)

The selling price (SP) is the amount of money a seller receives when selling an item to a customer.

Profit

Profit is the extra money a seller makes when the selling price of an item is more than its cost price.

When a seller sells an item for more than they bought it, they make a profit. To calculate profit, subtract the cost price from the selling price.

$$ \text{Profit} = \text{Selling Price (SP)} – \text{Cost Price (CP)} $$

This happens when $\text{SP} > \text{CP}$.

Loss

Loss is the money a seller loses when the selling price of an item is less than its cost price.

When a seller sells an item for less than they bought it, they make a loss. To calculate loss, subtract the selling price from the cost price.

$$ \text{Loss} = \text{Cost Price (CP)} – \text{Selling Price (SP)} $$

This happens when $\text{CP} > \text{SP}$.

Worked Examples for Profit and Loss

Example 1 (Profit): A trader bought a bag of oranges for ₦2,500.00 and sold it for ₦3,200.00. Did the trader make a profit or a loss? How much?

Solution:

1. Cost Price (CP) = ₦2,500.00
2. Selling Price (SP) = ₦3,200.00

Since SP (₦3,200.00) is greater than CP (₦2,500.00), the trader made a profit.

$$ \text{Profit} = \text{SP} – \text{CP} $$
$$ \text{Profit} = ₦3,200.00 – ₦2,500.00 $$
$$ \text{Profit} = ₦700.00 $$

The trader made a profit of ₦700.00.

Example 2 (Loss): A hawker bought a tray of groundnuts for ₦1,800.00. Due to spoilage, the hawker sold the groundnuts for ₦1,550.00. Did the hawker make a profit or a loss? How much?

Solution:

1. Cost Price (CP) = ₦1,800.00
2. Selling Price (SP) = ₦1,550.00

Since CP (₦1,800.00) is greater than SP (₦1,550.00), the hawker made a loss.

$$ \text{Loss} = \text{CP} – \text{SP} $$
$$ \text{Loss} = ₦1,800.00 – ₦1,550.00 $$
$$ \text{Loss} = ₦250.00 $$

The hawker made a loss of ₦250.00.

Quantitative Reasoning with Money

Quantitative reasoning involves using numbers and mathematical operations to solve problems. When dealing with money, these problems often combine multiplication, division, addition, and subtraction to find answers related to real-life buying and selling situations.

Worked Examples

Example 1: A baker buys 5 bags of flour, each costing ₦8,500.00. The baker also buys sugar for ₦1,250.00. If the baker sells all the flour and sugar for ₦45,000.00, did the baker make a profit or a loss?

Solution:

1. Calculate the total cost of flour:

$$ 5 \times ₦8,500.00 = ₦42,500.00 $$

2. Calculate the total Cost Price (CP):

$$ \text{CP} = \text{Cost of flour} + \text{Cost of sugar} $$
$$ \text{CP} = ₦42,500.00 + ₦1,250.00 = ₦43,750.00 $$

3. Compare CP and Selling Price (SP):

$$ \text{SP} = ₦45,000.00 $$
$$ \text{CP} = ₦43,750.00 $$
Since SP (₦45,000.00) is greater than CP (₦43,750.00), the baker made a profit.

4. Calculate the profit:

$$ \text{Profit} = \text{SP} – \text{CP} $$
$$ \text{Profit} = ₦45,000.00 – ₦43,750.00 = ₦1,250.00 $$

The baker made a profit of ₦1,250.00.

Example 2: A group of 4 friends contributed equally to buy a gift that cost ₦6,480.00. If they later sold the gift for ₦5,000.00, how much money did each friend lose?

Solution:

1. Calculate each friend’s contribution (initial cost per friend):

$$ ₦6,480.00 \div 4 = ₦1,620.00 $$
So, each friend’s share of the Cost Price (CP) was ₦1,620.00.

2. Calculate the total loss:

$$ \text{Loss} = \text{Original Cost Price} – \text{Selling Price} $$
$$ \text{Loss} = ₦6,480.00 – ₦5,000.00 = ₦1,480.00 $$

3. Calculate how much each friend lost:

$$ \text{Loss per friend} = \text{Total Loss} \div \text{Number of friends} $$
$$ \text{Loss per friend} = ₦1,480.00 \div 4 = ₦370.00 $$

Each friend lost ₦370.00.

Example 3: A farmer harvested 25 baskets of tomatoes. The farmer sold 15 baskets at ₦1,200.00 each and the remaining baskets at ₦1,000.00 each. What was the total amount of money the farmer made from selling all the tomatoes?

Solution:

1. Calculate money from the first batch of baskets:

$$ 15 \text{ baskets} \times ₦1,200.00/\text{basket} = ₦18,000.00 $$

2. Calculate the number of remaining baskets:

$$ 25 \text{ total baskets} – 15 \text{ baskets sold} = 10 \text{ remaining baskets} $$

3. Calculate money from the remaining baskets:

$$ 10 \text{ baskets} \times ₦1,000.00/\text{basket} = ₦10,000.00 $$

4. Calculate the total money made:

$$ \text{Total money} = ₦18,000.00 + ₦10,000.00 = ₦28,000.00 $$

The farmer made a total of ₦28,000.00 from selling all the tomatoes.