Multiplication of Whole Numbers, Fractions and Decimals for Primary 4

Multiplication (1)

Performance Objectives

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

1. multiply whole numbers less than or equal to 50;
2. perform multiplication of fractions.
3. multiply decimals by 2-digit numbers;
4. solve quantitative aptitude problems involving multiplication of numbers;

Understanding Multiplication

Multiplication is a quick way to do repeated addition. For example, if a person buys 3 packets of biscuits and each packet has 5 biscuits, the total number of biscuits can be found by adding $5 + 5 + 5 = 15$. Using multiplication, this is written as $3 \times 5 = 15$. The symbol ‘$\times$’ means ‘multiplied by’ or ‘times’.

The numbers being multiplied are called factors, and the answer is called the product.

Multiplication of Whole Numbers (Product up to 50)

Multiplying whole numbers means finding the total when a number is added to itself a certain number of times. At this level, the focus is on products that are 50 or less.

Multiplying Single-Digit Numbers

This involves multiplying two numbers, each from 0 to 9. For example, $6 \times 7$ means 6 groups of 7, or 7 added 6 times ($7+7+7+7+7+7$).

The multiplication table helps to quickly find these products.

Worked Examples:

1. Multiply $5 \times 8$.

Solution:

$$ 5 \times 8 = 40 $$

2. Multiply $7 \times 6$.

Solution:

$$ 7 \times 6 = 42 $$

3. Multiply $9 \times 5$.

Solution:

$$ 9 \times 5 = 45 $$

Multiplying a Two-Digit Number by a Single-Digit Number (Product up to 50)

This involves multiplying a number with two digits by a number with one digit, ensuring the final product does not exceed 50.

Worked Examples:

1. Multiply $12 \times 4$.

Solution:

First, multiply the ones digit: $4 \times 2 = 8$. Write 8 in the ones place.

Next, multiply the tens digit: $4 \times 1 = 4$. Write 4 in the tens place.

$$
\begin{array}{r}
12 \\
\times 4 \\
\hline
48
\end{array}
$$

So, $12 \times 4 = 48$.

2. Multiply $25 \times 2$.

Solution:

First, multiply the ones digit: $2 \times 5 = 10$. Write 0 in the ones place and carry over 1 to the tens place.

Next, multiply the tens digit: $2 \times 2 = 4$. Add the carried over 1: $4 + 1 = 5$. Write 5 in the tens place.

$$
\begin{array}{r}
25 \\
\times 2 \\
\hline
50
\end{array}
$$

So, $25 \times 2 = 50$.

3. Multiply $16 \times 3$.

Solution:

First, multiply the ones digit: $3 \times 6 = 18$. Write 8 in the ones place and carry over 1 to the tens place.

Next, multiply the tens digit: $3 \times 1 = 3$. Add the carried over 1: $3 + 1 = 4$. Write 4 in the tens place.

$$
\begin{array}{r}
16 \\
\times 3 \\
\hline
48
\end{array}
$$

So, $16 \times 3 = 48$.

Multiplication of Fractions

A fraction represents a part of a whole. It has a numerator (the top number) and a denominator (the bottom number).

Multiplying a Fraction by a Whole Number

To multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number. The denominator remains the same.

Worked Examples:

1. Multiply $\frac{1}{3}$ by 2.

Solution:

Multiply the numerator (1) by the whole number (2): $1 \times 2 = 2$.

The denominator (3) stays the same.

$$ 2 \times \frac{1}{3} = \frac{2 \times 1}{3} = \frac{2}{3} $$

This means two groups of one-third make two-thirds.

2. Multiply $\frac{3}{4}$ by 3.

Solution:

Multiply the numerator (3) by the whole number (3): $3 \times 3 = 9$.

The denominator (4) stays the same.

$$ 3 \times \frac{3}{4} = \frac{3 \times 3}{4} = \frac{9}{4} $$

The answer $\frac{9}{4}$ is an improper fraction. It can be written as a mixed number: $2\frac{1}{4}$.

3. Multiply $\frac{2}{5}$ by 4.

Solution:

Multiply the numerator (2) by the whole number (4): $2 \times 4 = 8$.

The denominator (5) stays the same.

$$ 4 \times \frac{2}{5} = \frac{4 \times 2}{5} = \frac{8}{5} $$

The answer $\frac{8}{5}$ can be written as $1\frac{3}{5}$.

Multiplying a Fraction by Another Fraction

To multiply two fractions, multiply their numerators together and multiply their denominators together.

Worked Examples:

1. Multiply $\frac{1}{2}$ by $\frac{1}{4}$.

Solution:

Multiply the numerators: $1 \times 1 = 1$.

Multiply the denominators: $2 \times 4 = 8$.

$$ \frac{1}{2} \times \frac{1}{4} = \frac{1 \times 1}{2 \times 4} = \frac{1}{8} $$

This means finding one-half of one-fourth.

2. Multiply $\frac{2}{3}$ by $\frac{1}{5}$.

Solution:

Multiply the numerators: $2 \times 1 = 2$.

Multiply the denominators: $3 \times 5 = 15$.

$$ \frac{2}{3} \times \frac{1}{5} = \frac{2 \times 1}{3 \times 5} = \frac{2}{15} $$

3. Multiply $\frac{3}{4}$ by $\frac{2}{3}$.

Solution:

Multiply the numerators: $3 \times 2 = 6$.

Multiply the denominators: $4 \times 3 = 12$.

$$ \frac{3}{4} \times \frac{2}{3} = \frac{3 \times 2}{4 \times 3} = \frac{6}{12} $$

The fraction $\frac{6}{12}$ can be simplified by dividing both the numerator and denominator by 6:

$$ \frac{6 \div 6}{12 \div 6} = \frac{1}{2} $$

Multiplication of Decimals by Two-Digit Numbers

A decimal number is a number that contains a decimal point, separating the whole number part from the fractional part. For example, $0.5$ or $12.75$.

Steps for Multiplying Decimals by Two-Digit Numbers

1. Ignore the decimal point and multiply the numbers as if they were whole numbers.
2. Count the total number of decimal places in the decimal number (the number of digits after the decimal point).
3. In the product, place the decimal point so that it has the same number of decimal places as counted in step 2.

Worked Examples:

1. Multiply $0.5$ by $12$.

Solution:

Step 1: Multiply $5 \times 12$ as whole numbers.

$$
\begin{array}{r}
12 \\
\times 5 \\
\hline
60
\end{array}
$$

Step 2: Count decimal places in $0.5$. There is 1 decimal place.

Step 3: Place the decimal point in 60 so there is 1 decimal place.

$$ 6.0 $$

So, $0.5 \times 12 = 6.0$ or $6$.

2. Multiply $1.25$ by $20$.

Solution:

Step 1: Multiply $125 \times 20$ as whole numbers.

$$
\begin{array}{r}
125 \\
\times 20 \\
\hline
000 \\
2500 \\
\hline
2500
\end{array}
$$

Step 2: Count decimal places in $1.25$. There are 2 decimal places.

Step 3: Place the decimal point in 2500 so there are 2 decimal places.

$$ 25.00 $$

So, $1.25 \times 20 = 25.00$ or $25$.

3. Multiply $0.75$ by $15$.

Solution:

Step 1: Multiply $75 \times 15$ as whole numbers.

$$
\begin{array}{r}
75 \\
\times 15 \\
\hline
375 \quad (5 \times 75) \\
750 \quad (10 \times 75) \\
\hline
1125
\end{array}
$$

Step 2: Count decimal places in $0.75$. There are 2 decimal places.

Step 3: Place the decimal point in 1125 so there are 2 decimal places.

$$ 11.25 $$

So, $0.75 \times 15 = 11.25$.

Quantitative Reasoning Problems Involving Multiplication

Quantitative reasoning involves using mathematical skills to solve real-life problems, often presented as word problems. For multiplication, this means identifying situations where quantities are grouped or repeated.

Worked Examples:

1. A farmer plants 8 rows of maize. Each row has 6 maize plants. How many maize plants are there in total?

Solution:

Number of rows = 8

Number of plants in each row = 6

Total maize plants = Number of rows $\times$ Number of plants in each row

$$ 8 \times 6 = 48 $$

There are 48 maize plants in total.

2. A tailor uses 3 metres of fabric to make one school uniform. How many metres of fabric are needed to make 15 school uniforms?

Solution:

Fabric for one uniform = 3 metres

Number of uniforms = 15

Total fabric needed = Fabric for one uniform $\times$ Number of uniforms

$$ 3 \times 15 = 45 $$

45 metres of fabric are needed.

3. A box contains 10 pencils. If a school buys 5 such boxes, how many pencils does the school have?

Solution:

Pencils in one box = 10

Number of boxes = 5

Total pencils = Pencils in one box $\times$ Number of boxes

$$ 10 \times 5 = 50 $$

The school has 50 pencils.

4. A baker bakes 4 cakes every hour. How many cakes will the baker bake in 12 hours?

Solution:

Cakes baked per hour = 4

Number of hours = 12

Total cakes baked = Cakes baked per hour $\times$ Number of hours

$$ 4 \times 12 = 48 $$

The baker will bake 48 cakes.