Whole Numbers

In this article, we are learning about Whole Numbers as per the Primary $5$ Maths level. 

The learning objectives are:

1. Reading and Writing Numbers
2. Multiplying or Dividing by $10, 100$ or $1000$ and their multiples

1. Reading And Writing Numbers

Whole numbers include zero and counting numbers. They are without fractions.

In Primary $5$, we will learn Numbers up to $10$ million.

Let’s place the digits in $675 \;840$ in their respective place values.

We read $675 \;840$ as six hundred and seventy-five thousand, eight hundred and forty.

The place value of the digit $6$ is hundred thousands. The value of the digit $6$ is $600 \;000$.

The place value of the digit $7$ is ten thousands. The value of the digit $7$ is $70 \;000$.

The place value of the digit $5$ is thousands. The value of the digit $5$ is $5000$.

The place value of the digit $8$ is hundreds. The value of the digit $8$ is $800$.

The place value of the digit $4$ is tens. The value of the digit $4$ is $40$.

Remember the ‘s’ for the place values!
 

Let us try placing the digits in $9 \;675 \;840$ in their respective place values.

We read $9 \;675 \;840$ as nine million, six hundred and seventy-five thousand, eight hundred and forty.

The place value of the digit $9$ is $\text{millions}$. The value of the digit $9$ is $9\;000\;000$.

It is a good habit to include spaces at the appropriate places when writing numbers in numerals.

Remember to include a comma and hyphen(s) at the appropriate places when writing numbers in words.

Question 1: 

Write the following in numerals.

Solution: 

Place the digits in a place value chart as shown below.

Three million, three hundred thousand, four hundred and thirty-five $= 3 \;300\;435$

Answer:

$3\;300\;435$

Question 2: 

Write the following number in numerals.

Solution: 

Place the digits in a place value chart as shown below.

Answer:

$8\;450\;207$

Question 3: 

Write the following in numerals.

Solution: 

Place the digits in a place value chart as shown below.

Answer: 

$4\;015\;068$

Question 4: 

Write the following in words.

Solution:

Place the digits in a place value chart as shown below.

$3\;051\;043 =$ Three million, fifty-one thousand and forty-three

Answer:

Three million, fifty-one thousand and forty-three

Question 5: 

Write in words the following number.

Solution: 

Place the digits in a place value chart as shown below.

$7\;250\;025 =$ Seven million, two hundred and fifty thousand and twenty-five

Answer: 

Seven million, two hundred and fifty thousand and twenty-five

Question 6:

Write the following in words.

Solution: 

Place the digits in a place value chart as shown below.

$4\;325\;630 =$ Four million, three hundred and twenty-five thousand, six hundred and thirty

Answer:

Four million, three hundred and twenty-five thousand, six hundred and thirty

2. Multiplying or Dividing by 10, 100 or 1000 and their multiples

Multiplying by 10, 100 or 1000 

When we multiply a whole number by $10$, we add one ‘0’ after the number.

Example: 

$5 × \textbf{10} = 50$

When we multiply a whole number by $100$, we add two $'0'$s after the number.

Example: 

$5 × \textbf{100} = 500$

When we multiply a whole number by $1000$, we add three $'0'$s after the number.

Example: 

$5 × \textbf{1000} = 5000$

Question 1: 

Match.

Solution: 

Multiplying by the multiples of 10, 100 or 1000 

Now let’s multiply a number by the multiples of $10, 100$ or $1000$.

When we multiply a whole number by a multiple of $10$, we express the multiple of $10$ as a product of a number and $10$. 

Example:

$\begin{align} 12 \times \textbf{50} &= 12 \times \textbf{5} \times \textbf{10}\\[2ex] &= 60 \times 10\\[2ex] &= 600 \end{align}$

When we multiply a whole number by a multiple of $100$, we express the multiple of $100$ as a product of a number and $100$. 

Example:

$\begin{align} 12 \times \textbf{500} &= 12 \times \textbf{5} \times \textbf{100}\\[2ex] &= 60 \times 100\\[2ex] &= 6000 \end{align}$

When we multiply a whole number by a multiple of $1000$, we express the multiple of $1000$ as a product of a number and $1000$. 

Example:

$\begin{align} 12 \times \textbf{5000} &= 12 \times \textbf{5} \times \textbf{1000}\\[2ex] &= 60 \times 1000\\[2ex] &= 60\,000 \end{align}$

Question 1: 

Do the following multiplication.

A. $27 × 1000 =$ __________
B. $27 × 5000 =$ __________

Solution: 

A. $27 × 1000 = 27\,000$

B. $\begin{align} 27 \times \textbf{5000} &= 27 \times \textbf{5} \times \textbf{1000}\\[2ex] &= 135 \times 1000\\[2ex] &= 135\,000 \end{align}$

Answer:

A. $27\;000$
B. $135\;000$

Question 2: 

Do the following multiplication.

$319 × 6000 =$ _________

Solution: 

$\begin{align} 319 × 6000 &= 319 × 6 × 1000\\[2ex] &= 1\;914\;000 \end{align}$

Answer: 

$1\;914\;000$

Question 3: 

Do the following multiplication.

$700 × 9000 =$ _________

Solution: 

$\begin{align} 7 × 100 × 9 × 1000 &= 7 × 9 × 100 × 1000 \\[2ex]   &= 6\;300\;000 \end{align}$

Answer: 

$6 \,300 \,000$

Question 4: 

Fill in the blanks.

A. $12 \;\times$ __________ $= 12 \,000$
B. $12 \;\times$ __________ $= 120 \,000$

Solution: 

A. $\color{#F00}{12} \times \underline{\quad1000\quad}    = \color{#F00}{12} \,000$
B. $\color{#F00}{12}     \times \underline{\quad10\;000\quad}   = \color{#F00}{12}0 \,000$

Answer: 

A. $1000$
B. $10 \;000$

Question 5: 

Fill in the blanks

$60\;\times$ __________ $= 720$

Solution:  

$6\color{#F00}{0} \;\times$ ________ $= 72\color{#F00}{0}$

$6\color{#F00}{0} \times \underline{\quad12\quad}    = 72\color{#F00}{0}$

Answer: 

$12$

Dividing by 10, 100 or 1000 

When we divide a whole number by $10$, we remove one $''0’'$ after the number.

Example: 

$70 \;00\textbf{0 ÷ 10} = 7000$

When we divide a whole number by $100$, we remove two $''0’'$s after the number.

Example:

$70 \;0\textbf{00 ÷ 100} = 700$

When we divide a whole number by $1000$, we remove three $''0’'$s after the number.

Example:

$70 \textbf{ 000 ÷ 1000} = 70$

Question 1: 

Do the following division. 

$880 ÷ 10 =$ __________

Solution:  

$880 ÷ 10 = 88$

Answer: 

$88$

Question 2: 

Do the following division.

$293 \;000 ÷ 100 =$ __________

Solution:  

$293 \;000 ÷ 100 = 2930$

Answer: 

$2930$

Question 3: 

Do the following division.

$630 \;000 ÷ 1000 =$__________

Solution: 

$630 \;000 ÷ 1000 = 630$

Answer: 

$630$

Dividing by the multiples of 10, 100 or 1000 

Now let’s divide a number by the multiples of $10$, $100$ or $1000$.

When we divide a whole number by a multiple of $10$, we break the multiple of $10$ into $10$ and a number. We will divide by $10$ first, followed by the number. 

Example:

$\begin{align} 30 \;000 \div  \textbf{60} &= 30 000 ÷ \textbf{10 ÷ 6}\\[2ex] &= 3000 ÷ 6\\[2ex] &= 500 \end{align}$

When we divide a whole number by a multiple of $100$, we break the multiple of $100$ into $100$ and a number. We will divide by $100$ first, followed by the number. 

Example:

$\begin{align} 30 \;000 \div  \textbf{600} &= 30 \;000 ÷ \textbf{100 ÷ 6}\\[2ex] &= 300 ÷ 6\\[2ex] &= 50 \end{align}$

When we divide a whole number by a multiple of $1000$, we break the multiple of $1000$ into $1000$ and a number. We will divide by $1000$ first, followed by the number. 

Example:

$\begin{align} 30 \;000 \div  \textbf{6000} &= 30 000 ÷ \textbf{1000 ÷ 6}\\[2ex] &= 30 ÷ 6\\[2ex] &= 5 \end{align}$

Question 1: 

Do the following division.

$36 600 ÷ 60 =$ __________

Solution: 

$\begin{align} 36 \;600 ÷ 60 &= 36 \;600 ÷ 10 ÷ 6\\[2ex] &= 3660 ÷ 6\\[2ex] &= 610 \end{align}$

Answer: 

$610$

Question 2: 

Do the following division.

$44 \;800 ÷ 800 =$ __________

Solution: 

$\begin{align} 44\;800 ÷ 800 &= 44 \;800 ÷ 100 ÷ 8\\[2ex] &= 448 ÷ 8\\[2ex] &= 56 \end{align}$

Answer: 

$56$

Question 3: 

Do the following division.

$630 \;000 ÷ 9000 =$ __________

Solution: 

$\begin{align} 630 \;000 ÷ 9000 &= 630 \;000 ÷ 1000 ÷ 9\\[2ex] &= 630 ÷ 9\\[2ex] &= 70 \end{align}$

Answer: 

$70$

Question 4: 

Fill in the blanks with the correct answer.

$8400 \;÷\;$ __________ $= 70$

Solution:

$\begin{align} 8400 ÷ 70 &= 8400 ÷ 10 ÷ 7\\[2ex] &= 840 ÷ 7\\[2ex] &= 120 \end{align}$

Answer:

$120$

Conclusion

In this article, we learnt about the Whole Numbers as per the Primary $5$ Math level. We learnt the following subtopics in Whole Numbers:

• Reading and Writing Numbers up to $10$ million
• Multiplication and Division by $10$, $100$, or $1000$ and their multiples.