# Basic Whole Number Operations

## Rounding Whole Numbers

Rounding is the process of finding the closest number to a specific value. You round a number up or down based on the last digit you are interested in.

${\displaystyle {{down} \atop \overbrace {0,1,2,3,4,5} }{{up} \atop \overbrace {,6,7,8,9} }}$

For example, rounding the number 245 to the nearest tens place would round up to 250, while the number 324 rounded to the nearest tens place would be rounded down to 320.

Following the same logic, one could round to the nearest whole number. For example, 1.5 (pronounced as "one point five" or "one and a half") would be rounded up to 2, and 2.1 would be rounded down to 2.

First, arrange the numbers in columns. For example, ${\displaystyle 134+937}$

{\displaystyle {\begin{aligned}134\\+{\underline {937}}\\{\underline {\ \quad }}\end{aligned}}}

Add the first column (starting on the right)

{\displaystyle {\begin{aligned}134\\+{\underline {937}}\\{\underline {\quad 1}}\\1\end{aligned}}}

Note the 10's digit put under the next column. Now add the next column and the number underneath:

{\displaystyle {\begin{aligned}134\\+{\underline {937}}\\{\underline {\ \ 71}}\\1\end{aligned}}}

Finish it off with the other columns:

{\displaystyle {\begin{aligned}134\\+{\underline {937}}\\{\underline {1071}}\\1\ 1\end{aligned}}}

So the answer to 134 + 937 is 1071

## Subtracting Whole numbers

To subtract numbers think of a basket of oranges. If you have ten oranges in a basket and you remove eight oranges you are left with two oranges. For example:

{\displaystyle {\begin{aligned}10\\{\underline {-8}}\\2\end{aligned}}}

If you have ten oranges in a basket and you remove all ten then you will no longer have any oranges so you are left with zero oranges. For example:

{\displaystyle {\begin{aligned}10\\{\underline {-10}}\\0\end{aligned}}}

To subtract large numbers use this method:

1. Arrange the number that is being subtracted from on top of the number being subtracted from it(ex. 2594-1673)

{\displaystyle {\begin{aligned}{2594}\\{\underline {-1673}}\\{\underline {\qquad }}\\\end{aligned}}}

2. Subtract each column starting from the right and going to the left

 2 5 9 4
-1 6 7 3
________
2 1


3. If you encounter a number that can't be subtracted without becoming negative,"borrow" subtract(if possible) 1 from the next digit over and add 10 to the digit that can't be subtracted(if not possible continue to borrow from the next digit).

 1 15
X X 9 4
-1 6 7 3
________
9 2 1


4. continue until done

note: that 921+1673=2594.

## Multiplying Whole Numbers

### Single number times Single number producing a Single number

Take the first number as ${\displaystyle a}$ . Take the second number as ${\displaystyle b}$ . Add ${\displaystyle a}$  to itself ${\displaystyle b}$  times.

${\displaystyle a=2}$
${\displaystyle b=3}$
${\displaystyle (a)\times (b)=2\times 3={{\text{3 times}} \atop \overbrace {2+2+2} }=6}$

### Multiplication Table

To help with multiplying larger numbers by each other, a multiplication table is used. Hopefully this can be memorized to make multiplication easier for you in the future.

1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100

## Dividing Whole Numbers

Dividing whole numbers is the process of determining how many times one number, called the dividend, contains another number, called the divisor.

${\displaystyle 12\div 3}$

In this example, 12 is the dividend and 3 is the divisor. Performing a division gives a quotient.

${\displaystyle 8\div 4=2}$

In the above example, 4 goes into 8 twice; therefore, the quotient would be 2.

What happens when the dividend cannot be evenly split by the divisor? This leftover quantity is called the remainder. It's usually separated from the main part of the answer by a lowercase letter “r”.

${\displaystyle 13\div 5=2\ {\mbox{r}}\ 3}$

Divisions are often represented as fractions. For example,

${\displaystyle 68\div 43={\frac {68}{43}}}$

Some tips:

Any number that ends in 0, 2, 4, 6, or 8 can be divided by 2.

Any number that ends in 0 or 5 can be divided by 5.

Any number thats digits add to 3, 6, or 9 can be divided by 3.

Any number thats digits add to 9 can be divided by 9.

Any number that ends in 0 can be divided by 10.

If the last two digits of any number are divisible by 4 then the whole number is divisible by 4. For example:

${\displaystyle 1024\rightarrow 10{\textbf {24}}\rightarrow 24\rightarrow 24\div 4=6r0}$

So 1024 is divisible by four because 24 is divisible by 4.

## Factoring Whole Numbers

Factoring is the process of determining what prime numbers (numbers that cannot be divided by any number but 1 and itself; 2,3, and 5 are prime numbers) when multiplied will give a specific number. This process of factoring is very important in reducing fractions, which is covered in the Fractions chapter of this book. For example:

${\displaystyle 4=2\times 2\ }$

Or a more complicated example:

${\displaystyle 180=2\times 2\times 3\times 3\times 5\ }$

A method of factoring numbers is doing a factor tree. For example:

${\displaystyle 180\div {\textbf {2}}=90}$

${\displaystyle 90\div {\textbf {2}}=45}$

${\displaystyle 45\div {\textbf {5}}=9}$

${\displaystyle 9\div {\textbf {3}}=3}$

${\displaystyle 3\div {\textbf {3}}=1}$

All of the numbers in bold, known as the divisors, are the prime factors.