Numbers and Operations

Numbers and Operations

Types of Numbers

A long, long time ago, the only numbers humans required were numbers used to count their possessions. Numbers such as 5, 8 and 12 were sufficient. These types of numbers are called natural numbers.

The natural numbers are 1, 2, 3, 4, ...

With these numbers, people could solve problems like 2x = 8,

or 2 + x = 7

Types of Numbers continued

Whole numbers belong to the set of numbers 0, 1, 2, 3, 4 …

Natural numbers are a part of the whole numbers set.

Then the number system was extended to include Integers. Integers consist of the natural numbers, their opposites, and zero.

The integers are in the number set

… -3, -2, -1, 0, 1, 2, 3 … 

Rational Numbers

The inclusion of rational numbers was developed to answer such equations as 2x=5. 

A rational number is any number that can be expressed in the form of a/b, where a and b are integers and b is not zero. 

Rational numbers are also called fractions. 

Operations with Integers

When we are working with whole numbers it is easy to add, subtract, multiply and divide. When we are working with integers, however, it becomes a little more complicated. 

A number line can be helpful when trying to add and subtract integers

Remember, when you subtract a negative number, it is the same as adding a positive number.

For example: 3 - (-2) = 3 + 2 = 5

PRACTICE QUESTIONS

Rules of Multiplying and Dividing

When we multiply or divide 2 positive or negative integers, the answer will ALWAYS be positive

When we multiply or divide a positive and a negative integer, the answer will ALWAYS be negative

PRACTICE QUESTIONS

Order of Operations (BEDMAS)

Recall that we need to follow an order of operations to solve math questions. We can remember the order by using the acronym BEDMAS:

B - Brackets

E - Exponents

D - Division

M - Multiplication

A - Addition

S - Subtraction

PRACTICE QUESTIONS

Multiple Choice

 $7^2+1$  

• 8

• 15

• 50

• 65

Multiple Choice

(5)(3) - (2)(3)

• 9

• 19

• 29

• 39

Multiple Choice

(1+2)(1-3)

• -6

• 0

• 3

• 6

Multiple Choice

 $\left(11-8\right)+2^2$  

• 1

• 3

• 5

• 7

Comparing Numbers

We can easily tell when integers are bigger or smaller than one another. But when it comes to rational numbers, it can be a bit more tricky, especially if our rational numbers are in different forms.

Rational Numbers

Consider the fraction  $\frac{1}{2}$  . 

It can be written in:

Fraction form:  $\frac{1}{2}$  
Decimal form: 0.5
Percent form: 50%

To go from fraction form to decimal form, just do the division in the fraction. For example:  $1\div2=0.5$  
Then to go from decimal to percent, multiply the decimal by 100 

PRACTICE QUESTIONS

Multiple Choice

Convert $\frac{3}{4}$  to a percentage.

• 25%

• 50%

• 75%

• 85%

Multiple Choice

Convert $\frac{7}{10}$  to a percentage

• 7%

• 10%

• 70%

• 77%

Comparing Numbers

Once we have converted our numbers into the same form, they become much easier to compare.

For example, if we try to compare $\frac{1}{4}$  and 0.3, it might be difficult to tell which one is bigger. But if we change $\frac{1}{4}$  to a decimal $\left(1\div4=0.25\right)$  then it becomes easier to see that 0.3 is bigger than 0.25

Using Number Lines

Rational numbers, like integers, can be represented by points on a number line.

This diagram gives examples of rational numbers on a number line

PRACTICE QUESTIONS

Multiple Choice

Which number is bigger?

• 4

• $\frac{1}{4}$

Multiple Choice

Which number is bigger?

• 0.2

• 0.02

Multiple Choice

Which number is bigger?

• -3.5

• 2.1

Multiple Choice

Which of the following numbers is biggest?

• -7.1

• $3.2$

• $6\ \frac{1}{5}$

• $-1\ \frac{1}{2}$

Conclusion

We use numbers all the time, so it's important to know the different rules of their operations, as well as how numbers compare to one another.

By doing this, we can gain a better idea of how to estimate answers and solve problems and gain experience using flexible and critical thinking.