Numbers are essential elements in mathematics, and understanding their properties and how to manipulate them using various operations is crucial, especially in a competitive exam situation. This section will guide you through a deeper understanding of numbers, their placement on the number line, and the correct way to perform calculations using the four basic mathematical operators.

Numbers and the Number Line

Positive and Negative Numbers: On a number line, numbers greater than 0 are called 'positive' numbers, while numbers less than 0 are 'negative' numbers.

Rules for Dealing with Positive and Negative Numbers:

• Negative (-) and Positive (+) = Negative (-)
• Negative (-) and Negative (-) = Positive (+)
• Positive (+) and Positive (+) = Positive (+)
• When two signs are adjacent, simplify them into one sign using the above rules.
• When adding or subtracting two numbers with the same sign, keep the sign and add the numbers.
• If adding numbers with opposite signs, use the sign of the number farther from zero, then subtract the numbers, ignoring their signs.
• To subtract two numbers, change the minus sign to addition and change the sign of the number being subtracted to its opposite.
• The same rules apply for multiplying and dividing numbers, with the final sign determined by the rules above.

Ordering of Operations: The BODMAS Rule

Operations in mathematics follow a specific order, famously remembered as the BODMAS rule:

• Brackets
• Order (powers and roots)
• Division
• Multiplication
• Addition
• Subtraction

This rule indicates that calculations should not always be done from left to right. Instead, certain parts of an equation should be calculated first, following the order of operations listed above. Not adhering to this order can lead to incorrect results.
There is an order in which operations should be done which follows this rule.

Let’s see how this works (and also how negative / positive number rules come into play) through the following examples below.

Example Question/s

Watch the video for an explanation of the following question/s:

-2 + -3 x 2 - -4 = ?

A -14 B 14 C -4 D 4

-(-4)^ 2

A -16 B -12 C 16 D 8 E None of these

Using the addition pyramid, the number in the box between 5 and 15 at the fourth layer will be

A 15 B 8 C 10 D 20

The number in the box between 1 and 2 at the second layer will be

A 0 B 1 C 2 D 3

Key Rules to remember

• Ordering of operators is: Brackets, Order (powers & roots), Division OR Multiplication, Addition OR Subtraction.
• Number exist on a number line – know the rules when dealing with negative and positive numbers.

Practice time!

Now, it's your turn to practice.

Click on the button below and start your practice questions. We recommend doing untimed mode first, and then, when you're ready, do timed mode.

Every question has two solutions videos after you complete the question. The first is a quick 60 second video that shows you how our expert answers the question quickly. The second video is a more in-depth 5-steps or less explainer video that shows you the steps to take to answer the question. It's really important that you review the second video because that's where you'll learn additional tips and tricks.

Once you're done with the practice questions, move on to the next checkpoint.

Now, let’s get started on your practice questions.

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