Chapter 1 ยท ICSE Class 6 Math

Number System

Numbers can go below zero too. Drag the sliders and watch two integers add together on a number line.

The Integer Machine
(-3) + 5 = 2
-3
5

Try it: make B negative to see subtraction in action!

1.1

Natural numbers, whole numbers, and integers

You already know natural numbers (1, 2, 3...) and whole numbers (0, 1, 2, 3...). Integers extend this further to include negative numbers: ...โˆ’3, โˆ’2, โˆ’1, 0, 1, 2, 3...

Natural numbers
1, 2, 3...

Counting numbers, starting from 1.

Whole numbers
0, 1, 2, 3...

Natural numbers plus zero.

Integers
...โˆ’2,โˆ’1,0,1,2...

Whole numbers plus all negative numbers.

Everyday example โ€” A temperature of โˆ’5ยฐC, a submarine 200m below sea level, or a bank overdraft of โ‚น500 are all negative numbers used in daily life.
1.2

The integer number line

1Comparing integers

On a number line, numbers get bigger as you move right and smaller as you move left. Compare โˆ’7 and โˆ’2. Since โˆ’2 is to the right of โˆ’7 on the number line, โˆ’2 > โˆ’7

2A common mistake

Which is greater: โˆ’10 or 3? Even though 10 is a "bigger" number, โˆ’10 is far to the left of zero, so 3 > โˆ’10

Watch out โ€” A negative number is always less than a positive number, no matter how large its digits look. โˆ’100 is still less than 1!
1.3

Adding and subtracting integers

1Same signs โ€” add and keep the sign

Solve: (โˆ’4) + (โˆ’6). Add the numbers and keep the negative sign: โˆ’10

2Different signs โ€” subtract and keep the bigger sign

Solve: (โˆ’8) + 5. Subtract the smaller from the bigger (8โˆ’5=3), and keep the sign of the bigger number: โˆ’3

3Subtracting a negative

Solve: 6 โˆ’ (โˆ’4). Subtracting a negative is the same as adding: 6 + 4 = 10

1.4

Ordering large numbers

1Arranging in ascending order

Arrange 45,231, 8,900, and 102,450 in ascending order (smallest to largest).

8,900 < 45,231 < 102,450

2Arranging in descending order

Arrange 7,65,432, 98,765, and 8,05,000 in descending order (largest to smallest).

8,05,000 > 7,65,432 > 98,765

Tip โ€” First compare the number of digits โ€” more digits usually means a bigger number. Only compare digit by digit (left to right) when two numbers have the same number of digits.
๐ŸŽฎ Number Kingdom

Complete the Mission

Answer 3 out of 4 correctly to complete this quest and unlock Ratio Rapids.

Practice

Exercises

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Assess

Sample tests

Two 20-mark, 30-minute tests. Reveal answers question by question.