Number Line
ICSE Class 6 · Mathematics · Chapter 7
What this chapter covers
- Drawing a number line
- Whole numbers and integers on the number line
- Comparing numbers using the number line
- Addition on the number line
- Subtraction on the number line
Key definitions
Natural numbers are the counting numbers 1, 2, 3, 4 and so on, without end.
Whole numbers are the numbers 0, 1, 2, 3, 4 and so on, without end.
Integers are all the whole numbers together with the negative numbers -1, -2, -3 and so on.
Opposite numbers are two numbers that lie at the same distance from 0, on opposite sides of it.
Key points
- A number line is a straight line with numbers marked in order at equal gaps, and it goes on without end in both directions.
- Every gap on one number line has the same unit length; a mark may stand for 1, 10 or 100.
- Natural numbers start at 1 and whole numbers start at 0; both go to the right; negative numbers go to the left of 0.
- Integers are the whole numbers together with -1, -2, -3 and so on.
- A number and its opposite, such as 5 and -5, are the same distance from 0 on opposite sides.
- Of two numbers on a number line, the one on the right is greater.
- Every negative number is less than 0, and less than every positive number.
- To add a positive number, move right; to add a negative number, move left.
- To subtract a positive number, move left; to subtract a negative number, move right.
- The distance between two numbers on a number line is their difference.
Questions answered
Why does a number line have an arrowhead at each end?
The arrowheads show that the line goes on without end in both directions. There is no last number on either side.
A student draws a number line where the gap from 0 to 1 is 1 cm and the gap from 1 to 2 is 2 cm. What is wrong?
All gaps on a number line must have the same unit length. With unequal gaps, the distance between two marks no longer shows the difference between the numbers.
Which integer is 4 units to the right of -7?
Start at -7 and move 4 units right to reach -3.
Write the opposite of 9 and the opposite of -12.
The opposite of 9 is -9, and the opposite of -12 is 12.
Which is greater, -8 or -3? Give a reason.
-3 is greater, because it lies to the right of -8 on the number line.
Arrange 4, -2, -9, 0 and 1 in descending order.
Read the number line from right to left: 4 > 1 > 0 > -2 > -9.
Use the number line to find -6 + 4 and 2 - 7.
Start at -6 and move 4 right to land on -2. Start at 2 and move 7 left to land on -5.
At 6 a.m. the temperature in a hill town is -4 °C. By noon it has risen by 9 degrees. What is the temperature at noon?
Start at -4 and move 9 units right. The noon temperature is 5 °C.