Page 70 - Ganit Kaushal

198 will lie within the two marks indicating 100 and 200. The number 525 will lie within the marks 500 and
600, as shown in the figure. Similarly, other three-digit numbers can be marked.

Sometimes, we mark 0, 1000, 2000, 3000, … at equal distances to the right of 0 on the number line. Usually,
this is done to cover large numbers within a notebook space. In this case, the number 2198 will lie within the
two marks indicating 2000 and 3000, and 5725 will lie within the marks 5000 and 6000, as shown in the
adjoining figure. Similarly, other four-digit numbers can be 2198 5725
marked. 0 1000 2000 3000 4000 5000 6000 7000 8000
Now, after getting ourselves familiar with the number line, let’s see if we can place some numbers lying between
1,000 and 10,000 in their appropriate positions on the number line.

Ex. Place the numbers: 2170, 2744, 1500, 3600, 9950, 9590, 1050, 3050, 5030, 5300 and 8400 on the
number line.
Sol. First, write these numbers in ascending order. It will help in placing them on the number line easily.
1050, 1500, 2170, 2744, 3050, 3600, 5030, 5300, 8400, 9590, 9950 is the ascending order. Label the
number line starting with 1000 and at a gap of 1000. Now, place the numbers on the number line; the
smallest number 1050 will come first and the largest 9950 at the last, as shown in the figure.

1050 2170 2744 3050 5030 8400 9950

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
1500 3600 5300 9590

Remark

Number lines help us to compare two whole numbers, that is, to decide which of the two given numbers is
greater or smaller. A whole number to the right of another whole number is greater, and the whole number
to the left is the smaller number.

Division Rules to Remember

In our earlier classes, we have learnt about addition, subtraction, multiplication and division of whole numbers.
Let us recall a few rules of division to learn the division algorithm:
1. If a is any whole number, then a ÷ 0 is not defined.

2. If a is any whole number, then a ÷ 1 = a.
3. If a is any non-zero whole number, then (i) a ÷ a = 1, (ii) 0 ÷ a = 0.
4. Division algorithm:

We already know how to divide a bigger whole number by a smaller whole number. To make things easier, let
us look at 33 divided by 7 from a different perspective. Assume that we have 33 bananas and we must separate
them into different bags. Each bag should hold 7 bananas. During this process, we notice that there are still 5
bananas left after filling 4 bags of 7 bananas each. Here, 33 bananas are known as the dividend; the divisor is 7,
and the quotient is 4, which is the number of bags manufactured. This procedure yields 4 bags, each containing
7 bananas, with 5 bananas remaining. The term “remainder” refers to the last 5 remaining bananas.

It can be noted that 33 = 7 × 4 + 5,

i.e., dividend = (divisor × quotient) + remainder

68 Mathematics-6