LATEST NCERT CLASS 7 MATHS GANITA PRAKASH CHAPTER 8G WORKING WITH FRACTIONS PAGES 184 TO 189

Описание: LATEST NCERT CLASS 7 MATHS GANITA PRAKASH CHAPTER 8G WORKING WITH FRACTIONS PAGES 184 TO 189

IS THE PRODUCT GREATER THAN THE NUMBERS MULTIPLIED ?

we know that when a number is multiplied by 1, the product remains unchanged, we will look at multiplying pairs of numbers where neither of them is 1.

When we multiply two counting numbers greater than 1, say 3 and 5, the product is greater than both the numbers being multiplied.
3 × 5 = 15
The product, 15, is more than both 3 and 5.

But what happens when we multiply 1/4 and 8?
In the above multiplication the product, 2, is greater than 1/4 , but less than 8.

What happens when we multiply 3/4 and 2/5 ?
Let us compare this product 6/20 with the numbers 3/4 and 2/5 .
From this we can see that the product is less than both the numbers.

When do you think the product is greater than both the numbers multiplied, when is it in between the two numbers, and when is it smaller than both?

Situation
Situation 1
Situation 2
Situation 3

What can you conclude about the relationship between the numbers
multiplied and the product? Fill in the blanks:

• When one of the numbers being multiplied is between 0 and 1, the product is ____________ (greater/less) than the other number.

• When one of the numbers being multiplied is greater than 1, the product is _____________ (greater/less) than the other number.

ORDER OF MULTIPLICATION

We know that 1/2 × 1/4 = 1/8 .

Now, what is 1/4 × 1/2 ?

That is 1/8 too.

In general, note that the area of a rectangle remains the same even if the length and breadth are interchanged.
The order of multiplication does not matter.

DIVISION OF FRACTIONS

What is 12 ÷ 4?
But can this problem be restated as a multiplication problem?

What is 1 ÷ 2/3 ?

What should be multiplied by 2/3 to get the product 1?

Let us try another problem

3 ÷ 2/3 .

2/3 × ? = 3.
Can you find the answer?

What is 1/5 ÷ 1/2 ?

1/2 × ? = 1/5 .
How do we solve this?

What is 2/3 ÷ 3/5 ?

3/5 × ? = 2/3
How will we solve this?

Discussion
In each of the division problems above, observe how we found the answer. Can we frame a rule that tells us how to divide two fractions?
Let us consider the previous problem.In every division problem we have
a dividend, divisor and quotient. The technique we have been using to get
the quotient is:

1. First, find the number which gives 1 when multiplied by the divisor.
We see that the resulting number is a fraction whose numerator is the
divisor’s denominator and denominator is the divisor’s numerator.
For the divisor 3/5 this fraction is 5/3 . We call 5/3 the reciprocal of 3/5 .
When we multiply a fraction by its reciprocal, we get 1. So, the first step in our technique is to find the divisor’s reciprocal.

2. We then multiply the dividend with this reciprocal to get the quotient.

for example, 2/3 ÷ 3/5 using Brahmagupta’s formula above, we write:
2/3 ÷ 3/5

= 2/3 × 5/3

= 2 × 5 / 3 × 3

= 10/9 .

DIVIDEND , DIVISOR AND THE QUOTIENT

When we divide two whole numbers, say 6 ÷ 3, we get the quotient 2.
Here the quotient is less than the dividend.
6 ÷ 3 = 2, 2 less than 6

what happens when we divide 6 by 1/4 ?
6 ÷ 1/4 = 24.
Here the quotient is greater than the dividend!

What happens when we divide 1/8 by 1/4 ?
the quotient is greater than the dividend.

When do you think the quotient is less than the dividend and when is it greater than the dividend?

Is there a similar relationship between the divisor and the quotient?
Use your understanding of such relationships in multiplication to answer the questions above.