Page 14 - Maths Skills - 7

12 Maths

4. Write the absolute value of

(i) – 4 (ii) 0 (iii) 9 (iv) –8
5. In three rounds of a quiz, Shivi secured – 10, 5 and 25. Find her final score.
6. A cloud is at a height of 4000 m above the sea level. At a particular point it is exactly above a submarine
which is floating 2400 m below the sea level. What is the vertical distance between them?

7. Write a negative integer and a positive integer whose sum is –15.
8. Write a negative integer and a positive integer whose difference is 11.

9. In a quiz, team A scored 20, –10, 34 and team B scored –10, 34, 20 in three successive rounds. Which
team scored more?

10. Fill in the blanks to make the following statements true:
(i) (–7) + (–9) = (–9) + (...) (ii) (–82) + (...) = 0

(iii) 19 + (...) = 0 (iv) {8 + (–7)} + (...) = 8 + {(–7) + (–4)}

MULTIPLICATION OF INTEGERS
We know that ‘Multiplication is the repeated process of addition’.
For example; 4 × (– 2) = (– 2) + (– 2) + (– 2) + (– 2) = – 8 [– 2 is added 4 times]

Here, we observe that the two integers are multiplied by repeated addition.

RULES FOR MULTIPLICATION OF INTEGERS
Now, we will study few rules on integers.
1. When the integers are of like signs: Find the product of the absolute values of the two integers and put a plus
sign in front of the product.

For example; (i) 3 × 3 = + 9 or 9
(ii) (– 5) × (– 6) = 5 × 6 = + 30 or 30 Fact-o-meter

2. When the integers are of unlike signs: Find the product of absolute � (+) × (+) = +
values of the integers and put a minus sign in front of the product. � (–) × (–) = +
For example; (i) 2 × (– 3) = – (2 × 3) = – 6 � (+) × (–) = –
(ii) (– 5) × 4 = – (5 × 4) = – 20 � (–) × (+) = –

PROPERTIES OF MULTIPLICATION OF INTEGERS
1. Closure Property: The product of any two integers is always an integer.
In other words, if a and b are any two integers and a × b = c, then c is also an integer.

For example; (i) (– 4) × 3 = – 12, which is an integer. (ii) 2 × 3 = 6, which is an integer.
2. Commutative Property: The product of any two integers in different orders remains the same.

In other words, if a and b are any two integers, then a × b = b × a.
For example;

(i) (– 9) × (– 3) = 27 and (ii) 3 × (– 5) = – 15 and
(– 3) × (– 9) = 27 (– 5) × (3) = – 15
\ (– 9) × (– 3) = (– 3) × (– 9) \ 3 × (– 5) = (– 5) × 3