Integers Lesson 7

CLASS 7 MATHS INTEGERS BLOG 7

March 31, 2020

HELLO BOYS!! 

WELCOME TO THE BLOG.

From the following blog, the students will be able to:

1. Observe that the product of integers is also an integer.
2. Verify that the integers can be multiplied in whichever order brings the same result.

Guidelines to follow: (REMINDER!!!)

1. The text in blue has to be noted in the notebooks
2. The links in violet are to be viewed.

EX- 1.3

Before starting the with the rest of the questions in the Exercise 1.3, let us look into properties of Multiplication of Integers. You have already seen two: Multiplicative identity and Multiplicative Inverse.

We will be looking at other Properties of Multiplication of Integers:

1. Closure under Multiplication
2. Commutativity of Multiplication
3. Associativity of Multiplication
4. Multiplication by Zero
5. Distributive Property

 1. The first Property Closure under Multiplication suggest that multiplying any two integers will give us an integer.

a x b= c, where a, b and c are integers.

It is called CLOSURE UNDER MULTIPLICATION.

Let us prove it with some examples

(-2) x 3 = -6, here -2, 3 and 6 are integers

(-6) x (-4) = 24

2. If multiplying an integer by 0, the result is always zero.

Here, lets see some examples,

(-4) x 0 = 0

2 x (-9) x 0 = (-18) x 0= 0

You have verified this property in Q1 (e)  and Q3 (c)

We will take the other three properties in the next blog. For now let us look into the word problems. 
Please put the negative integers within brackets while solving any operations e.g. 2 x (-18)

(-4) x (-12) x (-5) (I KNOW YOU MAY KNOW IT BUT JUST REMINDING!!!)

Let us begin the Exercise:

Ex 1.3 Q6: Certain freezing process requires that room temperature be lowered from 40°C at the rate of 5°C very hour. What will be the room temperature 10 hours after the process begins?

Solution: Present room temperature = 40°C

Temperature to be reduced every hour = 5°C

Temperature to be reduced after 10 hours = 10 x 5℃

Therefore, the room temperature after 10 hours = 40°C − (10 x 5°C)

= 40°C − 50°C

= −10°C 

Ex 1.3 Q7: In a class test containing 10 questions, 5 marks are awarded for every correct answer and (−2) marks are awarded for every incorrect answer and 0 for questions not attempted.

(i) Mohan gets four correct and six incorrect answers. What is his score?

(ii) Reshma gets five correct answers and five incorrect answers, what is her score?

(iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?

Solution:

(i) Four correct answers = 4 x 5 = 20

Six incorrect answers = 6 x (−2) = −12

Therefore, Mohan’s total scores = 20 − 12 = 8

(ii)Five correct answers = 5 x 5 = 25

Five incorrect answers = 5 x (−2) = −10

Therefore, Reshma’s total scores = 25 − 10 = 15

(iii)Two correct answers = 2 x 5 = 10

Five incorrect answers = 5 x (−2) = −10

Therefore, Heena’s total scores = 10 − 10 = 0 

Ex 1.3 Q8: A cement company earns a profit of Rs 8 per bag of white cement sold and a loss of Rs 5 per bag of grey cement sold.

(i) The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?

(ii)What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6,400 bags?

Solution: 

(i)Profit at Rs 8 on 3000 bags of white cement = 3000 x 8 = Rs 24000

Loss at Rs 5 on 5000 bags of grey cement = 5000 x 5 = Rs 25000

Since, Profit < Loss

Therefore, the loss = Loss - Profit

= 25000 - 24000

= Rs 1000

Thus, the company lost Rs 1000 on the sales.

(ii)Number of grey bags sold = 6400

Loss on grey bags = 6400 x 5 = Rs 32000

To have neither profit nor loss, the profit on white bags should equal the loss on grey bags =Rs 32000

Number of white bags to be sold at Rs 8 = 32000÷8 = 4000 bags

Therefore, the number of white bags is 4000 so that the loss is equal to the profit.
Do note down these solutions in your notebook. Post your queries in the comments.

ASSIGNMENTS: 1. Try completing the tables on page no. 15
QUESTION 2: A submarine dives 20 m each minute for 15 minutes. What is the total change in depth after 15 minutes?
QUESTION 3: The temperature rises 2°C each hour from 6:00 a.m. to 3:00 p.m. What is the total change in temperature during this period of time? 

See you tomorrow with the next blog.
BYE.
TAKE CARE.