Hello Everyone welcome to UTUG Education. We will see the solution of Composite Mathematics class 7th by S.K. Gupta and Anubhuti Gangal of S.Chand School Publication.
This is your Chapter – 1 , Integers of the book this is the part of Number system unit which is your 1st unit of the book.
What are Integers?
The set of whole numbers and negative of natural numbers is called the set of integers.
Thus, I or Z = {……-3,-2,-1,0,1,2,3……..} is the set of integers.
The numbers +1,+2,+3,……….., etc. are called positive integers.
The numbers -1,-2,-3,…...….., etc. are called negative integers.
Zero is neither negative nor positive.
EXERCISE 1 (A)
1. Fill in the blanks:
(i) The greatest negative integer is -1.
(ii) 0 is greater than every negative integer.
(iii) The absolute value of an integer is either equal to or greater than the integers, but never less than the integer.
(iv) The successor of -91 is -90.
Successor: One more than a given integer is called its successor. Thus, on the number line each integer is the successor of the integer just on the left of it. When we will add +1 in -91 we will get -90 as your answer.
(v) The predecessor of -380 is -381.
Predecessor: One less than a given integer is called its predecessor. Thus, on the number line each integer is the predecessor of the integer just the right of it. In other words, any number -1 is predecessor of the number. When we will -1 from -380 we will get -381 as your answer.
2. Replace each blank by < or > to make the given statement true:
(i) -8 > -18 as on the number line -18 is to left of the -8 so -8>-18
(ii) -4 < 0 as on the number line -4 is to left of the 0 so -4<0
(iii) -357 > -537 as on the number line -537 is to left of the -357 so 357 > -537
(iv) -71 < 17 as on the number line -71 is to left of the 17 so -71 < 17
3. (i) Arrange the following integers in ascending order.
-8,-4,0,-11,9,4,6,13,-27,19
Ans:- First of all we have to understand that ascending order means in increasing order i.e. first comes the least number then greater than first one and so on and in the last greatest number will be written so your ans is given below.
-27,-11,-8,-4,0,4,6,9,13,19
(ii) Arrange the following integers in descending order.
-6,-11,12,-32,-23,14,0,32,16,-19,-18
Ans:- First of all we have to understand that descending order means in decreasing order i.e. first comes the greatest number then smaller than first one and so on and in the last smallest number will be written so your ans is given below.
32,16,14,12,0,-6,-11,-18,-19,-23,-32
4. Add the following:
(i)-18,14 (ii)-26,-3 (iii) 46,-46
(iv) 400,-31,-71 (v) -613,-421,-700
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5. Subtract the first integer from the second in each case:
(i)6,18 (ii)-3,6 (iii) -27,-54 (iv) 12,-7
6. Find the value of:
(i)-37-(-15)-2 (ii)16-[14-(-2)-(-6)]
7. Using >,< or =, fill in the boxes to make each statement true.
(i)(-1)+(-5) [ ] (-7)-(-5) (ii) 43-35+12 [ ] 42-35-12
(iii) 6-(-2)+5 [ ] -1-(-2)-3 (iv) -135+64+41 [ ] -159-(-81)+160
Representing Integers On A Number Line:
Draw a line and mark a point O in the middle of that line. This point denotes the number 0. Since negative numbers are opposite of positive numbers, therefore if positive numbers +1,+2,+3…….are marked on the right side of 0 mark then negative integers marked on the left side of the 0 mark.
Predecessor and Successor :
Predecessor: One less than a given integer is called its predecessor. Thus, on the number line each integer is the predecessor of the integer just the right of it. In other words, any number -1 is predecessor of the number.
Examples
0 is the predecessor of 1.
Successor: One more than a given integer is called its successor. Thus, on the number line each integer is the successor of the integer just on the left of it.
1 is the Successor of 0.
Absolute Value Of An Integer
If a represents an integer, then |a|= a if a is +ive or 0 = -a if a is –ve
Addition of Integers:
Rule 1. To add two integers of like signs, find the sum of their absolute values and place the common sign before the sum.
Rule 2. To add two integers of unlike signs, find the difference of their absolute values and place the sign of the integer which has the larger absolute value before the difference.
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