Question

1.Add the following integers
(a) -3 +7
(b) - 15 + (-27)
(c) -1 + 6 + (-4)
(d) -48 +25

2.Subtract the first integer from the second in each case.
(a) +6+8
(b) -13, -7
(c) -8, 15
(d) 5,-8
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Answer 1

Answer:

We will get Addition of following integers.

 (a) -3 +7=4,  (b) - 15 + (-27)=-42,  (c) -1 + 6 + (-4)=1, (d) -48 +25=-23

 Subtract the first integer from the second in each case.

 (a) +6+8 is 2 , (b) -13, -7 is 6,  (c) -8, 15 is 23,  (d) 5,-8 is -13

Step-by-step explanation:

• As per the question we have to evaluate the given data.

          Given data:- Addition of following integers.

                               (a) -3 +7, (b) - 15 + (-27), (c) -1 + 6 + (-4),(d) -48 +25

                              Subtract the first integer from the second in each case.  

                              (a) +6+8 ,(b) -13, -7, (c) -8, 15, (d) 5,-8

        Solution:-

• Adding two or more numbers together is known as an addition.

• Addition as denoted by(+).
• We know that Subtraction means taking away some value from another value.

• Subtraction is denoted by (-).  
• We know that the rule of addition subtraction of integers,

         $\begin{array}{l}\text 1. (+) \times(+)=(+) \\2 .(+) \times(-)=(-) \\3 .(-) \times(-)=(+)\end{array}$

• Addition of

      $(a)-3+7\\ =4\\\\(b)-15+(-27)\\=-15-27=-42\\\\(c)-1+6+(-4)\\=-1+6-4\\=5-4=1\\\\(d)-48+25\\=-23$

• Subtraction of

         $(a)(+8)-(+6)\\=8-6\\=2\\\\(b)(-7)-(-13)\\=-7+13\\=6\\\\(c)15-(-8)\\=15+8\\=23\\\\(d)(-8)-5\\=-13$

Answer 2

Answer:

Answers for Q1 are : a ) $4$ , b) $-42$ ,  c) $1$ , d) $-23$  

Answers for Q2 are : a ) $2$ , b) $6$ ,  c) $23$ , d) $-13$

Step-by-step explanation:

Q1 ) To add following :

Solution :

• Addition is the arithmetic operation of adding two numbers together .  
• Addition rules for integers:

1. If two negative integers are to be added then addition operation is performed and sum obtained has negative sign .i.e. $(-)+(-)=-$
2. If one negative and one positive integers are to be Added then operation performed is subtraction and difference obtained has sign of greater integer. i.e. $(-)+(+)= sign \ of \ greater \ integer$
3. If both positive integers are to be added then operation performed is addition and sum obtained has positive sign i.e. $(+)+(+)= +$

• Therefore according to above rule we solve  

    a ) $-3 + 7$ $= 4$

    b) $-15 +(-27 )= -42$

    c) $-1 + 6 +(-4)= 1$  

    d) $-48 +25 = -23$  

Q 2 ) To subtract the first integer from the second in each case.

• Subtraction is the arithmetic operation of taking off difference between two numbers.
• Subtraction rules for integers:

1. If two negative integers are to be subtracted then addition operation is performed and difference obtained has negative sign . i.e. $(-)-(-)=-$
2. If one negative and one positive integers are to be subtracted then operation performed is subtraction and difference obtained has sign of greater integer. i.e.$(-)-(+)= sign \ of \ greater \ integer$
3. If both positive integers are to be subtracted then operation performed is subtraction and difference obtained has sign of greater number i.e. $(+)-(+)=sign \ of\ greater \ number$

• Therefore according to above rule we solve

      (a) $+6, +8$

            $8 -6 = 2$

    (b) $-13, -7$

           $( -7 )-(-13 ) = -7 + 13 = 6$

     (c) $-8, 15$

            $15 - (- 8 )= 15+ 8 = 23$

     (d) $5,-8$

           $-8 -5 = -13$