Let's go through each part step-by-step:
1. Evaluate:
(i) [tex]\(15 + (-8)\)[/tex]:
- Adding a negative number is equivalent to subtracting the absolute value of that number.
- [tex]\(15 - 8\)[/tex]
- Performing the subtraction: [tex]\(15 - 8 = 7\)[/tex]
So, [tex]\(15 + (-8) = 7\)[/tex].
(ii) [tex]\((-16) + 9\)[/tex]:
- Adding a positive number to a negative number involves subtracting the smaller absolute value from the larger absolute value and keeping the sign of the number with the larger absolute value.
- [tex]\(|9| < |-16|\)[/tex], so subtract the smaller absolute value from the larger one and keep the negative sign.
- [tex]\(-16 + 9 = -(16 - 9)\)[/tex]
- Performing the subtraction: [tex]\(16 - 9 = 7\)[/tex]
- Keeping the negative sign: [tex]\( -7 \)[/tex]
So, [tex]\((-16) + 9 = -7\)[/tex].
(iii) [tex]\((-7) + (-23)\)[/tex]:
- Adding two negative numbers involves adding their absolute values and keeping the negative sign.
- [tex]\(-7 + (-23) = - (7 + 23)\)[/tex]
- Performing the addition: [tex]\(7 + 23 = 30\)[/tex]
- Keeping the negative sign: [tex]\(-30\)[/tex]
So, [tex]\((-7) + (-23) = -30\)[/tex].
(iv) [tex]\((-32) + 47\)[/tex]:
- Adding a positive number to a negative number involves subtracting the smaller absolute value from the larger absolute value and keeping the sign of the number with the larger absolute value.
- [tex]\(|32| < |47|\)[/tex], so subtract the smaller absolute value from the larger one and keep the positive sign.
- [tex]\(-32 + 47 = 47 - 32\)[/tex]
- Performing the subtraction: [tex]\(47 - 32 = 15\)[/tex]
So, [tex]\((-32) + 47 = 15\)[/tex].
(v) [tex]\(53 + (-26)\)[/tex]:
- Adding a negative number is equivalent to subtracting the absolute value of that number.
- [tex]\(53 - 26\)[/tex]
- Performing the subtraction: [tex]\(53 - 26 = 27\)[/tex]
So, [tex]\(53 + (-26) = 27\)[/tex].
(vi) [tex]\((-48) + (-36)\)[/tex]:
- Adding two negative numbers involves adding their absolute values and keeping the negative sign.
- [tex]\((-48) + (-36) = - (48 + 36)\)[/tex]
- Performing the addition: [tex]\(48 + 36 = 84\)[/tex]
- Keeping the negative sign: [tex]\(-84\)[/tex]
So, [tex]\((-48) + (-36) = -84\)[/tex].
Therefore, the evaluated results are:
(i) [tex]\(15 + (-8) = 7\)[/tex]
(ii) [tex]\((-16) + 9 = -7\)[/tex]
(iii) [tex]\((-7) + (-23) = -30\)[/tex]
(iv) [tex]\((-32) + 47 = 15\)[/tex]
(v) [tex]\(53 + (-26) = 27\)[/tex]
(vi) [tex]\((-48) + (-36) = -84\)[/tex]
