Let's solve each part step-by-step.
### Part (h)
We need to calculate the expression:
[tex]\[ (-40) - 35 - (-20) \][/tex]
1. First, handle the subtraction of a negative number:
[tex]\[ - (-20) = +20 \][/tex]
2. Substitute this into the expression:
[tex]\[ (-40) - 35 + 20 \][/tex]
3. Now, combine [tex]\(-40\)[/tex] and [tex]\(-35\)[/tex]:
[tex]\[ -40 - 35 = -75 \][/tex]
4. Finally, add 20 to the result:
[tex]\[ -75 + 20 = -55 \][/tex]
So, the value of [tex]\( h \)[/tex] is:
[tex]\[ h = -55 \][/tex]
### Part (i)
We need to calculate the expression:
[tex]\[ (-19) - (-32) + 53 - (-81) \][/tex]
1. Handle the subtractions of negative numbers:
[tex]\[ - (-32) = +32 \][/tex]
[tex]\[ - (-81) = +81 \][/tex]
2. Substitute these into the expression:
[tex]\[ (-19) + 32 + 53 + 81 \][/tex]
3. Now, combine [tex]\(-19\)[/tex] and [tex]\(+32\)[/tex]:
[tex]\[ -19 + 32 = 13 \][/tex]
4. Add 53 to the result:
[tex]\[ 13 + 53 = 66 \][/tex]
5. Finally, add 81 to the result:
[tex]\[ 66 + 81 = 147 \][/tex]
So, the value of [tex]\( i \)[/tex] is:
[tex]\[ i = 147 \][/tex]
### Part (j)
We need to calculate the expression:
[tex]\[ [6 + (-15) - (-65)] - [-12 - (-45) + 23] \][/tex]
First, solve inside the square brackets:
1. For the first set of brackets:
[tex]\[ 6 + (-15) - (-65) \][/tex]
Handle the subtraction of a negative number:
[tex]\[ - (-65) = +65 \][/tex]
Substitute this:
[tex]\[ 6 - 15 + 65 \][/tex]
Combine 6 and [tex]\(-15\)[/tex]:
[tex]\[ 6 - 15 = -9 \][/tex]
Then add 65:
[tex]\[ -9 + 65 = 56 \][/tex]
So, the first set of brackets evaluates to:
[tex]\[ [6 + (-15) - (-65)] = 56 \][/tex]
2. For the second set of brackets:
[tex]\[ -12 - (-45) + 23 \][/tex]
Handle the subtraction of a negative number:
[tex]\[ - (-45) = +45 \][/tex]
Substitute this:
[tex]\[ -12 + 45 + 23 \][/tex]
Combine [tex]\(-12\)[/tex] and [tex]\(45\)[/tex]:
[tex]\[ -12 + 45 = 33 \][/tex]
Then add 23:
[tex]\[ 33 + 23 = 56 \][/tex]
So, the second set of brackets evaluates to:
[tex]\[ [-12 - (-45) + 23] = 56 \][/tex]
Finally, we subtract the two bracketed results:
[tex]\[ 56 - 56 \][/tex]
So, the value of [tex]\( j \)[/tex] is:
[tex]\[ j = 0 \][/tex]
### Summary
- [tex]\( h = -55 \)[/tex]
- [tex]\( i = 147 \)[/tex]
- [tex]\( j = 0 \)[/tex]
