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Question Perform basic arithmetic operations: (a) −355−(−139)-355-(-139), (b) −24+42−6\frac{-24+42}{-6}, (c) 13−(−5)13-(-5), (d) −216+138-216+138, (e) −125−(−341)-125-(-341).

Studdy Solution

STEP 1

Assumptions
1. The operations involve basic arithmetic with negative and positive integers.
2. The subtraction of a negative number is equivalent to addition.
3. The division of two numbers with the same sign results in a positive quotient, while division of two numbers with different signs results in a negative quotient.

STEP 2

For part (a), we need to subtract a negative number from a negative number. Remember that subtracting a negative is the same as adding a positive.
−355−(−139)-355 - (-139)

STEP 3

Rewrite the subtraction of a negative as addition.
−355+139-355 + 139

STEP 4

Perform the addition by subtracting the smaller absolute value from the larger absolute value and keeping the sign of the number with the larger absolute value.
−355+139=−(355−139)-355 + 139 = -(355 - 139)

STEP 5

Calculate the difference.
−355+139=−(355−139)=−(216)=−216-355 + 139 = -(355 - 139) = -(216) = -216

STEP 6

For part (b), we need to add two numbers and then divide the result by a negative number.
−24+42−6\frac{-24 + 42}{-6}

STEP 7

First, perform the addition in the numerator.
−24+42=18-24 + 42 = 18

STEP 8

Now, divide the result by the negative denominator.
18−6\frac{18}{-6}

STEP 9

Calculate the quotient, remembering that a positive divided by a negative is a negative.
18−6=−3\frac{18}{-6} = -3

STEP 10

For part (c), we need to subtract a negative number from a positive number.
13−(−5)13 - (-5)

STEP 11

Rewrite the subtraction of a negative as addition.
13+513 + 5

STEP 12

Perform the addition.
13+5=1813 + 5 = 18

STEP 13

For part (d), we need to add a negative number to a positive number.
−216+138-216 + 138

STEP 14

Perform the addition by subtracting the smaller absolute value from the larger absolute value and keeping the sign of the number with the larger absolute value.
−216+138=−(216−138)-216 + 138 = -(216 - 138)

STEP 15

Calculate the difference.
−216+138=−(216−138)=−(78)=−78-216 + 138 = -(216 - 138) = -(78) = -78

STEP 16

For part (e), we need to subtract a negative number from a negative number.
−125−(−341)-125 - (-341)

STEP 17

Rewrite the subtraction of a negative as addition.
−125+341-125 + 341

STEP 18

Perform the addition by subtracting the smaller absolute value from the larger absolute value and keeping the sign of the number with the larger absolute value.
−125+341=341−125-125 + 341 = 341 - 125

STEP 19

Calculate the difference.
−125+341=341−125=216-125 + 341 = 341 - 125 = 216
The solutions to the computations are: (a) −216-216 (b) −3-3 (c) 1818 (d) −78-78 (e) 216216

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