Question Find the values of $-22+5$ , $-22-(-5)$ , $(-22)(-5)$ , and $-22 \div 5$ .

Studdy Solution

STEP 1

Assumptions
1. We are dealing with basic arithmetic operations: addition, subtraction, multiplication, and division.
2. Negative numbers are involved in the calculations.
3. The order of operations is not relevant here as each expression involves only one operation.

STEP 2

For expression (a), we need to add a negative number to a positive number. The rule is to subtract the absolute values and keep the sign of the number with the larger absolute value.
$-22 + 5$

STEP 3

Calculate the sum by subtracting the absolute values and keeping the sign of the larger absolute value.
$-22 + 5 = -(22 - 5)$

STEP 4

Perform the subtraction.
$-22 + 5 = -(22 - 5) = -(17) = -17$
The value of expression (a) is $-17$ .

STEP 5

For expression (b), we need to subtract a negative number from a negative number. The rule is to add the absolute values when subtracting a negative number (since subtracting a negative is equivalent to adding a positive).
$-22 - (-5)$

STEP 6

Convert the subtraction of a negative number to addition.
$-22 - (-5) = -22 + 5$

STEP 7

This is the same expression as in (a), so we already know the result.
$-22 - (-5) = -22 + 5 = -17$
The value of expression (b) is $-17$ .

STEP 8

For expression (c), we need to multiply two negative numbers. The rule is that the product of two negative numbers is a positive number.
$(-22)(-5)$

STEP 9

Calculate the product.
$(-22)(-5) = 22 \times 5$

STEP 10

Perform the multiplication.
$(-22)(-5) = 22 \times 5 = 110$
The value of expression (c) is $110$ .

STEP 11

For expression (d), we need to divide a negative number by a positive number. The rule is that the quotient of a negative number and a positive number is a negative number.
$-22 \div 5$

STEP 12

Calculate the division.
$-22 \div 5 = -\left(\frac{22}{5}\right)$

STEP 13

Perform the division.
$-22 \div 5 = -\left(\frac{22}{5}\right) = -4.4$
The value of expression (d) is $-4.4$ .

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