3.3 Subtract integers (Page 3/6)

Prealgebra Page 3 / 6

Have you noticed that subtraction of signed numbers can be done by adding the opposite? You will often see the idea, the Subtraction Property , written as follows:

Subtraction property

a - b = a + (−b)

Look at these two examples.

This figure has two columns. The first column has 6 minus 4. Underneath, there is a row of 6 blue circles, with the first 4 separated from the last 2. The first 4 are circled. Under this row there is 2. The second column has 6 plus negative 4. Underneath there is a row of 6 blue circles with the first 4 separated from the last 2. The first 4 are circled. Under the first four is a row of 4 red circles. Under this there is 2.

We see that $6 - 4$ gives the same answer as $6 + (−4) .$

Of course, when we have a subtraction problem that has only positive numbers, like the first example, we just do the subtraction. We already knew how to subtract $6 - 4$ long ago. But knowing that $6 - 4$ gives the same answer as $6 + (−4)$ helps when we are subtracting negative numbers.

Simplify:

ⓐ $13 - 8 and 13 + (−8)$
ⓑ $17 - 9 and −17 + (−9)$

Solution

ⓐ
	$13 - 8$ and $13 + (−8)$
Subtract to simplify.	$13 - 8 = 5$
Add to simplify.	$13 + (−8) = 5$
Subtracting 8 from 13 is the same as adding −8 to 13.

ⓑ
	$−17 - 9$ and $−17 + (−9)$
Subtract to simplify.	$−17 - 9 = −26$
Add to simplify.	$−17 + (−9) = −26$
Subtracting 9 from −17 is the same as adding −9 to −17.

ⓐ
	$9 - (−15)$ and $9 + 15$
Subtract to simplify.	$9 - (−15) = −24$
Add to simplify.	$9 + 15 = 24$
9−(−15) Subtracting −15 from 9 is the same as adding 15 to 9.

ⓑ
	$−7 - (−4)$ and $−7 + 4$
Subtract to simplify.	$−7 - (−4) = −3$
Add to simplify.	$−7 + 4 = −3$
Subtracting −4 from −7 is the same as adding 4 to −7

$5 - 3$	$–5 - (–3)$
$2$	$–2$
2 positives	2 negatives
When there would be enough counters of the color to take away, subtract.
$–5 - 3$	$5 - (–3)$
$–8$	$8$
5 negatives, want to subtract 3 positives	5 positives, want to subtract 3 negatives
need neutral pairs	need neutral pairs
When there would not be enough of the counters to take away, add neutral pairs.

Simplify inside the parentheses first.
Subtract from left to right.
Subtract.

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3.3 Subtract integers (Page 3/6)

Subtraction property

Solution

Solution

Solution

Solution

Solution

Evaluate variable expressions with integers

Solution

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