Negative Numbers with Variables 3

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Question 1 of 4

1. Question
Evaluate

$4 a - 2 b - 6 a + 8 b$ $4a-2b-6a+8b$
- (-2a+6b, 6b-2a)
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Terms with the same variable can be added or subtracted.

First, solve for the values with an $a$ $a$ variable ( $4 a - 6 a$ $4a-6a$ ).

Since the signs are different $(+ -)$ $(+ -)$ we will find the difference of the two numbers

$6 - 4$ $6-4$ $=$ $=$ $2$ $2$ Find the Difference

$Difference$ $\text(Difference)$ $=$ $=$ $2$ $2$

Insert the sign of the larger number $(- 6)$ $(-6)$ to the difference as well as the variable $a$ $a$ .

$4 a - 6 a$ $4a-6a$ $=$ $=$ $- 2 a$ $-2a$ Insert a negative sign since the larger number, $6$ $6$ is negative

Next, solve for the values with a $b$ $b$ variable ( $- 2 b + 8 b$ $-2b+8b$ ).

Since the signs are different $(- +)$ $(- +)$ we will find the difference of the two numbers

$8 - 2$ $8-2$ $=$ $=$ $6$ $6$ Find the Difference

$Difference$ $\text(Difference)$ $=$ $=$ $6$ $6$

Insert the sign of the larger number $(+ 8)$ $(+8)$ to the difference as well as the variable $b$ $b$ .

$- 2 b + 8 b$ $-2b+8b$ $=$ $=$ $6 b$ $6b$ Use a positive sign since the larger number, $8$ $8$ is positive

Finally, combine the terms.

$- 2 a + 6 b$ $-2a+6b$

$- 2 a + 6 b$ $-2a+6b$
Question 2 of 4

2. Question
Evaluate

$- 24 a^{2} \div - 6 a$ $-24a^2divide-6a$
- (4a)
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Rules for Dividing Integers

Transform the expression into a fraction to make it easier to solve.

$- 24 a^{2} \div - 6 a$ $-24a^2divide-6a$ $=$ $=$ $\frac{- 24 a^{2}}{- 6 a}$ $(-24a^2)/(-6a)$

Simplify the fraction

$\frac{\color{#CC0000}{-24}a^2}{\color{#CC0000}{-6}a}$ $=$ $=$ $4$ $4$ $\frac{a^{2}}{a}$ $(a^2)/a$ Recall,

$=$ $=$ $4 a^{2 - 1}$ $4a^(2-1)$ Recall rules for indices

$=$ $=$ $4 a^{1}$ $4a^(1)$

$=$ $=$ $4 a$ $4a$

$4 a$ $4a$
Question 3 of 4

3. Question
Evaluate

$m + 3 n - 18 m - 4 n + 5$ $m+3n-18m-4n+5$
- (-17m-n+5)
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Terms with the same variable can be added or subtracted.

First, solve for the values with an $m$ $m$ variable ( $m - 18 m$ $m-18m$ ).

Since the signs are different $(+ -)$ $(+ -)$ we will find the difference of the two numbers

$18 - 1$ $18-1$ $=$ $=$ $17$ $17$ Find the Difference

$Difference$ $\text(Difference)$ $=$ $=$ $17$ $17$

Insert the sign of the larger number $(- 18)$ $(-18)$ to the difference as well as the variable $m$ $m$ .

$m - 18 m$ $m-18m$ $=$ $=$ $- 17 m$ $-17m$ Insert a negative sign since the larger number, $18$ $18$ is negative

Next, solve for the values with a $n$ $n$ variable ( $3 n - 4 n$ $3n-4n$ ).

Since the signs are different $(+ -)$ $(+ -)$ we will find the difference of the two numbers

$4 - 3$ $4-3$ $=$ $=$ $1$ $1$ Find the Difference

$Difference$ $\text(Difference)$ $=$ $=$ $1$ $1$

Insert the sign of the larger number $(- 4)$ $(-4)$ to the difference as well as the variable $n$ $n$ .

$3 n - 4 n$ $3n-4n$ $=$ $=$ $- n$ $-n$ Insert a negative sign since the larger number, $4$ $4$ is negative

Finally, combine the terms.

Don’t forget to add the constant, $5$ $5$ .

$- 17 m - n + 5$ $-17m-n+5$

$- 17 m - n + 5$ $-17m-n+5$

Question 4 of 4

Evaluate

8 a \times (- 3 b) \times 2

$8axx(-3b)xx2$

(-48ab)

$8 \times (- 3)$ $8xx(-3)$ $\times 2 \times a \times b$ $xx2xxaxxb$
$- 24$ $-24$ $\times 2 \times a \times b$ $xx2xxaxxb$			Recall,
$- 24 \times 2$ $-24xx2$ $\times a \times b$ $xxaxxb$
$- 48$ $-48$ $\times a \times b$ $xxaxxb$			Recall,
$- 48 a b$ $-48ab$			Add the variables back to the coefficient

Negative Numbers with Variables 3

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Quiz summary

Information

1. Question

Hint

Well Done!

2. Question

Hint

Fantastic!

Rules for Dividing Integers

3. Question

Hint

Correct!

4. Question

Hint

Nice Job!

Rules for Multiplying Integers

Quizzes

$6 - 4$ $6-4$	$=$ $=$	$2$ $2$	Find the Difference
$Difference$ $\text(Difference)$	$=$ $=$	$2$ $2$

$8 - 2$ $8-2$	$=$ $=$	$6$ $6$	Find the Difference
$Difference$ $\text(Difference)$	$=$ $=$	$6$ $6$

$\frac{\color{#CC0000}{-24}a^2}{\color{#CC0000}{-6}a}$	$=$ $=$	$4$ $4$ $\frac{a^{2}}{a}$ $(a^2)/a$	Recall,

	$=$ $=$	$4 a^{2 - 1}$ $4a^(2-1)$	Recall rules for indices
	$=$ $=$	$4 a^{1}$ $4a^(1)$
	$=$ $=$	$4 a$ $4a$

$18 - 1$ $18-1$	$=$ $=$	$17$ $17$	Find the Difference
$Difference$ $\text(Difference)$	$=$ $=$	$17$ $17$

$4 - 3$ $4-3$	$=$ $=$	$1$ $1$	Find the Difference
$Difference$ $\text(Difference)$	$=$ $=$	$1$ $1$