Integers Involving Variables 3

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Year 9

Directed Numbers

Integers Involving Variables

Integers Involving Variables 3

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Question 1 of 4

1. Question
Evaluate

$4a-2b-6a+8b$
- (-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 $a$ variable ( $4a-6a$ ).

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

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

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

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

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

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

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

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

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

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

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

Finally, combine the terms.

$-2a+6b$

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

2. Question
Evaluate

$-24a^2divide-6a$
- (4a)
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Rules for Dividing Integers

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

$-24a^2divide-6a$ $=$ $(-24a^2)/(-6a)$

Simplify the fraction

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

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

$=$ $4a^(1)$

$=$ $4a$

$4a$
Question 3 of 4

3. Question
Evaluate

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

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

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

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

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

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

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

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

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

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

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

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

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

Finally, combine the terms.

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

$-17m-n+5$

$-17m-n+5$
Question 4 of 4

4. Question
Evaluate

$8axx(-3b)xx2$
- (-48ab)
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Rules for Multiplying Integers

First, separate the variables from the coefficients to make the solution easier.

$8xx(-3)xx2xxaxxb$

Next, perform the multiplication.

$8xx(-3)$ $xx2xxaxxb$

$-24$ $xx2xxaxxb$ Recall,

$-24xx2$ $xxaxxb$

$-48$ $xxaxxb$ Recall,

$-48ab$ Add the variables back to the coefficient

$-48ab$

Integers Involving 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

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

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

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

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

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

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

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