Substitution with Integers 3

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Year 9

Directed Numbers

Substitution with Integers

Substitution with Integers 3

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Question 1 of 3

1. Question
Substitute $x = 6$ $x=6$ and $y = - 5$ $y=-5$ , then solve

$x y - y$ $xy-y$
- (-25)
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Rules for Multiplying Integers

First, plug in the given values

$x = 6$ $x=6$
$y = - 5$ $y=-5$

$x$ $x$ $y$ $y$ $-$ $-$ $y$ $y$ $=$ $=$ $($ $($ $6$ $6$ $) ($ $)($ $- 5$ $-5$ $) - ($ $)-($ $- 5$ $-5$ $)$ $)$

Next, solve the multiplication.

$6 (- 5)$ $6(-5)$ $- (- 5)$ $-(-5)$ $=$ $=$ $- 30$ $-30$ $- (- 5)$ $-(-5)$ Recall,

Next, recall the rules for subtracting integers

$- 30$ $-30$ $-$ $-$ $($ $($ $-$ $-$ $5)$ $5)$ $=$ $=$ $- 30$ $-30$ $+$ $+$ $5$ $5$ Recall,

Now, solve using the number line

Start at $- 30$ $-30$ , then since $5$ $5$ is positive move right $5$ $5$ places

$- 30$ $-30$ $+ 5$ $+5$ $=$ $=$

$- 30 + 5$ $-30+5$ $=$ $=$ $- 25$ $-25$

$- 25$ $-25$
Question 2 of 3

2. Question
Substitute $x = 4$ $x=4$ , $y = 5$ $y=5$ and $z = - 3$ $z=-3$ , then solve

$y x - 3 z$ $yx-3z$
- (29)
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Rules for Multiplying Integers

First, plug in the given values

$x = 4$ $x=4$
$y = 5$ $y=5$
$z = - 3$ $z=-3$

$y$ $y$ $x$ $x$ $- 3$ $-3$ $z$ $z$ $=$ $=$ $($ $($ $5$ $5$ $) ($ $)($ $4$ $4$ $) - 3 ($ $)-3($ $- 3$ $-3$ $)$ $)$

Next, solve the multiplication.

$(5) (4)$ $(5)(4)$ $- 3 (- 3)$ $-3(-3)$ $=$ $=$ $20$ $20$ $+ 9$ $+9$ Recall,

Now, solve using the number line

Start at $20$ $20$ , then since $9$ $9$ is positive move right $9$ $9$ places

$20$ $20$ $+ 9$ $+9$ $=$ $=$

$20 + 9$ $20+9$ $=$ $=$ $29$ $29$

$29$ $29$
Question 3 of 3

3. Question
Substitute $x = 6$ $x=6$ , then solve

$5 + x + (- 8)$ $5+x+(-8)$
- (3)
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Rules for Adding and Subtracting Integers

First, plug in the given values

$x = 6$ $x=6$

$5 +$ $5+$ $x$ $x$ $+ (- 8)$ $+(-8)$ $=$ $=$ $5 +$ $5+$ $6$ $6$ $+ (- 8)$ $+(-8)$

Now, solve the equation

Keep in mind the rules for adding integers.

$5 + 6$ $5+6$ $+ (- 8)$ $+(-8)$ $=$ $=$ $11$ $11$ $+$ $+$ $($ $($ $-$ $-$ $8)$ $8)$

$=$ $=$ $11$ $11$ $-$ $-$ $8$ $8$ Recall,

$=$ $=$ $3$ $3$

$3$ $3$

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Quiz summary

Information

1. Question

Hint

Great Work!

Rules for Multiplying Integers

2. Question

Hint

Excellent!

Rules for Multiplying Integers

3. Question

Hint

Fantastic!

Rules for Adding and Subtracting Integers

Quizzes

$5 + 6$ $5+6$ $+ (- 8)$ $+(-8)$	$=$ $=$	$11$ $11$ $+$ $+$ $($ $($ $-$ $-$ $8)$ $8)$
	$=$ $=$	$11$ $11$ $-$ $-$ $8$ $8$	Recall,
	$=$ $=$	$3$ $3$