Substitution with Integers 1

Years

Year 8

Directed Numbers

Substitution with Integers

Substitution with Integers 1

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Question 1 of 4

1. Question
Substitute $x = - 6$ $x=-6$ and $y = 4$ $y=4$ , then solve

$x + y$ $x+y$
- (-2)
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Rules for Adding and Subtracting Integers

First, plug in the given values

$x = - 6$ $x=-6$
$y = 4$ $y=4$

$x$ $x$ $+$ $+$ $y$ $y$ $=$ $=$ $- 6$ $-6$ $+$ $+$ $4$ $4$

Now, solve using the number line

Start at $- 6$ $-6$ , then since $4$ $4$ is positive move right $4$ $4$ places

$- 6$ $-6$ $+ 4$ $+4$ $=$ $=$

$- 6 + 4$ $-6+4$ $=$ $=$ $- 2$ $-2$

$- 2$ $-2$
Question 2 of 4

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

$y - 2 x$ $y-2x$
- (-3)
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Rules for Adding and Subtracting Integers

First, plug in the given values

$x = 4$ $x=4$
$y = 5$ $y=5$

$y$ $y$ $- 2$ $-2$ $x$ $x$ $=$ $=$ $5$ $5$ $- 2 ($ $-2($ $4$ $4$ $)$ $)$

$=$ $=$ $5 - 8$ $5-8$ Solve the multiplication

Now, solve using the number line

Start at $5$ $5$ , then subtract $8$ $8$ by moving left $8$ $8$ places

$5$ $5$ $- 8$ $-8$ $=$ $=$

$5 - 8$ $5-8$ $=$ $=$ $- 3$ $-3$

$- 3$ $-3$
Question 3 of 4

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

$3 x y \div z$ $3xy divide z$
- (-20)
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Rules for Dividing Integers

First, plug in the given values

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

$3$ $3$ $x$ $x$ $y$ $y$ $\div$ $divide$ $z$ $z$ $=$ $=$ $3 ($ $3($ $4$ $4$ $) ($ $)($ $5$ $5$ $) \div$ $) divide$ $- 3$ $-3$

Next, solve the multiplication.

$3 (4) (5)$ $3(4)(5)$ $\div - 3$ $divide -3$ $=$ $=$ $60$ $60$ $\div - 3$ $divide -3$

Finally, solve the division.

$60 \div - 3$ $60 divide -3$ $=$ $=$ $- 20$ $-20$ Recall,

$- 20$ $-20$
Question 4 of 4

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

$- 3 + 3 x + 3 y$ $-3+3x+3y$
- (0)
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Rules for Multiplying Integers

First, plug in the given values

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

$- 3 + 3$ $-3+3$ $x$ $x$ $+ 3$ $+3$ $y$ $y$ $=$ $=$ $- 3 + 3 ($ $-3+3($ $6$ $6$ $) + 3 ($ $)+3($ $- 5$ $-5$ $)$ $)$

Next, solve the multiplication.

$- 3 +$ $-3+$ $(3) (6)$ $(3)(6)$ $+ 3 (- 5)$ $+3(-5)$ $=$ $=$ $- 3 +$ $-3+$ $18$ $18$ $- 15$ $-15$ Recall,

Now, solve the equation

Keep in mind the rules for adding integers.

$- 3 + 18$ $-3+18$ $- 15$ $-15$ $=$ $=$ $15$ $15$ $- 15$ $-15$

$=$ $=$ $0$ $0$

$0$ $0$

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Quiz summary

Information

1. Question

Hint

Well Done!

Rules for Adding and Subtracting Integers

2. Question

Hint

Excellent!

Rules for Adding and Subtracting Integers

3. Question

Hint

Keep Going!

Rules for Dividing Integers

4. Question

Hint

Well Done!

Rules for Multiplying Integers

Quizzes

$y$ $y$ $- 2$ $-2$ $x$ $x$	$=$ $=$	$5$ $5$ $- 2 ($ $-2($ $4$ $4$ $)$ $)$
	$=$ $=$	$5 - 8$ $5-8$	Solve the multiplication

$- 3 + 18$ $-3+18$ $- 15$ $-15$	$=$ $=$	$15$ $15$ $- 15$ $-15$
	$=$ $=$	$0$ $0$