Question

activity 1
tell the value for the variable.

1. (mdiv8 = 6)
2. (4cdot7=n)
3. (5 + p=14)
4. (r - 8=9)
5. (35div5=t)
6. (3cdot u = 18)

activity 2

1. does (x + y=y + x) describe the pattern shown by these number sentences?

(4 + 5=5 + 4)
(3+2 = 2 + 3)
(7 + 8=8 + 7)

1. does (acdot bcdot c=ccdot bcdot a) describe the pattern shown by these number sentences?

(3cdot\frac{1}{3}cdot1=\frac{1}{3}cdot1cdot3)
(2cdot4cdot6 = 4cdot6cdot2)
(8cdot1.2cdot3=1.2cdot3cdot8)

1. does (acdot0 = 0) describe the pattern shown by these number sentences?

(0cdot0 = 0)
(3cdot3 = 9)
(\frac{1}{4}cdot\frac{1}{4}=\frac{1}{16})

1. does (0 + w=w) describe the pattern shown by these number sentences?

(0+\frac{1}{3}=\frac{1}{3})
(0 + 0.25=0.25)
(0+5 = 5)

Explanation:

Activity 1

1. Solve for m

Given $m\div8 = 6$, multiply both sides by 8.
$m=6\times8 = 48$

2. Solve for n

$4\cdot7=n$, so $n = 28$

3. Solve for p

Given $5 + p=14$, subtract 5 from both sides.
$p=14 - 5=9$

4. Solve for r

Given $r - 8=9$, add 8 to both sides.
$r=9 + 8=17$

5. Solve for t

$35\div5=t$, so $t = 7$

6. Solve for u

Given $3\cdot u=18$, divide both sides by 3.
$u=\frac{18}{3}=6$

Activity 2

1. Commutative property of addition

The equation $x + y=y + x$ is the commutative - property of addition. The number sentences $4 + 5=5 + 4$, $3+2 = 2 + 3$, $7 + 8=8 + 7$ follow this property. So, yes.

2. Commutative property of multiplication

The equation $a\cdot b\cdot c=c\cdot b\cdot a$ is related to the commutative property of multiplication. The number sentences $3\cdot\frac{1}{3}\cdot1=\frac{1}{3}\cdot1\cdot3$, $2\cdot4\cdot6 = 4\cdot6\cdot2$, $8\cdot1.2\cdot3=1.2\cdot3\cdot8$ follow this property. So, yes.

3. Zero - property of multiplication

The equation $a\cdot0 = 0$ is the zero - property of multiplication. But the number sentence $3\cdot3 = 9$ and $\frac{1}{4}\cdot\frac{1}{4}=\frac{1}{16}$ do not follow this property. So, no.

4. Identity property of addition

The equation $0+w = w$ is the identity property of addition. The number sentences $0+\frac{1}{3}=\frac{1}{3}$, $0 + 0.25=0.25$, $0+5 = 5$ follow this property. So, yes.

Answer:

Activity 1

1. $m = 48$
2. $n = 28$
3. $p = 9$
4. $r = 17$
5. $t = 7$
6. $u = 6$

Activity 2

1. Yes
2. Yes
3. No
4. Yes