Question

tell the value for the variable.

1. m÷8 = 6
2. 4·7 = n
3. 5 + p = 14
4. r - 8 = 9
5. 35÷5 = t
6. 3·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 a·b·c = c·b·a describe the pattern shown by these number sentences?

3·1/3·1 = 1/3·1·3
2·4·6 = 4·6·2
8·1.2·3 = 1.2·3·8

1. does a·0 = 0 describe the pattern shown by these number sentences?

0·0 = 0
3·3 = 9
1/4·1/4 = 1/16

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

0 + 1/3 = 1/3
0 + 0.25 = 0.25
0 + 5 = 5

Explanation:

Activity 1

1. Solve for m in m÷8 = 6

Multiply both sides by 8.
$m=6\times8$
$m = 48$

2. Solve for n in 4·7 = n

Multiply 4 and 7.
$n=4\times7$
$n = 28$

3. Solve for p in 5 + p = 14

Subtract 5 from both sides.
$p=14 - 5$
$p = 9$

4. Solve for r in r - 8 = 9

Add 8 to both sides.
$r=9 + 8$
$r = 17$

5. Solve for t in 35÷5 = t

Perform the division.
$t=\frac{35}{5}$
$t = 7$

6. Solve for u in 3·u = 18

Divide both sides by 3.
$u=\frac{18}{3}$
$u = 6$

Activity 2

1. Analyze x + y = y + x

The given number - sentences 4 + 5 = 5 + 4, 3+2 = 2 + 3, 7 + 8 = 8 + 7 follow the commutative property of addition (a + b=b + a). So, yes.

2. Analyze a·b·c = c·b·a

The given number - sentences 3·$\frac{1}{3}$·1=$\frac{1}{3}$·1·3, 2·4·6 = 4·6·2, 8·1.2·3 = 1.2·3·8 follow the commutative property of multiplication (a×b×c = c×b×a). So, yes.

3. Analyze a·0 = 0

The number - sentences 0·0 = 0 follow the zero - property of multiplication (a×0 = 0). But 3·3 = 9 and $\frac{1}{4}$·$\frac{1}{4}=\frac{1}{16}$ do not follow a·0 = 0. So, no.

4. Analyze 0 + w = w

The number - sentences 0+$\frac{1}{3}=\frac{1}{3}$, 0 + 0.25 = 0.25, 0 + 5 = 5 follow the identity property of addition (0 + a=a). 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