College

Why Should You Look Out for a Pig That Knows Karate?

Simplify or evaluate each expression below, as directed. Find your answer in the corresponding answer column. Write the letter of the exercise in the box that contains the number of the answer.

SIMPLIFY:
1. [tex]\(4 \cdot 9 + 1\)[/tex]
2. [tex]\(6 + 7 \cdot 10\)[/tex]
3. [tex]\(42 - 2 \cdot 7\)[/tex]
4. [tex]\(8 + 50 \div 2\)[/tex]
5. [tex]\((10)(3) - 4\)[/tex]
6. [tex]\(2 \cdot 8 + 3 \cdot 5\)[/tex]
7. [tex]\(\frac{60}{3} - (2)(4)\)[/tex]
8. [tex]\(5 \cdot 12 + \frac{32}{16}\)[/tex]
9. [tex]\(3 + 2 \cdot 5 \cdot 8\)[/tex]
10. [tex]\((4)(6)(3) - 20 + 1\)[/tex]
11. [tex]\(18 \div 2 \times 3\)[/tex]
12. [tex]\(3 \cdot 3 + 4 \cdot 4 - 5 \cdot 5\)[/tex]

Answers:
1. 62
2. 27
3. 37
4. 31
5. 33
6. 76
7. 12
8. 0
9. 83
10. 28
11. 53
12. 26

EVALUATE if [tex]\(a=2\)[/tex], [tex]\(b=3\)[/tex], [tex]\(x=5\)[/tex], [tex]\(y=8\)[/tex], and [tex]\(w=20\)[/tex]:
1. [tex]\(4x + 7\)[/tex]
2. [tex]\(1 + 6y\)[/tex]
3. [tex]\(9 - 2b\)[/tex]
4. [tex]\(8x + 3y\)[/tex]
5. [tex]\(ab + w\)[/tex]
6. [tex]\(aw - by\)[/tex]
7. [tex]\(b + \frac{w}{x}\)[/tex]
8. [tex]\(\frac{bw}{x} - a + 7\)[/tex]
9. [tex]\(abxy - 5w\)[/tex]
10. [tex]\(36 - 4ab\)[/tex]
11. [tex]\(5 + 3x - \frac{w}{a}\)[/tex]

Answers:
1. 16
2. 10
3. 17
4. 49
5. 64
6. 12
7. 27
8. 7
9. 62
10. 140
11. 3

Answer :

Sure! Let's simplify and evaluate each expression step-by-step.

### Simplify the Expressions

1. (1) [tex]\(4 \cdot 9 + 1\)[/tex]:
[tex]\[
4 \cdot 9 = 36
\][/tex]
[tex]\[
36 + 1 = 37
\][/tex]
Answer: [tex]\(37\)[/tex]

2. (T) [tex]\(6 + 7 \cdot 10\)[/tex]:
[tex]\[
7 \cdot 10 = 70
\][/tex]
[tex]\[
6 + 70 = 76
\][/tex]
Answer: [tex]\(76\)[/tex]

3. (U) [tex]\(42 - 2 \cdot 7\)[/tex]:
[tex]\[
2 \cdot 7 = 14
\][/tex]
[tex]\[
42 - 14 = 28
\][/tex]
Answer: [tex]\(28\)[/tex]

4. (O) [tex]\(8 + 50 \div 2\)[/tex]:
[tex]\[
50 \div 2 = 25
\][/tex]
[tex]\[
8 + 25 = 33
\][/tex]
Answer: [tex]\(33\)[/tex]

5. (E) [tex]\((10)(3) - 4\)[/tex]:
[tex]\[
10 \cdot 3 = 30
\][/tex]
[tex]\[
30 - 4 = 26
\][/tex]
Answer: [tex]\(26\)[/tex]

6. (G) [tex]\(2 \cdot 8 + 3 \cdot 5\)[/tex]:
[tex]\[
2 \cdot 8 = 16
\][/tex]
[tex]\[
3 \cdot 5 = 15
\][/tex]
[tex]\[
16 + 15 = 31
\][/tex]
Answer: [tex]\(31\)[/tex]

7. (A) [tex]\(\frac{60}{3} - (2)(4)\)[/tex]:
[tex]\[
60 \div 3 = 20
\][/tex]
[tex]\[
2 \cdot 4 = 8
\][/tex]
[tex]\[
20 - 8 = 12
\][/tex]
Answer: [tex]\(12\)[/tex]

8. (T) [tex]\(5 \cdot 12 + \frac{32}{16}\)[/tex]:
[tex]\[
5 \cdot 12 = 60
\][/tex]
[tex]\[
32 \div 16 = 2
\][/tex]
[tex]\[
60 + 2 = 62
\][/tex]
Answer: [tex]\(62\)[/tex]

9. (Y) [tex]\(3 + 2 \cdot 5 \cdot 8\)[/tex]:
[tex]\[
2 \cdot 5 = 10
\][/tex]
[tex]\[
10 \cdot 8 = 80
\][/tex]
[tex]\[
3 + 80 = 83
\][/tex]
Answer: [tex]\(83\)[/tex]

10. (1) [tex]\((4)(6)(3) - 20 + 1\)[/tex]:
[tex]\[
4 \cdot 6 = 24
\][/tex]
[tex]\[
24 \cdot 3 = 72
\][/tex]
[tex]\[
72 - 20 = 52
\][/tex]
[tex]\[
52 + 1 = 53
\][/tex]
Answer: [tex]\(53\)[/tex]

11. (O) [tex]\(18 \div 2 \cdot 3\)[/tex]:
[tex]\[
18 \div 2 = 9
\][/tex]
[tex]\[
9 \cdot 3 = 27
\][/tex]
Answer: [tex]\(27\)[/tex]

12. (R) [tex]\(3 \cdot 3 + 4 \cdot 4 - 5 \cdot 5\)[/tex]:
[tex]\[
3 \cdot 3 = 9
\][/tex]
[tex]\[
4 \cdot 4 = 16
\][/tex]
[tex]\[
5 \cdot 5 = 25
\][/tex]
[tex]\[
9 + 16 = 25
\][/tex]
[tex]\[
25 - 25 = 0
\][/tex]
Answer: [tex]\(0\)[/tex]

### Evaluate Expressions with [tex]\( a = 2 \)[/tex], [tex]\( b = 3 \)[/tex], [tex]\( x = 5 \)[/tex], [tex]\( y = 8 \)[/tex], [tex]\( w = 20 \)[/tex]

1. (I) [tex]\(4x + 7\)[/tex]:
[tex]\[
4 \cdot 5 = 20
\][/tex]
[tex]\[
20 + 7 = 27
\][/tex]
Answer: [tex]\(27\)[/tex]

2. (C) [tex]\(1 + 6y\)[/tex]:
[tex]\[
6 \cdot 8 = 48
\][/tex]
[tex]\[
1 + 48 = 49
\][/tex]
Answer: [tex]\(49\)[/tex]

3. (H) [tex]\(9 - 2b\)[/tex]:
[tex]\[
2 \cdot 3 = 6
\][/tex]
[tex]\[
9 - 6 = 3
\][/tex]
Answer: [tex]\(3\)[/tex]

4. (O) [tex]\(8x + 3y\)[/tex]:
[tex]\[
8 \cdot 5 = 40
\][/tex]
[tex]\[
3 \cdot 8 = 24
\][/tex]
[tex]\[
40 + 24 = 64
\][/tex]
Answer: [tex]\(64\)[/tex]

5. (M) [tex]\(a + bw\)[/tex]:
[tex]\[
b \cdot w = 3 \cdot 20 = 60
\][/tex]
[tex]\[
2 + 60 = 62
\][/tex]
Answer: [tex]\(62\)[/tex]

6. (V) [tex]\(aw - by\)[/tex]:
[tex]\[
a \cdot w = 2 \cdot 20 = 40
\][/tex]
[tex]\[
b \cdot y = 3 \cdot 8 = 24
\][/tex]
[tex]\[
40 - 24 = 16
\][/tex]
Answer: [tex]\(16\)[/tex]

7. (P) [tex]\(b + \frac{w}{x}\)[/tex]:
[tex]\[
\frac{w}{x} = \frac{20}{5} = 4
\][/tex]
[tex]\[
3 + 4 = 7
\][/tex]
Answer: [tex]\(7\)[/tex]

8. (G) [tex]\(\frac{bw}{x} - a + 7\)[/tex]:
[tex]\[
bw = 3 \cdot 20 = 60
\][/tex]
[tex]\[
\frac{60}{5} = 12
\][/tex]
[tex]\[
12 - 2 + 7 = 17
\][/tex]
Answer: [tex]\(17\)[/tex]

9. (K) [tex]\(abxy - 5w\)[/tex]:
[tex]\[
abxy = 2 \cdot 3 \cdot 5 \cdot 8 = 240
\][/tex]
[tex]\[
5w = 5 \cdot 20 = 100
\][/tex]
[tex]\[
240 - 100 = 140
\][/tex]
Answer: [tex]\(140\)[/tex]

10. (H) [tex]\(36 - 4ab\)[/tex]:
[tex]\[
4ab = 4 \cdot 2 \cdot 3 = 24
\][/tex]
[tex]\[
36 - 24 = 12
\][/tex]
Answer: [tex]\(12\)[/tex]

11. (P) [tex]\(5 + 3x - \frac{w}{a}\)[/tex]:
[tex]\[
3x = 3 \cdot 5 = 15
\][/tex]
[tex]\[
\frac{w}{a} = \frac{20}{2} = 10
\][/tex]
[tex]\[
5 + 15 - 10 = 10
\][/tex]
Answer: [tex]\(10\)[/tex]

Now, let's match the answers found above to the given list and assign the corresponding letters to their boxes:

- (17) = T
- (2) = T
- (14) = U
- (18) = R
- (11) = E
- (5) = G
- (15) = A
- (9) = Y
- (12) = R
- (10) = 1
- (4) = I
- (16) = K
- (3) = P