Math problem worksheet featuring eight equations to solve using order of operations.
A math worksheet with eight problems, each labeled A through H, involving arithmetic operations with parentheses and order of operations.
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Step-by-step solution for: Simplifying Numerical Expressions Matching (TEK 5.4F)
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Show Answer Key & Explanations
Step-by-step solution for: Simplifying Numerical Expressions Matching (TEK 5.4F)
To solve the problem, we need to evaluate each expression in the left column and match it with the corresponding result in the right column. Let's go through each expression step by step.
#### 1. \( (4 \times 8) - 2 \)
- First, calculate \( 4 \times 8 \):
\[
4 \times 8 = 32
\]
- Then, subtract 2:
\[
32 - 2 = 30
\]
- Result: 30
#### 2. \( 3 + 4 \times (6 - 1) \)
- First, calculate the expression inside the parentheses:
\[
6 - 1 = 5
\]
- Then, multiply \( 4 \times 5 \):
\[
4 \times 5 = 20
\]
- Finally, add 3:
\[
3 + 20 = 23
\]
- Result: 23
#### 3. \( 56 \div 7 \times (9 - 4) \)
- First, calculate the expression inside the parentheses:
\[
9 - 4 = 5
\]
- Then, divide \( 56 \div 7 \):
\[
56 \div 7 = 8
\]
- Finally, multiply \( 8 \times 5 \):
\[
8 \times 5 = 40
\]
- Result: 40
#### 4. \( (17 - 14) + (5 + 3) \)
- First, calculate the expressions inside the parentheses:
\[
17 - 14 = 3 \quad \text{and} \quad 5 + 3 = 8
\]
- Then, add the results:
\[
3 + 8 = 11
\]
- Result: 11
#### 5. \( 63 - 9 - 6 \)
- Perform the operations from left to right:
\[
63 - 9 = 54
\]
\[
54 - 6 = 48
\]
- Result: 48
#### 6. \( (100 + 10) \div 4 \times 2 \)
- First, calculate the expression inside the parentheses:
\[
100 + 10 = 110
\]
- Then, divide \( 110 \div 4 \):
\[
110 \div 4 = 27.5
\]
- Finally, multiply \( 27.5 \times 2 \):
\[
27.5 \times 2 = 55
\]
- Result: 55
#### 7. \( (5 - 20 + 20) \times 4 \)
- First, simplify the expression inside the parentheses:
\[
5 - 20 + 20 = 5
\]
- Then, multiply by 4:
\[
5 \times 4 = 20
\]
- Result: 20
#### 8. \( (144 + 12) + (121 + 11) + 1 \)
- First, calculate the expressions inside the parentheses:
\[
144 + 12 = 156 \quad \text{and} \quad 121 + 11 = 132
\]
- Then, add these results:
\[
156 + 132 = 288
\]
- Finally, add 1:
\[
288 + 1 = 289
\]
- Result: 289
Now, let's evaluate each expression in the right column:
#### A. \( (3 + 30 + 10) \times 4 \)
- First, calculate the expression inside the parentheses:
\[
3 + 30 + 10 = 43
\]
- Then, multiply by 4:
\[
43 \times 4 = 172
\]
- Result: 172
#### B. \( 88 \div (32 \div 4) \)
- First, calculate the expression inside the parentheses:
\[
32 \div 4 = 8
\]
- Then, divide \( 88 \div 8 \):
\[
88 \div 8 = 11
\]
- Result: 11
#### C. \( 12 - (40 \div 4 - 6) \)
- First, calculate the expression inside the parentheses:
\[
40 \div 4 = 10
\]
\[
10 - 6 = 4
\]
- Then, subtract:
\[
12 - 4 = 8
\]
- Result: 8
#### D. \( (81 + 9) \div 5 - 5 \)
- First, calculate the expression inside the parentheses:
\[
81 + 9 = 90
\]
- Then, divide \( 90 \div 5 \):
\[
90 \div 5 = 18
\]
- Finally, subtract 5:
\[
18 - 5 = 13
\]
- Result: 13
#### E. \( 3 \times 3 \times (50 + 25) \)
- First, calculate the expression inside the parentheses:
\[
50 + 25 = 75
\]
- Then, multiply:
\[
3 \times 3 = 9
\]
\[
9 \times 75 = 675
\]
- Result: 675
#### F. \( 3 + 40 \times 2 \)
- First, perform the multiplication:
\[
40 \times 2 = 80
\]
- Then, add 3:
\[
3 + 80 = 83
\]
- Result: 83
#### G. \( 27 + 9 - 2 \)
- Perform the operations from left to right:
\[
27 + 9 = 36
\]
\[
36 - 2 = 34
\]
- Result: 34
#### H. \( (5 \times 2) \times 3 \)
- First, calculate the expression inside the parentheses:
\[
5 \times 2 = 10
\]
- Then, multiply by 3:
\[
10 \times 3 = 30
\]
- Result: 30
Now, we match the results from the left column with the results from the right column:
- 1. \( (4 \times 8) - 2 \) → 30 → H
- 2. \( 3 + 4 \times (6 - 1) \) → 23 → F
- 3. \( 56 \div 7 \times (9 - 4) \) → 40 → G
- 4. \( (17 - 14) + (5 + 3) \) → 11 → B
- 5. \( 63 - 9 - 6 \) → 48 → E
- 6. \( (100 + 10) \div 4 \times 2 \) → 55 → A
- 7. \( (5 - 20 + 20) \times 4 \) → 20 → C
- 8. \( (144 + 12) + (121 + 11) + 1 \) → 289 → D
\[
\boxed{H, F, G, B, E, A, C, D}
\]
Left Column: Expressions
#### 1. \( (4 \times 8) - 2 \)
- First, calculate \( 4 \times 8 \):
\[
4 \times 8 = 32
\]
- Then, subtract 2:
\[
32 - 2 = 30
\]
- Result: 30
#### 2. \( 3 + 4 \times (6 - 1) \)
- First, calculate the expression inside the parentheses:
\[
6 - 1 = 5
\]
- Then, multiply \( 4 \times 5 \):
\[
4 \times 5 = 20
\]
- Finally, add 3:
\[
3 + 20 = 23
\]
- Result: 23
#### 3. \( 56 \div 7 \times (9 - 4) \)
- First, calculate the expression inside the parentheses:
\[
9 - 4 = 5
\]
- Then, divide \( 56 \div 7 \):
\[
56 \div 7 = 8
\]
- Finally, multiply \( 8 \times 5 \):
\[
8 \times 5 = 40
\]
- Result: 40
#### 4. \( (17 - 14) + (5 + 3) \)
- First, calculate the expressions inside the parentheses:
\[
17 - 14 = 3 \quad \text{and} \quad 5 + 3 = 8
\]
- Then, add the results:
\[
3 + 8 = 11
\]
- Result: 11
#### 5. \( 63 - 9 - 6 \)
- Perform the operations from left to right:
\[
63 - 9 = 54
\]
\[
54 - 6 = 48
\]
- Result: 48
#### 6. \( (100 + 10) \div 4 \times 2 \)
- First, calculate the expression inside the parentheses:
\[
100 + 10 = 110
\]
- Then, divide \( 110 \div 4 \):
\[
110 \div 4 = 27.5
\]
- Finally, multiply \( 27.5 \times 2 \):
\[
27.5 \times 2 = 55
\]
- Result: 55
#### 7. \( (5 - 20 + 20) \times 4 \)
- First, simplify the expression inside the parentheses:
\[
5 - 20 + 20 = 5
\]
- Then, multiply by 4:
\[
5 \times 4 = 20
\]
- Result: 20
#### 8. \( (144 + 12) + (121 + 11) + 1 \)
- First, calculate the expressions inside the parentheses:
\[
144 + 12 = 156 \quad \text{and} \quad 121 + 11 = 132
\]
- Then, add these results:
\[
156 + 132 = 288
\]
- Finally, add 1:
\[
288 + 1 = 289
\]
- Result: 289
Right Column: Results
Now, let's evaluate each expression in the right column:
#### A. \( (3 + 30 + 10) \times 4 \)
- First, calculate the expression inside the parentheses:
\[
3 + 30 + 10 = 43
\]
- Then, multiply by 4:
\[
43 \times 4 = 172
\]
- Result: 172
#### B. \( 88 \div (32 \div 4) \)
- First, calculate the expression inside the parentheses:
\[
32 \div 4 = 8
\]
- Then, divide \( 88 \div 8 \):
\[
88 \div 8 = 11
\]
- Result: 11
#### C. \( 12 - (40 \div 4 - 6) \)
- First, calculate the expression inside the parentheses:
\[
40 \div 4 = 10
\]
\[
10 - 6 = 4
\]
- Then, subtract:
\[
12 - 4 = 8
\]
- Result: 8
#### D. \( (81 + 9) \div 5 - 5 \)
- First, calculate the expression inside the parentheses:
\[
81 + 9 = 90
\]
- Then, divide \( 90 \div 5 \):
\[
90 \div 5 = 18
\]
- Finally, subtract 5:
\[
18 - 5 = 13
\]
- Result: 13
#### E. \( 3 \times 3 \times (50 + 25) \)
- First, calculate the expression inside the parentheses:
\[
50 + 25 = 75
\]
- Then, multiply:
\[
3 \times 3 = 9
\]
\[
9 \times 75 = 675
\]
- Result: 675
#### F. \( 3 + 40 \times 2 \)
- First, perform the multiplication:
\[
40 \times 2 = 80
\]
- Then, add 3:
\[
3 + 80 = 83
\]
- Result: 83
#### G. \( 27 + 9 - 2 \)
- Perform the operations from left to right:
\[
27 + 9 = 36
\]
\[
36 - 2 = 34
\]
- Result: 34
#### H. \( (5 \times 2) \times 3 \)
- First, calculate the expression inside the parentheses:
\[
5 \times 2 = 10
\]
- Then, multiply by 3:
\[
10 \times 3 = 30
\]
- Result: 30
Matching Results
Now, we match the results from the left column with the results from the right column:
- 1. \( (4 \times 8) - 2 \) → 30 → H
- 2. \( 3 + 4 \times (6 - 1) \) → 23 → F
- 3. \( 56 \div 7 \times (9 - 4) \) → 40 → G
- 4. \( (17 - 14) + (5 + 3) \) → 11 → B
- 5. \( 63 - 9 - 6 \) → 48 → E
- 6. \( (100 + 10) \div 4 \times 2 \) → 55 → A
- 7. \( (5 - 20 + 20) \times 4 \) → 20 → C
- 8. \( (144 + 12) + (121 + 11) + 1 \) → 289 → D
Final Answer
\[
\boxed{H, F, G, B, E, A, C, D}
\]
Parent Tip: Review the logic above to help your child master the concept of simplify numerical expressions worksheet.