The task involves simplifying mathematical expressions using the correct order of operations. The order of operations is often remembered by the acronym
PEMDAS:
1.
P - Parentheses (or Brackets)
2.
E - Exponents
3.
M - Multiplication
4.
D - Division
5.
A - Addition
6.
S - Subtraction
Explanation of Each Problem:
#### Left Column:
1.
Expression: \( (3 \times 4) + (7 + 9 - 10) \)
- Simplify inside parentheses first:
- \( 3 \times 4 = 12 \)
- \( 7 + 9 - 10 = 16 - 10 = 6 \)
- Add the results:
- \( 12 + 6 = 18 \)
2.
Expression: \( (10 \div 2) \times 7 + 5 - 4 \)
- Simplify inside parentheses first:
- \( 10 \div 2 = 5 \)
- Perform multiplication:
- \( 5 \times 7 = 35 \)
- Perform addition and subtraction from left to right:
- \( 35 + 5 = 40 \)
- \( 40 - 4 = 36 \)
3.
Expression: \( 6 \times (8 - 3 + 5) \div 10 \)
- Simplify inside parentheses first:
- \( 8 - 3 + 5 = 5 + 5 = 10 \)
- Perform multiplication:
- \( 6 \times 10 = 60 \)
- Perform division:
- \( 60 \div 10 = 6 \)
4.
Expression: \( (10 - 6 + 8 \div 2) \times 3 \)
- Simplify inside parentheses, following PEMDAS:
- \( 8 \div 2 = 4 \)
- \( 10 - 6 + 4 = 4 + 4 = 8 \)
- Multiply:
- \( 8 \times 3 = 24 \)
5.
Expression: \( 7 \div (4 \times 2 + 9 - 10) \)
- Simplify inside parentheses first:
- \( 4 \times 2 = 8 \)
- \( 8 + 9 - 10 = 17 - 10 = 7 \)
- Divide:
- \( 7 \div 7 = 1 \)
#### Right Column:
1.
Expression: \( 8 \times (10 - 6) \div 2 + 4 \)
- Simplify inside parentheses first:
- \( 10 - 6 = 4 \)
- Perform multiplication:
- \( 8 \times 4 = 32 \)
- Perform division:
- \( 32 \div 2 = 16 \)
- Add:
- \( 16 + 4 = 20 \)
2.
Expression: \( 8 \div (7 - 3) \times (4 + 6) \)
- Simplify inside parentheses first:
- \( 7 - 3 = 4 \)
- \( 4 + 6 = 10 \)
- Perform division:
- \( 8 \div 4 = 2 \)
- Perform multiplication:
- \( 2 \times 10 = 20 \)
3.
Expression: \( 10 - 6 \times 5 \div (2 + 4) \)
- Simplify inside parentheses first:
- \( 2 + 4 = 6 \)
- Perform multiplication and division from left to right:
- \( 6 \times 5 = 30 \)
- \( 30 \div 6 = 5 \)
- Subtract:
- \( 10 - 5 = 5 \)
4.
Expression: \( (4 + 4 - 6) \times 10 \)
- Simplify inside parentheses first:
- \( 4 + 4 - 6 = 8 - 6 = 2 \)
- Multiply:
- \( 2 \times 10 = 20 \)
5.
Expression: \( ((10 - 6) + 5) \div 9 \times 2 \)
- Simplify inside innermost parentheses first:
- \( 10 - 6 = 4 \)
- Simplify next level of parentheses:
- \( 4 + 5 = 9 \)
- Perform division:
- \( 9 \div 9 = 1 \)
- Perform multiplication:
- \( 1 \times 2 = 2 \)
Final Answers:
- Left Column:
1. \( 18 \)
2. \( 36 \)
3. \( 6 \)
4. \( 24 \)
5. \( 1 \)
- Right Column:
1. \( 20 \)
2. \( 20 \)
3. \( 5 \)
4. \( 20 \)
5. \( 2 \)
Boxed Final Answer:
\[
\boxed{18, 36, 6, 24, 1, 20, 20, 5, 20, 2}
\]
Parent Tip: Review the logic above to help your child master the concept of order of operations worksheet 5th grade.
