Here are the step-by-step solutions for each problem using the order of operations (PEMDAS/BODMAS):
a) $3 \times 5 + 6$
1. First, do the multiplication: $3 \times 5 = 15$.
2. Then, add 6: $15 + 6 = 21$.
b) $7 + 8 - 2 - 1 + 2 - 5$
1. Since there are only addition and subtraction, solve from left to right.
2. $7 + 8 = 15$
3. $15 - 2 = 13$
4. $13 - 1 = 12$
5. $12 + 2 = 14$
6. $14 - 5 = 9$
c) $7 \times 3 - 2 \times 4 + 1$
1. Do the multiplications first:
- $7 \times 3 = 21$
- $2 \times 4 = 8$
2. Now the equation is: $21 - 8 + 1$.
3. Solve from left to right:
- $21 - 8 = 13$
- $13 + 1 = 14$
d) $7 + (4 \times 5 - 3) - 2 \times 3$
1. Solve inside the parentheses first. Inside, do multiplication before subtraction:
- $4 \times 5 = 20$
- $20 - 3 = 17$
2. Now the equation is: $7 + 17 - 2 \times 3$.
3. Do the remaining multiplication: $2 \times 3 = 6$.
4. Now the equation is: $7 + 17 - 6$.
5. Solve from left to right:
- $7 + 17 = 24$
- $24 - 6 = 18$
e) $2 \times 3 \times 9 \div 3 - 2$
1. Do multiplication and division from left to right:
- $2 \times 3 = 6$
- $6 \times 9 = 54$
- $54 \div 3 = 18$
2. Now subtract 2: $18 - 2 = 16$.
f) $42 \div 7 + 3 \times 6$
1. Do division and multiplication first:
- $42 \div 7 = 6$
- $3 \times 6 = 18$
2. Now add the results: $6 + 18 = 24$.
g) $4 \times (9 - 4) + (3 + 28 \div 7) \times 2 - 8$
1. Solve the first set of parentheses: $(9 - 4) = 5$.
2. Solve the second set of parentheses. Inside, do division first:
- $28 \div 7 = 4$
- $3 + 4 = 7$
3. Now the equation looks like this: $4 \times 5 + 7 \times 2 - 8$.
4. Do the multiplications:
- $4 \times 5 = 20$
- $7 \times 2 = 14$
5. Now the equation is: $20 + 14 - 8$.
6. Solve from left to right:
- $20 + 14 = 34$
- $34 - 8 = 26$
Final Answer:
a) 21
b) 9
c) 14
d) 18
e) 16
f) 24
g) 26
Parent Tip: Review the logic above to help your child master the concept of worksheet order of operations.
