Let's solve each expression step by step using the given value:
y = 8.
We'll use the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Remember that a dot (·) means multiplication.
---
1. $ 6 \cdot (2 + y - 5) + 5 \cdot (6 + y) $
Substitute $ y = 8 $:
$$
6 \cdot (2 + 8 - 5) + 5 \cdot (6 + 8)
$$
Simplify inside parentheses:
$$
6 \cdot (5) + 5 \cdot (14)
$$
Now multiply:
$$
30 + 70 = 100
$$
✔ Answer: 100
---
2. $ (7 + y + 8) + (7 + y - 7) $
Substitute $ y = 8 $:
$$
(7 + 8 + 8) + (7 + 8 - 7)
$$
Simplify:
$$
(23) + (8) = 31
$$
✔ Answer: 31
---
3. $ (2 + y + 6) + (5 + y - 2) $
Substitute $ y = 8 $:
$$
(2 + 8 + 6) + (5 + 8 - 2)
$$
Simplify:
$$
(16) + (11) = 27
$$
✔ Answer: 27
---
4. $ 4 \cdot (2 + y - 3) + 3 \cdot (8 + y) $
Substitute $ y = 8 $:
$$
4 \cdot (2 + 8 - 3) + 3 \cdot (8 + 8)
$$
Simplify inside:
$$
4 \cdot (7) + 3 \cdot (16)
$$
Multiply:
$$
28 + 48 = 76
$$
✔ Answer: 76
---
5. $ 5 \cdot (4 + y - 5) + 7 \cdot (3 + y) $
Substitute $ y = 8 $:
$$
5 \cdot (4 + 8 - 5) + 7 \cdot (3 + 8)
$$
Simplify:
$$
5 \cdot (7) + 7 \cdot (11)
$$
Multiply:
$$
35 + 77 = 112
$$
✔ Answer: 112
---
6. $ (4 + y + 3) + (3 + y - 3) $
Substitute $ y = 8 $:
$$
(4 + 8 + 3) + (3 + 8 - 3)
$$
Simplify:
$$
(15) + (8) = 23
$$
✔ Answer: 23
---
7. $ 5 \cdot (4 + y - 3) + 3 \cdot (3 + y) $
Substitute $ y = 8 $:
$$
5 \cdot (4 + 8 - 3) + 3 \cdot (3 + 8)
$$
Simplify:
$$
5 \cdot (9) + 3 \cdot (11)
$$
Multiply:
$$
45 + 33 = 78
$$
✔ Answer: 78
---
8. $ 7 \cdot (5 + y - 2) + 2 \cdot (3 + y) $
Substitute $ y = 8 $:
$$
7 \cdot (5 + 8 - 2) + 2 \cdot (3 + 8)
$$
Simplify:
$$
7 \cdot (11) + 2 \cdot (11)
$$
Multiply:
$$
77 + 22 = 99
$$
✔ Answer: 99
---
9. $ (4 + y + 8) + (4 + y - 3) $
Substitute $ y = 8 $:
$$
(4 + 8 + 8) + (4 + 8 - 3)
$$
Simplify:
$$
(20) + (9) = 29
$$
✔ Answer: 29
---
10. $ 2 \cdot (5 + y - 4) + 5 \cdot (4 + y) $
Substitute $ y = 8 $:
$$
2 \cdot (5 + 8 - 4) + 5 \cdot (4 + 8)
$$
Simplify:
$$
2 \cdot (9) + 5 \cdot (12)
$$
Multiply:
$$
18 + 60 = 78
$$
✔ Answer: 78
---
✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1 | 100 |
| 2 | 31 |
| 3 | 27 |
| 4 | 76 |
| 5 | 112 |
| 6 | 23 |
| 7 | 78 |
| 8 | 99 |
| 9 | 29 |
| 10 | 78 |
Let me know if you'd like these written out with full steps for printing or classroom use!
Parent Tip: Review the logic above to help your child master the concept of evaluating expressions worksheet.
