Math worksheet for 5th-grade students focusing on solving numerical expressions using parentheses, brackets, and braces, with problems involving simplification, algebraic expressions, and real-world applications.

I'll solve each problem step by step, carefully checking my calculations.

## Problem 1: Simplify the expressions

a. 10 + (25 - 1) ÷ 5
- First: 25 - 1 = 24
- Then: 24 ÷ 5 = 4.8
- Finally: 10 + 4.8 = 14.8

b. 4 ÷ [25 - (5 - 2)]
- Innermost: 5 - 2 = 3
- Then: 25 - 3 = 22
- Finally: 4 22 = 2/11 or approximately 0.182

c. (4½ + 3½) ÷ (7/12 - 1/2) ÷ 2
- First bracket: 4½ + 3½ = 8
- Second bracket: 7/12 - 1/2 = 7/12 - 6/12 = 1/12
- Then: 8 ÷ (1/12) = 8 × 12 = 96
- Finally: 96 ÷ 2 = 48

d. 4.5 ÷ 3 × 5(3.2 + 1.1)4

Let me re-read this expression more carefully. It appears to be: 4.5 3 × 5(3.2 + 1.1)4

This is ambiguous notation. Let me interpret it as: 4.5 ÷ 3 × 5 × (3.2 + 1.1) × 4
- Inside parentheses: 3.2 + 1.1 = 4.3
- Working left to right: 4.5 ÷ 3 = 1.5
- Then: 1.5 × 5 = 7.5
- Then: 7.5 × 4.3 = 32.25
- Finally: 32.25 × 4 = 129

e. 2/5 + 7½ × 8
- First: 7½ × 8 = 15/2 × 8 = 120/2 = 60
- Then: 2/5 + 60 = 2/5 + 300/5 = 302/5 = 60.4 or 60⅖

## Problem 2: Solve algebraic expressions

a. 2(4p + 5y) - (3p + 7y) if p = 1; y = 2
- Substitute: 2(4(1) + 5(2)) - (3(1) + 7(2))
- = 2(4 + 10) - (3 + 14)
- = 2(14) - 17
- = 28 - 17 = 11

b. 3n × (5/n - 1/3) if n = 2
- Substitute: 3(2) × (5/2 - 1/3)
- = 6 × (5/2 - 1/3)
- Find common denominator for inside: 5/2 - 1/3 = 15/6 - 2/6 = 13/6
- = 6 × 13/6 = 13

c. ½ × (10m - 2) + 3 × 2 if m = 2/3
- Substitute: ½ × (10(2/3) - 2) + 6
- = ½ × (20/3 - 2) + 6
- = ½ × (20/3 - 6/3) + 6
- = ½ × (14/3) + 6
- = 7/3 + 6
- = 7/3 + 18/3 = 25/3 or 8⅓

d. ⅛ × (2t + 1) + 5 if t = ½
- Substitute: ⅛ × (2(½) + 1) + 5
- = ⅛ × (1 + 1) + 5
- = ⅛ × 2 + 5
- = 2/8 + 5
- = ¼ + 5 = 5¼ or 21/4

e. m + (n-1)/4 ÷ 5 if m = ¾; n = 2
- Substitute: ¾ + (2-1)/4 ÷ 5
- = ¾ + 1/4 ÷ 5
- = ¾ + 1/4 × 1/5
- = ¾ + 1/20
- = 15/20 + 1/20 = 16/20 = 4/5 or 0.8

## Problem 3: Use expression 5m + 4 × 2(m - 4)

The expression is: 5m + 4 × 2(m - 4) = 5m + 8(m - 4) = 5m + 8m - 32 = 13m - 32

For m = 3: 13(3) - 32 = 39 - 32 = $7
For m = 5: 13(5) - 32 = 65 - 32 = $33
For m = 7: 13(7) - 32 = 91 - 32 = $59

## Problem 4: Magazine and erasers

Expression: $5 + 4b (where b is cost per eraser)
If b = 0.75: 5 + 4(0.75) = 5 + 3 = $8

## Problem 5: Evaluate (3p)/4 - (p+2)/3 + (p+2)/12 if p = 3

Substitute p = 3:
= (3×3)/4 - (3+2)/3 + (3+2)/12
= 9/4 - 5/3 + 5/12

Find common denominator (12):
= 27/12 - 20/12 + 5/12
= (27 - 20 + 5)/12
= 12/12
= 1

Answer: a. 1

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Final Answer:

Problem 1:
a. 14.8
b. 2/11 (or 0.182)
c. 48
d. 129
e. 60.4 (or 60⅖)

Problem 2:
a. 11
b. 13
c. 25/3 (or 8⅓)
d. 21/4 (or 5¼)
e. 4/5 (or 0.8)

Problem 3:
For 3 people: $7
For 5 people: $33
For 7 people: $59

Problem 4: $8

Problem 5: a. 1