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Mathematical Operations - Expert Level: operation substitution EXPERT

Comprehensive self assessment worksheet covering 20 expert-level mathematical operations problems. Worksheet 28 of 30 emphasizes operation substitution. Master calculation puzzles, mathematical manipulation, operational logic through detailed explanations. Difficulty: challenging problems and time-bound practice. Tailored for expert-level preparation.

📝 Worksheet 28 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Mathematical Operations
Worksheet 28 of 30 (93% complete)

Question 1

A value increases by 24% and then decreases by 48%. What is the net percentage change?
Step 1: increase by 24% → multiply by 1.24
Step 2: decrease by 48% → multiply by 0.52
Net change = -35.5%
percentage, reasoning

Question 2

Simplify: (1/8 - 5/2) + 5/8
Following BODMAS, calculate step by step to get -7/4
fractions, bodmas

Question 3

If # means -, @ means +, $ means ×, % means ÷, then find the value of 20 % 19 $ 9
Substitute symbols: 20 ÷ 19 × 9 = 9.450000000000001
substitution, basic

Question 4

If @ means +, $ means -, # means ×, find 10 @ (6 # 7) $ 5
Step 1: (6 × 7) = 42
Step 2: 10 + 42 - 5 = 47
bodmas, brackets

Question 5

Given # means -, % means ÷, $ means ×, @ means +, which symbols should be interchanged to make 9 % 6 @ 4 $ 8 = 27?
The equation is already correct or no single interchange works
interchange, complex

Question 6

Which two numbers should be interchanged to make the equation 5 - 5 + 2 = 25 correct?
balance, interchange

Question 7

Given: S > Q, P < S, P > S. Which of the following is definitely true?
From S > Q and P < S, we can deduce R < Q
inequality, logic

Question 8

Given # means -, % means ÷, @ means +, $ means ×, which symbols should be interchanged to make 9 $ 9 % 15 @ 3 = 69?
The equation is already correct or no single interchange works
interchange, complex

Question 9

Find the missing number in the sequence: 3, 9, 27, ?
The pattern: Each term is multiplied by 3. Therefore, the missing number is 81
pattern, sequence

Question 10

A value increases by 25% and then decreases by 18%. What is the net percentage change?
Step 1: increase by 25% → multiply by 1.25
Step 2: decrease by 18% → multiply by 0.8200000000000001
Net change = 2.5%
percentage, reasoning

Question 11

If $ means ×, @ means +, % means ÷, # means -, then find the value of (15 % 2) $ 7 @ 2
Step 1: (15 ÷ 2) = 7.5
Step 2: 7.5 × 7 + 2 = 54.5
substitution, brackets

Question 12

Given: P < S, P > S, Q > P. Which of the following is definitely true?
From P < S and P > S, we can deduce Q < R
inequality, logic

Question 13

Given: Q > R, Q < R, S > Q. Which of the following is definitely true?
From Q > R and Q < R, we can deduce P > Q
inequality, logic

Question 14

Which two numbers should be interchanged to make the equation 7 - 6 - 9 = 33 correct?
balance, interchange

Question 15

Which two numbers should be interchanged to make the equation 3 - 8 × 9 = 24 correct?
balance, interchange

Question 16

Given # means -, $ means ×, @ means +, % means ÷, which symbols should be interchanged to make 4 # 11 % 8 $ 10 = 75?
The equation is already correct or no single interchange works
interchange, complex

Question 17

Given: S < Q, P > S, Q > R. Which of the following is definitely true?
From S < Q and P > S, we can deduce P < R
inequality, logic

Question 18

Given @ means +, # means -, % means ÷, $ means ×, which symbols should be interchanged to make 15 # 15 $ 9 @ 3 = 29?
The equation is already correct or no single interchange works
interchange, complex

Question 19

A value decreases by 11% and then increases by 49%. What is the net percentage change?
Step 1: decrease by 11% → multiply by 0.89
Step 2: increase by 49% → multiply by 1.49
Net change = 32.6%
percentage, reasoning

Question 20

Simplify: (10/11 + 2/9) × 3/7
Following BODMAS, calculate step by step to get 16/33
fractions, bodmas
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