Math Problem Statement

Evaluate the mathematical expressions provided in SET 1 and SET 2 of the worksheet.

Solution

I can see the math problems from the image you uploaded. Let’s work through the problems step by step. Here are the solutions to some of the questions in SET 1 and SET 2:


SET 1

Problem 5:

119411 - 9 \cdot 4 Follow the order of operations (PEMDAS):

  1. Multiply: 94=369 \cdot 4 = 36
  2. Subtract: 1136=2511 - 36 = -25

Answer: -25


Problem 17:

1(318)1 - (3 - 18)

  1. Simplify inside parentheses: 318=153 - 18 = -15
  2. Subtract: 1(15)=1+15=161 - (-15) = 1 + 15 = 16

Answer: 16


Problem 2:

(14)3(56)(1 - 4)^3 - (-5 \cdot 6)

  1. Simplify 14=31 - 4 = -3, so (3)3=27(-3)^3 = -27
  2. Simplify 56=30-5 \cdot 6 = -30
  3. Subtract: 27(30)=27+30=3-27 - (-30) = -27 + 30 = 3

Answer: 3


Problem 12:

(28)2+(68)(2 - 8)^2 + (6 - 8)

  1. Simplify 28=62 - 8 = -6, so (6)2=36(-6)^2 = 36
  2. Simplify 68=26 - 8 = -2
  3. Add: 36+(2)=362=3436 + (-2) = 36 - 2 = 34

Answer: 34


Problem 9:

(4)2(2+19)(-4)^2 - (-2 + 19)

  1. Simplify (4)2=16(-4)^2 = 16
  2. Simplify 2+19=17-2 + 19 = 17
  3. Subtract: 1617=116 - 17 = -1

Answer: -1


Problem 15:

(2)3(7+8)(-2)^3 \cdot (-7 + 8)

  1. Simplify (2)3=8(-2)^3 = -8
  2. Simplify 7+8=1-7 + 8 = 1
  3. Multiply: 81=8-8 \cdot 1 = -8

Answer: -8


SET 2

Problem 13:

22(7+16)-2^2 - (-7 + 16)

  1. Simplify 22=(22)=4-2^2 = -(2^2) = -4 (exponent first, then apply the negative)
  2. Simplify 7+16=9-7 + 16 = 9
  3. Subtract: 49=13-4 - 9 = -13

Answer: -13


Problem 4:

104(24÷3)10 - 4(24 \div -3)

  1. Simplify inside parentheses: 24÷3=824 \div -3 = -8
  2. Multiply: 48=324 \cdot -8 = -32
  3. Subtract: 10(32)=10+32=4210 - (-32) = 10 + 32 = 42

Answer: 42


If you'd like, I can solve the rest or provide more explanations. Let me know!


Relative Questions:

  1. What are the key steps to follow when solving equations with multiple operations?
  2. How can you double-check your solutions for accuracy?
  3. What are common mistakes students make in applying PEMDAS?
  4. How do negative numbers affect operations like multiplication or exponentiation?
  5. Can you think of real-world examples where these calculations might be used?

Tip:

Always evaluate expressions inside parentheses first and proceed methodically to avoid errors!

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Math Problem Analysis

Mathematical Concepts

Order of Operations (PEMDAS)
Arithmetic with Integers
Exponents

Formulas

Order of operations: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right)
Basic exponentiation: a^b

Theorems

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Suitable Grade Level

Grades 6-8