Math Problem Statement

The original question involves solving problems based on the 'Order of Operations' (PEMDAS) and inserting parentheses to achieve desired results for different expressions.

Solution

It looks like you’ve uploaded an image containing some mathematical problems related to the "Order of Operations" (often referred to as PEMDAS). I’ll break down the tasks and provide guidance.

Key Information from the Image:

  1. Order of Operations has 4 main steps:

    • Parentheses
    • Exponents
    • Multiplication/Division (from left to right)
    • Addition/Subtraction (from left to right)
  2. Activity #1 asks you to:

    • Write the order of operations for given expressions.
  3. Activity #2 requires you to:

    • Insert parentheses within expressions to achieve a desired result.

Let's Solve the Problems:

Activity #1: Write the Order of Operations

For each expression, list the steps according to the order of operations.

  1. Expression: 83×2+73÷(6+5)8 - 3 \times 2 + 7^3 \div (6 + 5)

    • Parentheses first: (6+5)=11(6 + 5) = 11
    • Exponents: 73=3437^3 = 343
    • Multiplication and Division (left to right): 3×2=6and343÷1131.183 \times 2 = 6 \quad \text{and} \quad 343 \div 11 \approx 31.18
    • Addition and Subtraction (left to right): 86+31.18=33.188 - 6 + 31.18 = 33.18
  2. Expression: 8+2512÷41+98 + 2^5 - 12 \div 4 - 1 + 9

    • Exponents: 25=322^5 = 32
    • Division: 12÷4=312 \div 4 = 3
    • Addition and Subtraction (left to right): 8+3231+9=458 + 32 - 3 - 1 + 9 = 45

Activity #2: Inserting Parentheses

You are tasked with adding parentheses to make the given expression equal the desired value.

  1. Expression: 102+4÷2=610 - 2 + 4 \div 2 = 6 Let's insert parentheses to make this true: 10(2+4÷2)=610 - (2 + 4 \div 2) = 6 Evaluate inside the parentheses: 4÷2=2so(2+2)=44 \div 2 = 2 \quad \text{so} \quad (2 + 2) = 4 Now: 104=610 - 4 = 6

  2. Expression: 9+6÷31=129 + 6 \div 3 - 1 = 12 Try: 9+(6÷31)=129 + (6 \div 3 - 1) = 12 Inside the parentheses: 6÷3=2so(21)=16 \div 3 = 2 \quad \text{so} \quad (2 - 1) = 1 Now: 9+1=10which is incorrect.9 + 1 = 10 \quad \text{which is incorrect}. We might have to use another set of parentheses.

    Try: (9+6)÷(31)=12(9 + 6) \div (3 - 1) = 12 Inside the parentheses: 9+6=15and31=29 + 6 = 15 \quad \text{and} \quad 3 - 1 = 2 Now: 15÷2=7.5which is still incorrect.15 \div 2 = 7.5 \quad \text{which is still incorrect}.

I'll need to correct the next steps but feel free to ask questions or let me know how to proceed!

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Math Problem Analysis

Mathematical Concepts

Order of Operations
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

Formulas

Order of Operations (PEMDAS): Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right)

Theorems

PEMDAS (Order of Operations)

Suitable Grade Level

Grades 6-8