Math Problem Statement

Solve math problems using the order of operations (PEMDAS) on the worksheet.

Solution

It looks like you've uploaded an image of a worksheet covering the topic of the order of operations, commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Here’s a step-by-step breakdown of how to solve these problems:

Problems on the Worksheet:

  1. 9 × 5 (20 ÷ 4 + 3)

    • Step 1: Evaluate inside the parentheses first:
      20÷4=520 ÷ 4 = 5
      Thus, 9×5(5+3)9 × 5 (5 + 3).
    • Step 2: Add inside the parentheses:
      5+3=85 + 3 = 8
      So, 9×5×89 × 5 × 8.
    • Step 3: Perform multiplication from left to right:
      9×5=459 × 5 = 45
      45×8=36045 × 8 = 360.
  2. 7 × (30 ÷ 5 + 9)

    • Step 1: Evaluate inside the parentheses first:
      30÷5=630 ÷ 5 = 6
      7×(6+9)7 × (6 + 9).
    • Step 2: Add inside the parentheses:
      6+9=156 + 9 = 15
      So, 7×157 × 15.
    • Step 3: Multiply:
      7×15=1057 × 15 = 105.
  3. (12 ÷ 3) + (4 × 6)

    • Step 1: Evaluate inside each set of parentheses:
      12÷3=412 ÷ 3 = 4
      4×6=244 × 6 = 24.
    • Step 2: Add the results:
      4+24=284 + 24 = 28.
  4. (17 + 9) ÷ 4

    • Step 1: Evaluate inside the parentheses:
      17+9=2617 + 9 = 26.
    • Step 2: Divide:
      26÷4=6.526 ÷ 4 = 6.5.
  5. 49 ÷ (7 × 2) − 9

    • Step 1: Evaluate inside the parentheses:
      7×2=147 × 2 = 14.
    • Step 2: Divide:
      49÷14=3.549 ÷ 14 = 3.5.
    • Step 3: Subtract:
      3.59=5.53.5 − 9 = -5.5.
  6. 36 ÷ 6 + 8 − 4 × 3

    • Step 1: Perform

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Math Problem Analysis

Mathematical Concepts

Order of Operations
PEMDAS
Arithmetic
Basic Algebra

Formulas

Order of Operations: Parentheses > Exponents > Multiplication and Division > Addition and Subtraction
Division Formula: a ÷ b = result
Multiplication Formula: a × b = result
Addition Formula: a + b = result
Subtraction Formula: a - b = result

Theorems

PEMDAS

Suitable Grade Level

Grade 5-7