Math Problem Statement

Solve the following expressions: 1) 4/(6-(6-4)) 2) (3+13-4)/2 3) (4+7+5)/4 4) (4-(1+2)+5)/2 5) 18/3 * 6 - 3 + 2

Solution

Let's solve the problems from the image one by one.

5) 46(64)\frac{4}{6 - (6 - 4)}

First, simplify the expression inside the parentheses: 64=26 - 4 = 2 Now substitute back: 62=46 - 2 = 4 So the expression becomes: 44=1\frac{4}{4} = 1 Answer: 1

7) 3+1342\frac{3 + 13 - 4}{2}

First, simplify the numerator: 3+13=163 + 13 = 16 Then: 164=1216 - 4 = 12 Now divide by 2: 122=6\frac{12}{2} = 6 Answer: 6

9) 4+7+54\frac{4 + 7 + 5}{4}

First, simplify the numerator: 4+7=114 + 7 = 11 Then: 11+5=1611 + 5 = 16 Now divide by 4: 164=4\frac{16}{4} = 4 Answer: 4

11) 4(1+2)+52\frac{4 - (1 + 2) + 5}{2}

First, simplify inside the parentheses: 1+2=31 + 2 = 3 Now substitute back: 43+5=64 - 3 + 5 = 6 Now divide by 2: 62=3\frac{6}{2} = 3 Answer: 3

13) 18363+2\frac{18}{3} \cdot 6 - 3 + 2

First, divide 183\frac{18}{3}: 183=6\frac{18}{3} = 6 Now multiply by 6: 66=366 \cdot 6 = 36 Now subtract 3: 363=3336 - 3 = 33 Finally, add 2: 33+2=3533 + 2 = 35 Answer: 35


Do you have any questions or would you like more details on a specific solution?

Here are some related questions you might consider:

  1. How do parentheses affect the order of operations?
  2. Why do we simplify inside parentheses before handling other operations?
  3. Can you think of other examples where simplifying inside parentheses changes the outcome?
  4. How does division distribute over addition or subtraction in expressions like these?
  5. Can this type of expression have more complex operations, like exponents?

Tip: Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right)) when solving expressions.

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Math Problem Analysis

Mathematical Concepts

Order of Operations
Basic Arithmetic
Fractions
Division

Formulas

PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction)
Division formula a/b

Theorems

Order of Operations

Suitable Grade Level

Grades 6-8