Math Problems: Step-by-Step Solutions

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Math Problems: Step-by-Step Solutions

Hey guys! Let's break down these math problems step by step. I'll provide detailed solutions, explanations, and some handy tips along the way. Let's dive in!

a) 9/22 - 2*(1/2) + 2/11

This problem involves fractions and basic arithmetic operations. Remember the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's solve it step-by-step:

  1. Simplify the multiplication: First, we handle the multiplication part: 2 * (1/2) = 1. So, the expression becomes: 9/22 - 1 + 2/11
  2. Find a common denominator: To add and subtract fractions, we need a common denominator. The least common multiple (LCM) of 22 and 11 is 22. Convert all fractions to have this denominator:
    • 9/22 remains the same.
    • 1 = 22/22
    • 2/11 = 4/22 The expression now looks like: 9/22 - 22/22 + 4/22
  3. Perform the operations: Now, we can add and subtract the fractions: (9 - 22 + 4) / 22 = -9/22

Therefore, the final answer is -9/22.

b) 16 ÷ 2^3 * 5

This problem involves division, exponents, and multiplication. Again, follow the order of operations (PEMDAS/BODMAS).

  1. Evaluate the exponent: First, calculate 2^3 = 2 * 2 * 2 = 8. The expression becomes: 16 ÷ 8 * 5
  2. Perform division and multiplication from left to right:
    • 16 ÷ 8 = 2
    • 2 * 5 = 10

Therefore, the final answer is 10.

c) This Subquestion is Incomplete

Explanation: This question is incomplete and I cannot complete it. I would need the complete expression to provide a solution. Please provide the full expression so I can assist you accurately.

d) 3/16 * 2/9 + 4/1 - 2/4

This problem involves multiplication, addition, subtraction, and fractions. Let's solve it step-by-step:

  1. Multiply the fractions: First, multiply 3/16 * 2/9. (3 * 2) / (16 * 9) = 6/144 Simplify the fraction 6/144 by dividing both numerator and denominator by their greatest common divisor, which is 6: 6/144 = 1/24 The expression becomes: 1/24 + 4/1 - 2/4
  2. Simplify 2/4: Simplify 2/4 to 1/2: 1/24 + 4/1 - 1/2
  3. Find a common denominator: The least common multiple (LCM) of 24, 1, and 2 is 24. Convert all fractions to have this denominator:
    • 1/24 remains the same.
    • 4/1 = 96/24
    • 1/2 = 12/24 The expression now looks like: 1/24 + 96/24 - 12/24
  4. Perform the operations: Add and subtract the fractions: (1 + 96 - 12) / 24 = 85/24

Therefore, the final answer is 85/24.

e) 7/2 * 4/3 + 1/2 - 3/3

Let's solve this step-by-step:

  1. Multiply the fractions: Multiply 7/2 * 4/3: (7 * 4) / (2 * 3) = 28/6 Simplify the fraction 28/6 by dividing both numerator and denominator by their greatest common divisor, which is 2: 28/6 = 14/3 The expression becomes: 14/3 + 1/2 - 3/3
  2. Simplify 3/3: Simplify 3/3 to 1: 14/3 + 1/2 - 1
  3. Find a common denominator: The least common multiple (LCM) of 3 and 2 is 6. Convert all fractions to have this denominator:
    • 14/3 = 28/6
    • 1/2 = 3/6
    • 1 = 6/6 The expression now looks like: 28/6 + 3/6 - 6/6
  4. Perform the operations: Add and subtract the fractions: (28 + 3 - 6) / 6 = 25/6

Therefore, the final answer is 25/6.

f) 3/5 + 4/6 - 9/3

Let's solve this problem step-by-step:

  1. Simplify 4/6 and 9/3: Simplify 4/6 to 2/3 and 9/3 to 3: 3/5 + 2/3 - 3
  2. Find a common denominator: The least common multiple (LCM) of 5 and 3 is 15. Convert all fractions to have this denominator:
    • 3/5 = 9/15
    • 2/3 = 10/15
    • 3 = 45/15 The expression now looks like: 9/15 + 10/15 - 45/15
  3. Perform the operations: Add and subtract the fractions: (9 + 10 - 45) / 15 = -26/15

Therefore, the final answer is -26/15.

g) 1/3 - 5/4 + 3/6

Here’s how to solve it:

  1. Simplify 3/6: Simplify 3/6 to 1/2: 1/3 - 5/4 + 1/2
  2. Find a common denominator: The least common multiple (LCM) of 3, 4, and 2 is 12. Convert all fractions to have this denominator:
    • 1/3 = 4/12
    • 5/4 = 15/12
    • 1/2 = 6/12 The expression now looks like: 4/12 - 15/12 + 6/12
  3. Perform the operations: Add and subtract the fractions: (4 - 15 + 6) / 12 = -5/12

Therefore, the final answer is -5/12.

h) 5 - 11/121 + 11/109

Let's break this down:

  1. Simplify 11/121: Simplify 11/121 to 1/11: 5 - 1/11 + 11/109
  2. Find a common denominator: The least common multiple (LCM) of 11 and 109 is 1199. Convert all terms to have this denominator:
    • 5 = 5995/1199
    • 1/11 = 109/1199
    • 11/109 = 121/1199 The expression now looks like: 5995/1199 - 109/1199 + 121/1199
  3. Perform the operations: Add and subtract the fractions: (5995 - 109 + 121) / 1199 = 6007/1199

Therefore, the final answer is 6007/1199.

I hope this helps! If you have more questions, feel free to ask.