Math Problem Statement

((3/4)+(5/12)•1/3

Solution

To solve the expression (34)+(51213)\left( \frac{3}{4} \right) + \left( \frac{5}{12} \cdot \frac{1}{3} \right), we proceed step by step:

  1. Multiplication first: 51213=51123=536\frac{5}{12} \cdot \frac{1}{3} = \frac{5 \cdot 1}{12 \cdot 3} = \frac{5}{36}.

    Now the expression becomes: 34+536\frac{3}{4} + \frac{5}{36}

  2. Finding a common denominator: The least common denominator (LCD) of 4 and 36 is 36.

    • Convert 34\frac{3}{4} to a fraction with a denominator of 36: 34=3949=2736\frac{3}{4} = \frac{3 \cdot 9}{4 \cdot 9} = \frac{27}{36}
  3. Adding the fractions: 2736+536=27+536=3236\frac{27}{36} + \frac{5}{36} = \frac{27 + 5}{36} = \frac{32}{36}

  4. Simplifying the result: 3236=89\frac{32}{36} = \frac{8}{9}

So, the final answer is 89\frac{8}{9}.

Would you like more details or have any questions?

Here are 5 related questions to explore:

  1. How do you find the least common denominator for adding fractions?
  2. Can you explain how to simplify fractions?
  3. What is the process for multiplying fractions?
  4. How do you convert mixed numbers to improper fractions for addition?
  5. How can you check if two fractions are equivalent?

Tip: Always perform operations like multiplication or division before addition or subtraction when dealing with expressions.

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Math Problem Analysis

Mathematical Concepts

Fraction Addition
Fraction Multiplication
Common Denominators
Simplifying Fractions

Formulas

Multiplication of fractions: (a/b) • (c/d) = (a•c) / (b•d)
Finding common denominator: LCM of denominators
Addition of fractions: (a/b) + (c/b) = (a+c)/b
Simplifying fractions: divide both numerator and denominator by their greatest common divisor (GCD)

Theorems

Fundamental Theorem of Fractions
Least Common Multiple (LCM)

Suitable Grade Level

Grades 6-8