Math Problem Statement

What is the sum of the fractions 14/32 + 8/32?

Solution

To determine the sum of the fractions 1432+832\frac{14}{32} + \frac{8}{32}, follow these steps:


Step 1: Add fractions with the same denominator

Since the denominators are the same (32), you can add the numerators directly:
1432+832=14+832=2232.\frac{14}{32} + \frac{8}{32} = \frac{14 + 8}{32} = \frac{22}{32}.


Step 2: Simplify the fraction

To simplify 2232\frac{22}{32}, find the greatest common divisor (GCD) of 22 and 32.

  • The factors of 22: 1,2,11,221, 2, 11, 22
  • The factors of 32: 1,2,4,8,16,321, 2, 4, 8, 16, 32
  • The GCD is 2.

Divide both the numerator and denominator by 2:
2232=22÷232÷2=1116.\frac{22}{32} = \frac{22 \div 2}{32 \div 2} = \frac{11}{16}.


Final Answer:

The sum of the fractions is:
1116\boxed{\frac{11}{16}}


Related Questions:

  1. How do you simplify fractions with large numerators and denominators?
  2. What is the method to add fractions with different denominators?
  3. How can you convert improper fractions to mixed numbers?
  4. How do you find the least common denominator (LCD) of two fractions?
  5. How is simplifying fractions related to finding their GCD?

Tip:

When adding fractions, always check if the final result can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD).

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Math Problem Analysis

Mathematical Concepts

Adding Fractions
Simplifying Fractions
Greatest Common Divisor (GCD)

Formulas

a/b + c/b = (a+c)/b
Simplification using GCD: gcd(numerator, denominator)

Theorems

Fraction Addition Theorem
Simplification of Fractions using GCD

Suitable Grade Level

Grade 5-6