Math Problem Statement

Shari is adding these fractions:

1/3 + 1/4

What's her next step?

Solution

To add the fractions 13\frac{1}{3} and 14\frac{1}{4}, Shari needs to follow these steps:

  1. Find a common denominator: The denominators are 3 and 4. The least common denominator (LCD) of 3 and 4 is 12.

  2. Convert the fractions to have the common denominator:

    • For 13\frac{1}{3}, multiply both the numerator and the denominator by 4:
      13=1×43×4=412\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}
    • For 14\frac{1}{4}, multiply both the numerator and the denominator by 3:
      14=1×34×3=312\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
  3. Add the fractions: Now that both fractions have the same denominator, add the numerators: 412+312=4+312=712\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}

So, Shari’s next step is to convert both fractions to have a denominator of 12 and then add them together to get 712\frac{7}{12}.

Would you like more details on this process or have any questions?

Here are 5 related questions to explore further:

  1. How do you find the least common denominator of two fractions?
  2. Can fractions with different denominators be added without converting them first?
  3. What happens if the denominators are already the same?
  4. How do you subtract fractions with different denominators?
  5. How can you simplify fractions after adding or subtracting them?

Tip: When adding fractions, always make sure the denominators match before adding the numerators.

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Math Problem Analysis

Mathematical Concepts

Fraction Addition
Least Common Denominator
Simplification of Fractions

Formulas

Find the Least Common Denominator (LCD)
Convert fractions to the LCD

Theorems

Adding Fractions with Different Denominators

Suitable Grade Level

Grades 4-6