Adding and Simplifying Fractions

Adding Fractions with Like Denominators

• To add fractions with like denominators, add the numerators and keep the denominator the same.
• Example: 1/5 + 2/5 = (1 + 2)/5 = 3/5
• The denominator represents the total number of equal parts.
• The numerator represents the number of those parts being considered.
• The result is a new fraction that describes the combined portions.

Simplifying Fractions

• Simplifying a fraction means expressing it in its lowest terms.
• This involves dividing both the numerator and the denominator by their greatest common divisor (GCD).
• The GCD is the largest whole number that divides both the numerator and the denominator evenly.
• Example: 6/8 can be simplified by finding the GCD of 6 and 8, which is 2. Dividing both by 2 results in 3/4.
• Simplifying does not change the value of the fraction, only its representation.
• Simplifying is often a necessary step in adding, subtracting, and working with fractions.
• Identifying common factors is crucial for simplifying.

Adding and Simplifying Fractions (Combined)

• When adding fractions with like denominators, the result is often an unsimplified improper fraction, which must be simplified.
• Example: 3/8 + 5/8 = 8/8.
• 8/8 is an improper fraction that can be simplified to 1 whole.
• Simplifying is vital for clarity and to ensure that the answer is expressed in the lowest possible terms.
• Simplifying fractions is crucial for making calculations more efficient and easily understood.
• The combined procedure of adding fractions with like denominators and simplifying the result should be followed consistently.