Subtracting Fractions by Rewriting with Common Denominators
Subtracting Fractions by Rewriting with Common Denominators is a Grade 5 math skill in Eureka Math where students apply the full algorithmic process of finding a common denominator, generating equivalent fractions, and subtracting numerators to compute exact differences of fractions with unlike denominators. This skill formalizes the numerical procedure introduced pictorially in earlier chapters.
Key Concepts
To subtract fractions with unlike denominators, they must first be rewritten as equivalent fractions with a common denominator. Once the fractions have like denominators, subtract the numerators and keep the denominator the same. $$\frac{a}{c} \frac{b}{c} = \frac{a b}{c}$$.
Common Questions
What are the steps for subtracting fractions with unlike denominators?
Step 1: Find the least common denominator (LCD). Step 2: Rewrite each fraction as an equivalent fraction with the LCD. Step 3: Subtract the numerators and keep the denominator. Step 4: Simplify the result if possible.
How do you find the least common denominator?
The LCD is the least common multiple (LCM) of the two denominators. For 2/3 and 1/4, the LCM of 3 and 4 is 12, so the LCD is 12.
What equivalent fractions would you use to subtract 2/3 - 1/4?
Convert 2/3 to 8/12 and 1/4 to 3/12. Then subtract: 8/12 - 3/12 = 5/12.
When do you need to simplify after subtracting fractions?
Simplify when the resulting fraction is not in lowest terms, meaning the numerator and denominator share a common factor greater than 1.