Subtract Mixed Numbers with Unlike Denominators
Subtracting mixed numbers with unlike denominators is a key Grade 5 fraction skill in Pengi Math, Chapter 5. Students find a common denominator for the fractional parts, then subtract the fractions and whole numbers separately. For example, 5¾ − 2⅛ requires converting ¾ to ⅝ (LCM of 4 and 8 is 8), giving 5⅝ − 2⅛ = 3⅝. Similarly, 4⅔ − 1⅗ uses LCM 15 to rewrite as 4 10/15 − 1 9/15 = 3 1/15. This lesson focuses on cases where the first fraction is already larger, so no regrouping is needed.
Key Concepts
Property To subtract mixed numbers with unlike denominators, first find a common denominator for the fractional parts. Then, subtract the fractions, and subtract the whole numbers. Simplify the result if necessary.
Examples $5 \frac{3}{4} 2 \frac{1}{8} = 3 \frac{5}{8}$ $$ \begin{align } 5\frac{3}{4} 2\frac{1}{8} &= 5\frac{3\times2}{4\times2} 2\frac{1}{8} \quad \text{(Find common denominator: LCM of 4 and 8 is 8)} \\ &= 5\frac{6}{8} 2\frac{1}{8} \\ &= (5 2) + \left(\frac{6}{8} \frac{1}{8}\right) \quad \text{(Subtract whole numbers and fractions separately)} \\ &= 3 + \frac{5}{8} \\ &= 3\frac{5}{8} \end{align } $$ $4\frac{2}{3} 1\frac{3}{5} = 3\frac{1}{15}$ $$ \begin{align } 4\frac{2}{3} 1\frac{3}{5} &= 4\frac{2\times5}{3\times5} 1\frac{3\times3}{5\times3} \quad \text{(Find common denominator: LCM of 3 and 5 is 15)} \\ &= 4\frac{10}{15} 1\frac{9}{15} \\ &= (4 1) + \left(\frac{10}{15} \frac{9}{15}\right) \quad \text{(Subtract whole numbers and fractions separately)} \\ &= 3 + \frac{1}{15} \\ &= 3\frac{1}{15} \end{align } $$.
Explanation This skill focuses on subtracting mixed numbers where the fraction in the first number is larger than the fraction in the second number, so no regrouping (or borrowing) is needed. The first step is to convert the fractions to have a common denominator. After that, you can subtract the fractional parts from each other and the whole numbers from each other to find the final answer.
Common Questions
What is the first step when subtracting mixed numbers with unlike denominators?
Find the least common multiple (LCM) of the two denominators and convert both fractions to equivalent fractions with that common denominator.
How do you subtract 5¾ − 2⅛?
The LCM of 4 and 8 is 8. Convert ¾ to 6/8. Then subtract: 5 6/8 − 2 1/8 = 3 5/8.
How do you subtract 4⅔ − 1⅗?
The LCM of 3 and 5 is 15. Convert ⅔ to 10/15 and ⅗ to 9/15. Then subtract: 4 10/15 − 1 9/15 = 3 1/15.
When do you need to regroup (borrow) with mixed number subtraction?
Regrouping is needed when the fractional part of the first mixed number is smaller than the fractional part being subtracted. This lesson covers only cases where no regrouping is required.
How do you find the least common denominator for unlike fractions?
List multiples of both denominators and find the smallest number that appears in both lists. That number is the least common multiple, used as the common denominator.
What grade and textbook covers subtracting mixed numbers with unlike denominators?
Grade 5, Chapter 5: Add and Subtract Fractions and Mixed Numbers in Pengi Math.