Subtracting Fractions Worksheet

Introduction to Subtracting Fractions

When dealing with fractions, addition, subtraction, multiplication, and division are the four basic operations. Among these, subtracting fractions can be a bit tricky, especially when the fractions have different denominators. In this post, we will explore how to subtract fractions with the same and different denominators, along with examples and a worksheet to practice.

Subtracting Fractions with the Same Denominator

Subtracting fractions that have the same denominator is relatively straightforward. You simply subtract the numerators (the numbers on top) while keeping the denominator (the number on the bottom) the same. The formula looks like this: [ \frac{a}{c} - \frac{b}{c} = \frac{a - b}{c} ] Here, (a), (b), and (c) are numbers, and (c) is the common denominator.

Example 1: Subtracting Fractions with the Same Denominator

Suppose we want to subtract (\frac{3}{8}) from (\frac{5}{8}). [ \frac{5}{8} - \frac{3}{8} = \frac{5 - 3}{8} = \frac{2}{8} ] We can simplify (\frac{2}{8}) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. [ \frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4} ] So, (\frac{5}{8} - \frac{3}{8} = \frac{1}{4}).

Subtracting Fractions with Different Denominators

When the fractions have different denominators, we need to find a common denominator before we can subtract them. The easiest way to do this is to find the least common multiple (LCM) of the two denominators. Once we have the LCM, we convert each fraction so that their denominators are the same, and then we can subtract them as before.

Example 2: Subtracting Fractions with Different Denominators

Suppose we want to subtract (\frac{1}{4}) from (\frac{1}{6}). 1. First, find the LCM of 4 and 6. The multiples of 4 are 4, 8, 12, 16, … and the multiples of 6 are 6, 12, 18, 24, … . The smallest number that appears in both lists is 12, so the LCM of 4 and 6 is 12. 2. Convert each fraction to have a denominator of 12. [ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} ] [ \frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12} ] 3. Now, subtract the fractions. [ \frac{3}{12} - \frac{2}{12} = \frac{3 - 2}{12} = \frac{1}{12} ]

Practice Worksheet

To get more comfortable with subtracting fractions, practice with the following exercises:

• Subtract (\frac{2}{5}) from (\frac{4}{5}).
• Subtract (\frac{3}{8}) from (\frac{7}{8}).
• Subtract (\frac{1}{9}) from (\frac{2}{9}).
• Subtract (\frac{2}{3}) from (\frac{5}{6}). Remember to find a common denominator first.

Fraction 1	Fraction 2	Result
\frac{2}{5}	\frac{4}{5}	\frac{4-2}{5} = \frac{2}{5}
\frac{3}{8}	\frac{7}{8}	\frac{7-3}{8} = \frac{4}{8} = \frac{1}{2}
\frac{1}{9}	\frac{2}{9}	\frac{2-1}{9} = \frac{1}{9}
\frac{2}{3}	\frac{5}{6}	First, find the LCM of 3 and 6, which is 6. Convert \frac{2}{3} to \frac{4}{6}, then subtract: \frac{5}{6} - \frac{4}{6} = \frac{1}{6}

📝 Note: When subtracting fractions, especially those with different denominators, always find a common denominator first to simplify the process.

In essence, subtracting fractions involves simple arithmetic operations once you understand how to handle fractions with the same and different denominators. With practice, you’ll become more comfortable and proficient in performing these operations, making it easier to tackle more complex mathematical problems.