Subtract these two fractions:
[tex]$\frac{1}{2}-\frac{1}{3}=?$[/tex]
Answer (1)
Find a common denominator for the fractions, which is 6.
Rewrite the fractions with the common denominator: 2 1 = 6 3 and 3 1 = 6 2 .
Subtract the fractions: 6 3 − 6 2 = 6 1 .
The result of the subtraction is 6 1 .
Explanation
Understanding the Problem We are asked to subtract the fraction 3 1 from the fraction 2 1 . To do this, we need to find a common denominator.
Finding a Common Denominator The least common multiple of 2 and 3 is 6. So, we will rewrite both fractions with a denominator of 6.
Rewriting the Fractions To convert 2 1 to a fraction with a denominator of 6, we multiply both the numerator and the denominator by 3: 2 1 = 2 × 3 1 × 3 = 6 3 . To convert 3 1 to a fraction with a denominator of 6, we multiply both the numerator and the denominator by 2: 3 1 = 3 × 2 1 × 2 = 6 2 .
Subtracting the Fractions Now we can subtract the fractions: 2 1 − 3 1 = 6 3 − 6 2 = 6 3 − 2 = 6 1 .
Final Answer Therefore, the result of subtracting 3 1 from 2 1 is 6 1 .
Examples
Fractions are used in everyday life, such as when baking, cooking, or measuring ingredients. For example, if you have a recipe that calls for 2 1 cup of flour and you only want to make half of the recipe, you would need to calculate 2 1 of 2 1 , which is 4 1 cup of flour. Understanding how to subtract fractions is also useful when calculating time, distance, or quantities in various real-world scenarios.
