Subtract these two fractions:
\[\frac{1}{2}-\frac{1}{8}=?\]
Answer (1)
Find a common denominator for the fractions, which is 8.
Convert 2 1 to 8 4 .
Subtract the fractions: 8 4 − 8 1 = 8 3 .
The result is 8 3 .
Explanation
Understanding the Problem We are asked to subtract two fractions: 2 1 and 8 1 . To do this, we need to find a common denominator.
Finding a Common Denominator The least common multiple of 2 and 8 is 8. So, we will rewrite both fractions with a denominator of 8.
Converting Fractions To convert 2 1 to a fraction with a denominator of 8, we multiply both the numerator and the denominator by 4: 2 1 = 2 × 4 1 × 4 = 8 4 .
Subtracting Fractions Now we can subtract the two fractions: 8 4 − 8 1 = 8 4 − 1 = 8 3 .
Simplifying the Result The fraction 8 3 is in its simplest form because 3 is a prime number and does not divide 8.
Final Answer Therefore, the answer is 8 3 .
Examples
Fractions are used in everyday life, such as when baking a cake. If a recipe calls for 2 1 cup of flour and you only want to make 8 1 of the recipe, you need to know how to subtract fractions to determine how much flour to use. In this case, you would calculate 2 1 − 8 1 to find the difference.
