Subtract these two fractions: [tex]$\frac{4}{3}-\frac{1}{2}=?$[/tex]
Answer (1)
Find a common denominator for the fractions, which is 6.
Convert 3 4 to 6 8 and 2 1 to 6 3 .
Subtract the fractions: 6 8 − 6 3 = 6 5 .
The result is 6 5 .
Explanation
Finding a Common Denominator We are asked to subtract the fraction 2 1 from the fraction 3 4 . To do this, we need to find a common denominator.
LCM of 3 and 2 The least common multiple of 3 and 2 is 6. So, we will convert both fractions to have a denominator of 6.
Converting 4/3 To convert 3 4 to a fraction with a denominator of 6, we multiply both the numerator and the denominator by 2: 3 4 = 3 × 2 4 × 2 = 6 8 .
Converting 1/2 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 .
Subtracting the Fractions Now we can subtract the two fractions: 6 8 − 6 3 = 6 8 − 3 = 6 5 .
Final Answer The result of subtracting 2 1 from 3 4 is 6 5 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you have a pizza cut into 3 slices and you eat 1 slice, you have eaten 3 1 of the pizza. If you then give half of the remaining pizza to a friend, you need to calculate 2 1 of 3 2 to determine how much pizza your friend receives, which is 3 1 of the whole pizza. Understanding how to add, subtract, multiply, and divide fractions is essential for many practical tasks.
