Work out $\frac{3}{4}-\frac{1}{3}$. Give your answer in its simplest form.
Answer (1)
Find a common denominator for the fractions, which is 12.
Convert the fractions to equivalent fractions with the common denominator: 4 3 = 12 9 and 3 1 = 12 4 .
Subtract the fractions: 12 9 − 12 4 = 12 5 .
The result is in its simplest form: 12 5 .
Explanation
Understanding the Problem We are asked to subtract the fraction 3 1 from the fraction 4 3 and express the result in its simplest form.
Finding a Common Denominator To subtract two fractions, we need to find a common denominator. The least common multiple (LCM) of 4 and 3 is 12. So, we will convert both fractions to equivalent fractions with a denominator of 12.
Converting to Equivalent Fractions To convert 4 3 to a fraction with a denominator of 12, we multiply both the numerator and the denominator by 3: 4 3 = 4 × 3 3 × 3 = 12 9 To convert 3 1 to a fraction with a denominator of 12, we multiply both the numerator and the denominator by 4: 3 1 = 3 × 4 1 × 4 = 12 4
Subtracting the Fractions Now we can subtract the two fractions: 4 3 − 3 1 = 12 9 − 12 4 = 12 9 − 4 = 12 5
Simplifying the Result The fraction 12 5 is in its simplest form because 5 and 12 have no common factors other than 1.
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to subtract fractions is essential for accurate calculations in these situations. For example, if you have 4 3 of a cup of flour and use 3 1 of a cup, you need to subtract the fractions to determine how much flour is left. The calculation 4 3 − 3 1 = 12 5 tells you that you have 12 5 of a cup of flour remaining.
