Subtract these two fractions: [tex]$\frac{12}{7}-\frac{1}{3}=?$
Answer (1)
Find the least common denominator (LCD) of 7 and 3, which is 21.
Rewrite the fractions with the common denominator: 7 12 = 21 36 and 3 1 = 21 7 .
Subtract the fractions: 21 36 − 21 7 = 21 29 .
The final answer is 21 29 .
Explanation
Finding a Common Denominator We are asked to subtract two fractions: 7 12 and 3 1 . To do this, we need to find a common denominator.
Calculating the LCD The least common denominator (LCD) of 7 and 3 is their least common multiple (LCM). Since 7 and 3 are both prime numbers, their LCM is simply their product: 7 × 3 = 21 .
Rewriting the Fractions Now we rewrite both fractions with the denominator of 21. To rewrite 7 12 with a denominator of 21, we multiply both the numerator and the denominator by 3: 7 12 = 7 × 3 12 × 3 = 21 36 . To rewrite 3 1 with a denominator of 21, we multiply both the numerator and the denominator by 7: 3 1 = 3 × 7 1 × 7 = 21 7 .
Subtracting the Fractions Now we can subtract the two fractions: 7 12 − 3 1 = 21 36 − 21 7 = 21 36 − 7 = 21 29 .
Final Answer The resulting fraction is 21 29 . Since 29 is a prime number and does not divide 21, the fraction is already in its simplest form. Therefore, the final answer is 21 29 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you have 7 12 of a pizza and you eat 3 1 of the pizza, you need to subtract the fractions to find out how much pizza is left. This problem demonstrates how to subtract fractions with different denominators, which is a fundamental skill in arithmetic.
