Subtract and simplify the answer. $\frac{5}{12}-\frac{7}{24}$
Answer (1)
Find a common denominator: Rewrite 12 5 as 24 10 .
Subtract the fractions: 24 10 − 24 7 = 24 3 .
Simplify the fraction: 24 3 = 8 1 .
The simplified answer is 8 1 .
Explanation
Understanding the problem We are asked to subtract two fractions and simplify the result. The given expression is 12 5 − 24 7 .
Finding a common denominator To subtract fractions, we need to find a common denominator. The least common multiple (LCM) of 12 and 24 is 24. We can rewrite the first fraction with the common denominator 24: 12 5 = 12 × 2 5 × 2 = 24 10 .
Subtracting the fractions Now we can subtract the second fraction from the first: 24 10 − 24 7 = 24 10 − 7 = 24 3 .
Simplifying the result Finally, we simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3: 24 3 = 24 ÷ 3 3 ÷ 3 = 8 1 .
Final Answer Therefore, the simplified result of the subtraction is 8 1 .
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 12 slices and you eat 5 slices, you have eaten 12 5 of the pizza. If your friend eats 7 slices from another pizza cut into 24 slices, they have eaten 24 7 of the pizza. To find out how much more pizza you ate compared to your friend, you would subtract the two fractions, as we did in the problem.
