Subtract the fractions. Write your answer in simplest form.
$\frac{4}{6}-\frac{5}{12}$
We are tasked with subtracting two fractions: \(\frac{4}{6}\) and \(\frac{5}{12}\). To subtract fractions, they must have the same denominator. The denominators are 6 and 12. We can either find a common denominator or simplify the fractions first to make calculations easier. Let's simplify the first fraction, \(\frac{4}{6}\), by dividing both the numerator and the denominator by their greatest common divisor, which is 2. This gives \(\frac{4 \div 2}{6 \div 2} = \frac{2}{3}\). Now the problem becomes \(\frac{2}{3} - \frac{5}{12}\).
To subtract \(\frac{2}{3}\) from \(\frac{5}{12}\), we need a common denominator for 3 and 12. The least common multiple (LCM) of 3 and 12 is 12. We convert \(\frac{2}{3}\) into an equivalent fraction with 12 as the denominator by multiplying both the numerator and the denominator by 4: \(\frac{2 \times 4}{3 \times 4} = \frac{8}{12}\).
Now that both fractions have the same denominator, we can subtract the numerators while keeping the denominator the same: \(\frac{8}{12} - \frac{5}{12} = \frac{8 - 5}{12} = \frac{3}{12}\).
Finally, we simplify the resulting fraction \(\frac{3}{12}\). Dividing both the numerator and the denominator by their greatest common divisor, which is 3, we get \(\frac{3 \div 3}{12 \div 3} = \frac{1}{4}\). Thus, the simplest form of the subtraction is \(\frac{1}{4}\).
Fractions are used in everyday life, such as measuring ingredients for a recipe. For instance, if a recipe calls for \(\frac{2}{3}\) of a cup of flour and you only have \(\frac{5}{12}\) of a cup left in your measuring scoop, you might need to determine the difference between what is needed and what you have. Understanding how to subtract fractions allows you to accurately measure and adjust amounts in cooking, carpentry, or finance, ensuring precision in your tasks.