Question

Solve each problem in your head. $$\frac{12}{17}-\frac{4}{17}=$$

Short answer

\(\frac{8}{17}\)

Step-by-step solution

- Identify common denominators

Both fractions, \(\frac{12}{17}\) and \(\frac{4}{17}\), have the same denominator, 17.

- Subtract the numerators

Since the denominators are the same, subtract the numerators: 12 - 4.

- Simplify the result

Perform the subtraction: 12 - 4 = 8. The result is \(\frac{8}{17}\).

Key concepts

headline of the respective core concept

When you want to subtract fractions, the first thing you need to check is if the fractions have the same denominators. The denominator is the bottom number of the fraction. If the denominators are the same, like in \(\frac{12}{17}-\frac{4}{17}\) where both fractions have 17 as the denominator, it means you can easily subtract the numerators. The numerator is the top number of the fraction.
Both fractions having the same denominator makes the subtraction process straightforward since you only need to focus on subtracting the top numbers (numerators). This concept is important because it simplifies the process of handling and combining fractions. If the denominators were different, you would first need to make them the same by finding a common denominator before you could subtract the fractions.

headline of the respective core concept

Once you have ensured that the denominators are the same, you only need to subtract the numerators when subtracting fractions. In this problem, you have \(\frac{12}{17}-\frac{4}{17}\). The denominators are already the same (17), so you only subtract the numerators: 12 - 4. The subtraction of the numerators works just like regular subtraction with whole numbers, making it easier to handle the fractions. This step is straightforward because the denominator, which is 17 in this case, does not change. It is essential to remember that only the numerators get subtracted and the common denominator remains the same.

headline of the respective core concept

After subtracting the numerators, you get a new fraction which may need simplification. Simplifying a fraction involves reducing it to its simplest form so that it's easier to read and understand. However, in our exercise \(\frac{8}{17}-\frac{4}{17}\), the result is \(\frac{8}{17}\), which is already in its simplest form because 8 and 17 have no common factors other than 1. If they had common factors, like \(\frac{8}{16}\), you would simplify it by dividing both the numerator and the denominator by their greatest common factor, which in this case is 8, giving you \(\frac{1}{2}\). Simplifying fractions makes them neater and easier to understand.