Problem 62 - Algebra 1

Question

Find the difference. $$\frac{4}{5}-\frac{2}{5}$$

Step-by-Step Solution

Answer

The difference is \(\frac{2}{5}\).

Step 1: Identify the Like Denominators

Observe that the denominators of both fractions are the same, which is 5.

Step 2: Subtract the Numerators

Since the denominators are the same, keep the denominator as is and subtract the numerators. The operation becomes \(4 - 2 = 2\).

Step 3: Write Down the Result

The difference between the two fractions is the resultant fraction, which is \(\frac{2}{5}\).

Key Concepts

Like Denominators

When subtracting fractions, having like denominators is important because it simplifies the process. Denominators are the bottom parts of fractions that tell you into how many pieces the whole is being divided. If fractions share the same denominator, they effectively have equal-sized parts. This means you can directly subtract the numerators without making any changes to the denominators. In the case of the problem \( \frac{4}{5} - \frac{2}{5} \), both denominators are 5, making them like denominators. It's crucial because it allows subtraction to focus entirely on what's on top - the numerators.

Numerators

The numerators are the top numbers in fractions, representing how many parts out of the whole you have or are dealing with. In fractional subtraction with like denominators, the numerators are subtracted from each other. Looking at the exercise \( \frac{4}{5} - \frac{2}{5} \), the numerators are 4 and 2. Since the denominators are alike, you subtract the smaller numerator from the larger one. Therefore, the operation simplifies to subtracting the numerators while maintaining the same denominator: \( 4 - 2 = 2 \). This calculation gives the numerator of the resultant fraction.

Mathematical Operations

Subtraction is the mathematical operation used in this exercise, specifically for the numerators, because the denominators are alike. In mathematics, subtraction is one of the basic operations used to find the difference between numbers. A fraction subtraction like \( \frac{4}{5} - \frac{2}{5} \) involves a straightforward subtraction of the numerators due to like denominators. When applying operations to fractions, it is essential to maintain the integrity of the denominator. This simplifies the process and enables an accurate calculation of the difference in fractional form.

Resultant Fraction

The resultant fraction is what you end up with after performing the subtraction of the fractions. It's important because it gives you the final answer, which represents the difference between the two fractions. For our exercise \( \frac{4}{5} - \frac{2}{5} \), after subtracting the numerators and keeping the denominator the same, you get \( \frac{2}{5} \). The number 2 is the new numerator, as determined by the subtraction \( 4 - 2 \). Meanwhile, the denominator remains 5, as no changes are required when dealing with like denominators. Hence, \( \frac{2}{5} \) is your simplified solution, showing the fractional difference.