Problem 65 - Prealgebra

Question

These problems review the four basic operations with fractions from this chapter. Perform the indicated operations. $$\frac{3}{7}-\frac{2}{7}$$

Step-by-Step Solution

Answer

\(\frac{1}{7}\)

Step 1: Identify the Operation

The problem requires you to perform a subtraction operation on fractions: \( \frac{3}{7} - \frac{2}{7} \).

Step 2: Ensure Like Denominators

Both fractions have the same denominator, 7, which means they are like fractions and we can subtract them directly.

Step 3: Subtract the Numerators

To subtract like fractions, subtract their numerators while keeping the denominator the same. So, subtract 2 from 3: \( 3 - 2 = 1 \).

Step 4: Write the Resulting Fraction

The result of the subtraction is \( \frac{1}{7} \), which is the resulting fraction after performing the operation.

Key Concepts

Subtracting Fractions

Subtracting fractions might seem tricky at first but it's straightforward when you break it down into simple steps. The goal is to take one fraction away from another. Picture it as having some parts of a whole and then taking a few parts away. For example, if you have \( \frac{3}{7} \) and you subtract \( \frac{2}{7} \), you are taking two out of the three parts, which leaves you with \( \frac{1}{7} \).
It's important to focus on the numerators when subtracting fractions. Then, once you've subtracted the numerator of the second fraction from the first, your denominator stays the same. Remember, the numerator is the top number while the denominator is the bottom number.

• Always ensure your denominators are the same before subtracting.
• Subtract only the numerators and maintain the common denominator.

Like Denominators

Understanding the concept of like denominators is crucial when dealing with fractions. Like denominators mean that the fractions share the same denominator.
This is essential because it lets us treat the fractions as parts of the same whole. In our example, \( \frac{3}{7} \) and \( \frac{2}{7} \) have the same denominator of 7. This means they are two parts of something divided into 7 equal parts.

• Fractions must have like denominators to be added or subtracted directly.
• If denominators are unlike, you may need to find a common denominator first.

Having like denominators eliminates the need for extra steps or adjustments, making the subtraction simpler and faster.

Fractions Subtraction Steps

Subtracting fractions involves a few clear steps that you can follow every time. Let's go through these steps to ensure you understand how to tackle any similar problem:

• **Step 1: Identify the Fractions** - Look at the given fractions and see what operation you need to perform.
• **Step 2: Check for Like Denominators** - Ensure the fractions have the same denominator. If not, you'll need to adjust them to have a common one.
• **Step 3: Subtract the Numerators** - With like denominators, subtract the numerator of the second fraction from the numerator of the first.
• **Step 4: Write the Result** - Place the result of the subtraction over the common denominator.

Using these steps makes subtracting fractions less intimidating and much more manageable. Practice them to gain confidence in subtracting fractions, and soon it'll be second nature!