Subtracting Fractions $$ \frac{3}{4} - 2 $$

Subtracting Fractions with Whole Numbers

Subtracting fractions follows similar rules to adding fractions. When a fraction is subtracted from a whole number, both values must be written in the same fractional form. This helps ensure the subtraction is done correctly and avoids confusion.

1. Theory of Subtracting Fractions

In fraction subtraction, a whole number must be converted into a fraction before performing the operation. By giving both numbers the same denominator, we can subtract the numerators directly while keeping the denominator unchanged.

2. Concept Explanation

The key concept in subtracting fractions with whole numbers is understanding equivalent fractions. A whole number can be written as a fraction over 1, then converted into an equivalent fraction that matches the denominator of the given fraction. This allows subtraction to be done easily.

When the result is negative, it means the value is less than zero. Negative fractions can also be written as mixed numbers for better understanding.

3. Formula or Steps

1. Convert the whole number into a fraction.
2. Change the fraction so both denominators are the same.
3. Subtract the numerators and keep the denominator.
4. Simplify the result and write it as a mixed number if needed.

4. Example Problem

Problem:

$$ \frac{3}{4} - 2 $$

Solution:

Step 1: Change the whole number into a fraction.

$$ 2 = \frac{2}{1} $$

Step 2: Make the denominators the same.

$$ \frac{2}{1} = \frac{8}{4} $$

Step 3: Subtract the fractions.

$$ \frac{3}{4} - \frac{8}{4} = \frac{3 - 8}{4} = -\frac{5}{4} $$

Step 4: Simplify the negative result.

$$ -\frac{5}{4} = -1 \frac{1}{4} $$

5. Visual Explanation Using a Number Line

To better understand this subtraction, imagine a number line. Start at three fourths. Then move two whole units to the left, which is the same as moving eight fourths. You will land at negative one and one fourth on the number line.

Final Answer:

$$ \frac{3}{4} - 2 = -\frac{5}{4} = -1 \frac{1}{4} $$