Adding Fractions $$ \frac{3}{4} + 1 = \frac{7}{4} = 1 \frac{3}{4} $$

Adding Fractions with Whole Numbers

Adding fractions is a basic mathematical skill that helps us combine numbers written in different forms. Sometimes, we need to add a fraction and a whole number. To solve this problem correctly, both numbers must be written in the same form before adding them together.

1. Theory of Adding Fractions

When adding fractions and whole numbers, the whole number must first be converted into a fraction. This allows both numbers to have a denominator, making the addition process easier and more accurate.

2. Concept Explanation

The key concept in adding fractions with whole numbers is making sure that both numbers have the same denominator. A whole number can be written as a fraction by placing it over 1. After that, the fraction is adjusted so its denominator matches the other fraction.

3. Formula or Steps

1. Convert the whole number into a fraction.
2. Make the denominators the same.
3. Add the numerators and keep the denominator.
4. Simplify the result if necessary.

4. Example Problem

Problem:

$$ \frac{3}{4} + 1 $$

Solution:

Step 1: Change the whole number into a fraction.

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

Step 2: Make the denominators the same.

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

Step 3: Add the fractions.

$$ \frac{3}{4} + \frac{4}{4} = \frac{7}{4} $$

Step 4: Simplify the result.

$$ \frac{7}{4} = 1 \frac{3}{4} $$

Final Answer:

$$ \frac{3}{4} + 1 = \frac{7}{4} = 1 \frac{3}{4} $$