Question
How to add fractions
Answers
GPT-4o mini
Adding fractions involves a few steps, especially if the fractions have different denominators. Here’s a step-by-step guide:
### Step 1: Identify the Fractions
Let's say you want to add two fractions, for example: \(\frac{a}{b}\) and \(\frac{c}{d}\).
### Step 2: Find a Common Denominator
If the denominators \(b\) and \(d\) are different, you'll need to find a common denominator. This can often be done by finding the least common multiple (LCM) of the two denominators. The common denominator will be used for both fractions.
### Step 3: Convert Fractions
Convert each fraction to an equivalent fraction with the common denominator:
- For \(\frac{a}{b}\): Multiply the numerator and denominator by \(d\) (the denominator of the second fraction).
- For \(\frac{c}{d}\): Multiply the numerator and denominator by \(b\) (the denominator of the first fraction).
So, the fractions become:
\[
\frac{a \cdot d}{b \cdot d} \quad \text{and} \quad \frac{c \cdot b}{d \cdot b}
\]
### Step 4: Add the Numerators
Now that both fractions have the same denominator, you can add them:
\[
\frac{a \cdot d + c \cdot b}{b \cdot d}
\]
### Step 5: Simplify the Fraction
Finally, simplify the resulting fraction if possible. This can include reducing the fraction or converting to a mixed number if the numerator is larger than the denominator.
### Example
Let’s add \(\frac{1}{4}\) and \(\frac{1}{6}\).
1. **Identify the fractions**: \(\frac{1}{4}\) and \(\frac{1}{6}\).
2. **Find a common denominator**: The LCM of 4 and 6 is 12.
3. **Convert fractions**:
- \(\frac{1}{4} = \frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}\)
- \(\frac{1}{6} = \frac{1 \cdot 2}{6 \cdot 2} = \frac{2}{12}\)
4. **Add the numerators**:
\[
\frac{3}{12} + \frac{2}{12} = \frac{3 + 2}{12} = \frac{5}{12}
\]
5. **Simplify if possible**: \(\frac{5}{12}\) is already in its simplest form.
So, \(\frac{1}{4} + \frac{1}{6} = \frac{5}{12}\).
That’s how you add fractions! If you have any specific fractions in mind or further questions, feel free to ask!
### Step 1: Identify the Fractions
Let's say you want to add two fractions, for example: \(\frac{a}{b}\) and \(\frac{c}{d}\).
### Step 2: Find a Common Denominator
If the denominators \(b\) and \(d\) are different, you'll need to find a common denominator. This can often be done by finding the least common multiple (LCM) of the two denominators. The common denominator will be used for both fractions.
### Step 3: Convert Fractions
Convert each fraction to an equivalent fraction with the common denominator:
- For \(\frac{a}{b}\): Multiply the numerator and denominator by \(d\) (the denominator of the second fraction).
- For \(\frac{c}{d}\): Multiply the numerator and denominator by \(b\) (the denominator of the first fraction).
So, the fractions become:
\[
\frac{a \cdot d}{b \cdot d} \quad \text{and} \quad \frac{c \cdot b}{d \cdot b}
\]
### Step 4: Add the Numerators
Now that both fractions have the same denominator, you can add them:
\[
\frac{a \cdot d + c \cdot b}{b \cdot d}
\]
### Step 5: Simplify the Fraction
Finally, simplify the resulting fraction if possible. This can include reducing the fraction or converting to a mixed number if the numerator is larger than the denominator.
### Example
Let’s add \(\frac{1}{4}\) and \(\frac{1}{6}\).
1. **Identify the fractions**: \(\frac{1}{4}\) and \(\frac{1}{6}\).
2. **Find a common denominator**: The LCM of 4 and 6 is 12.
3. **Convert fractions**:
- \(\frac{1}{4} = \frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}\)
- \(\frac{1}{6} = \frac{1 \cdot 2}{6 \cdot 2} = \frac{2}{12}\)
4. **Add the numerators**:
\[
\frac{3}{12} + \frac{2}{12} = \frac{3 + 2}{12} = \frac{5}{12}
\]
5. **Simplify if possible**: \(\frac{5}{12}\) is already in its simplest form.
So, \(\frac{1}{4} + \frac{1}{6} = \frac{5}{12}\).
That’s how you add fractions! If you have any specific fractions in mind or further questions, feel free to ask!