Question

how to turn a mixed number into an improper fraction?

Answer 1

To convert a mixed number into an improper fraction, follow these steps:

1. **Identify the parts of the mixed number**: A mixed number consists of a whole number and a proper fraction (for example, \( 2 \frac{3}{4} \), where \( 2 \) is the whole number and \( \frac{3}{4} \) is the fraction).

2. **Multiply the whole number by the denominator of the fractional part**: Multiply the whole number by the denominator of the fraction. In our example, the denominator of \( \frac{3}{4} \) is \( 4 \), and the whole number is \( 2 \):
\[
2 \times 4 = 8
\]

3. **Add the numerator of the fractional part to the result from step 2**: Take the result from step 2 and add the numerator of the fraction. In our example, the numerator is \( 3 \):
\[
8 + 3 = 11
\]

4. **Write the result as the numerator over the original denominator**: Combine the result from step 3 with the original denominator to form the improper fraction. In this case, the improper fraction is:
\[
\frac{11}{4}
\]

So, the mixed number \( 2 \frac{3}{4} \) converts to the improper fraction \( \frac{11}{4} \).

In summary, the formula for converting a mixed number \( a \frac{b}{c} \) into an improper fraction is:
\[
\frac{(a \times c) + b}{c}
\]