To convert a mixed number into an improper fraction, follow these steps:
-
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).
-
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 \( 2 \): \[ 2 \times 4 = 8 \]
-
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 \( 3 \): \[ 8 + 3 = 11 \]
-
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: \[ \frac{(a \times c) + b}{c} \]
23 answers