Question

c. Convert the following mixed number into an improper fraction. Simplify your answer and express it in lowest terms, if applicable. Enter any negative signs in the numerator

Ask by John Stanley. in Canada
Mar 10,2025

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Answer

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. Simplify if possible.

Solution

To convert a mixed number into an improper fraction, follow these steps: 1. **Identify the mixed number**: A mixed number consists of a whole number and a proper fraction. For example, if we have \( a \frac{b}{c} \), where \( a \) is the whole number, \( b \) is the numerator of the fraction, and \( c \) is the denominator. 2. **Convert to an improper fraction**: The formula to convert a mixed number \( a \frac{b}{c} \) into an improper fraction is: \[ \text{Improper Fraction} = \frac{(a \cdot c) + b}{c} \] 3. **Simplify the fraction**: If the resulting fraction can be simplified, divide both the numerator and the denominator by their greatest common divisor (GCD). Please provide the mixed number you would like to convert, and I will perform the conversion and simplification for you.

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Extra Insights

To convert a mixed number into an improper fraction, you multiply the whole number by the denominator, add the numerator, and then write that sum over the original denominator. For example, with the mixed number 2 3/4, you'd calculate (2 * 4) + 3 = 8 + 3 = 11, so it would become 11/4. If you have a negative mixed number like -1 1/2, it converts to -(1 * 2 + 1)/2, resulting in -3/2. Remember to always check for simplification! If your final improper fraction's numerator and denominator have a common factor (like 4 and 8 both being divisible by 4), divide them down to get it in lowest terms. For instance, 8/12 simplifies to 2/3. Keeping your answers neat and tidy makes math much more enjoyable!

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