What is the result of multiplying a fraction by a whole number?

What is the result of multiplying a fraction by a whole number?

• A. It converts the fraction to a whole number
• B. It results in an improper fraction
• C. It combines the fraction with the whole number to create a mixed number
• D. It results in another fraction

Answer: (D)

Multiplying a fraction by a whole number results in another fraction. This is because when you multiply a fraction, such as \( \frac{a}{b} \), by a whole number \( c \), you express it as \( \frac{a \times c}{b} \). The numerator is multiplied by the whole number while the denominator remains the same, which keeps the result in fraction form. For example, if you take the fraction \( \frac{2}{3} \) and multiply it by the whole number 4, the calculation would be \( \frac{2 \times 4}{3} = \frac{8}{3} \). The result, \( \frac{8}{3} \), is still a fraction, although it may also be expressed as a mixed number (\( 2 \frac{2}{3} \)), but it fundamentally remains a fraction in its improper form. This confirms that multiplying a fraction by a whole number does not convert it to a whole number, nor does it inherently create a mixed number. It might result in an improper fraction if the numerator exceeds the denominator, but it is still classified as a fraction overall.

Multiplying a fraction by a whole number results in another fraction. This is because when you multiply a fraction, such as ( \frac{a}{b} ), by a whole number ( c ), you express it as ( \frac{a \times c}{b} ). The numerator is multiplied by the whole number while the denominator remains the same, which keeps the result in fraction form.

For example, if you take the fraction ( \frac{2}{3} ) and multiply it by the whole number 4, the calculation would be ( \frac{2 \times 4}{3} = \frac{8}{3} ). The result, ( \frac{8}{3} ), is still a fraction, although it may also be expressed as a mixed number (( 2 \frac{2}{3} )), but it fundamentally remains a fraction in its improper form.

This confirms that multiplying a fraction by a whole number does not convert it to a whole number, nor does it inherently create a mixed number. It might result in an improper fraction if the numerator exceeds the denominator, but it is still classified as a fraction overall.