Final answer:
The product of multiplying a fraction by a mixed number can be an improper fraction, fraction, a whole number, or a mixed number, depending on the numbers involved. Multiplication of these numbers involves converting the mixed number to an improper fraction and then multiplying numerators and denominators accordingly.
Step-by-step explanation:
When considering the multiplication of a fraction by a mixed number, the result can vary based on the values involved. A mixed number consists of a whole number and a fraction. To multiply a fraction by a mixed number, you first convert the mixed number to an improper fraction. Then, you multiply the numerators (top numbers) of both fractions together and the denominators (bottom numbers) together.
For example, multiplying the fraction ½ by the mixed number 1¾ (which is 7/4 as an improper fraction) would entail calculating (½) * (7/4) = 7/8, which is still a fraction. However, certain combinations can yield different results:
- a) It is not always the case that the product of a fraction and a mixed number is a mixed number.
- b) The product could be an improper fraction, which can be simplified or converted into a mixed number, if needed.
- c) If the numerator of the resulting fraction is a multiple of the denominator, the product can indeed be a whole number.
- d) The product is not always greater than 1; it depends on the size of the fraction and mixed number you are multiplying.
In conclusion, the result of multiplying a fraction by a mixed number can be a fraction, an improper fraction, a mixed number, or even a whole number, depending on the specific numbers involved in the multiplication.