If you change 8 3/4 into its improper fraction, what would it be? a. 35/4 b. 28/4 c. 32/4 d. 11/4
The correct answer and explanation is:
To convert the mixed number 8 3/4 into an improper fraction, follow these steps:
- Multiply the whole number by the denominator of the fraction:
The whole number is 8, and the denominator of the fraction is 4.
Multiply: 8×4=328 \times 4 = 32 - Add the result to the numerator:
The numerator of the fraction is 3. Add this to the result from step 1. 32+3=3532 + 3 = 35 - Write the result as an improper fraction:
Now, the improper fraction is the result from step 2 over the denominator, which is 4.
So, the improper fraction is 35/4.
Therefore, the correct answer is a. 35/4.
Explanation:
A mixed number is a combination of a whole number and a fraction. To convert it into an improper fraction (where the numerator is greater than the denominator), the process involves first multiplying the whole number by the denominator and then adding the numerator. This gives the total number of parts (out of the denominator) in the improper fraction.
For example, in 8 3/4, you have 8 whole parts, and each whole is divided into 4 parts. So, 8 whole parts are equivalent to 32/4. Then, you have an additional 3/4, giving a total of 35/4.
This is helpful because improper fractions are easier to work with in calculations, especially when adding, subtracting, or multiplying fractions. Converting mixed numbers to improper fractions simplifies the process of solving problems.