Convert the improper fraction 35/8 into a mixed number
The Correct Answer and Explanation is:
To convert the improper fraction ( \frac{35}{8} ) into a mixed number, follow these steps:
- Identify the Numerator and Denominator: Here, the numerator is 35, and the denominator is 8.
- Divide the Numerator by the Denominator: Perform the division ( 35 \div 8 ). When you divide, you will determine how many whole parts of 8 fit into 35. [
35 \div 8 = 4 \quad \text{(because } 8 \times 4 = 32\text{)}
] The result, 4, indicates that 8 fits into 35 four times completely. - Calculate the Remainder: Next, calculate the remainder of this division. [
35 – 32 = 3
] Thus, the remainder is 3. - Form the Mixed Number: A mixed number consists of a whole number and a proper fraction. From the division, we have:
- Whole number part: 4 (the quotient)
- Proper fraction part: ( \frac{3}{8} ) (the remainder over the original denominator) Combining these gives us the mixed number: [
4 \frac{3}{8}
]
- Final Answer: Therefore, the mixed number equivalent of the improper fraction ( \frac{35}{8} ) is ( 4 \frac{3}{8} ).
Explanation
An improper fraction is a fraction where the numerator (top number) is larger than or equal to the denominator (bottom number). Converting it into a mixed number can often make it easier to understand and work with, especially in practical situations such as cooking or dividing items.
The process of converting an improper fraction into a mixed number not only involves division to find out how many whole parts fit into the total but also requires attention to the remainder, which forms the fractional part of the mixed number. This conversion highlights the relationship between the whole and fractional quantities, making it a valuable skill in both academic settings and everyday applications. Mixed numbers can also enhance clarity in communication, particularly in mathematical discussions and problem-solving, as they provide a more intuitive representation of quantities than improper fractions.