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, we will follow a straightforward process that involves division and understanding of fractions.
Steps for Conversion:
- Divide the Numerator by the Denominator:
We start by dividing 35 by 8. This can be done either by long division or simple division. When you divide ( 35 ) by ( 8 ), the quotient is ( 4 ) and the remainder is ( 3 ) because:
[
35 \div 8 = 4 \quad \text{(since ( 8 \times 4 = 32 ))}
]
The difference between 35 and 32 gives us a remainder of ( 3 ):
[
35 – 32 = 3
] - Write the Mixed Number:
A mixed number consists of a whole number and a proper fraction. From our division, we found that the quotient is ( 4 ) (this represents the whole number part), and the remainder ( 3 ) is placed over the original denominator ( 8 ) (which represents the fractional part). Therefore, we can express ( \frac{35}{8} ) as:
[
4 \frac{3}{8}
]
This tells us that ( \frac{35}{8} ) can be represented as four whole parts and three-eighths of another part. - Check the Conversion:
To verify our conversion, we can convert the mixed number back to an improper fraction:
[
4 \frac{3}{8} = 4 + \frac{3}{8} = \frac{32}{8} + \frac{3}{8} = \frac{32 + 3}{8} = \frac{35}{8}
]
This confirms that our conversion is correct.
Conclusion:
The improper fraction ( \frac{35}{8} ) is converted into the mixed number ( 4 \frac{3}{8} ). This process of dividing the numerator by the denominator and organizing the result into a whole number and a proper fraction is essential when converting improper fractions into mixed numbers. It allows for clearer understanding and easier visualization of the value represented by the fraction.