Which number is equivalent to the improper fraction 35/4
The Correct Answer and Explanation is :
The correct answer is: 8.75
To find the number equivalent to the improper fraction ( \frac{35}{4} ), we need to convert this fraction into a mixed number and a decimal.
Step 1: Converting to a Mixed Number
An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). To convert ( \frac{35}{4} ) into a mixed number, we perform the following steps:
- Divide the numerator by the denominator:
- ( 35 \div 4 = 8 ) (this is the whole number part)
- The remainder of this division can be found by calculating ( 35 – (4 \times 8) ).
- ( 4 \times 8 = 32 )
- ( 35 – 32 = 3 )
- Write the mixed number:
- The quotient (8) is the whole number, and the remainder (3) becomes the numerator of the fractional part.
- Thus, ( \frac{35}{4} ) can be expressed as ( 8 \frac{3}{4} ).
Step 2: Converting to a Decimal
To convert ( \frac{35}{4} ) into a decimal:
- Perform the division:
- ( 35 \div 4 = 8.75 )
So, ( \frac{35}{4} ) is equivalent to both the mixed number ( 8 \frac{3}{4} ) and the decimal ( 8.75 ).
Conclusion
In summary, the improper fraction ( \frac{35}{4} ) can be expressed as the mixed number ( 8 \frac{3}{4} ) or as a decimal ( 8.75 ). Each form provides a different way to represent the same quantity, allowing for greater flexibility in mathematical applications. Mixed numbers are often easier to visualize in terms of quantities, while decimal representations can be more straightforward for calculations, particularly in contexts like financial transactions or scientific measurements.