What is 7/4 as a mixed number
The Correct Answer and Explanation is :
To convert the improper fraction ( \frac{7}{4} ) into a mixed number, follow these steps:
- Divide the numerator by the denominator: Divide ( 7 ) (the numerator) by ( 4 ) (the denominator).
[
7 \div 4 = 1 \quad \text{(with a remainder of 3)}
] This tells us that ( 4 ) fits into ( 7 ) one time. - Find the remainder: The remainder from the division is ( 3 ).
- Write the mixed number: The whole number part of the mixed number is the quotient from the division (which is ( 1 )), and the fractional part is formed from the remainder over the original denominator. Thus, the remainder ( 3 ) becomes the numerator of the fraction, while the denominator remains ( 4 ). Therefore, we can write:
[
\frac{7}{4} = 1 \frac{3}{4}
]
Explanation
A mixed number combines a whole number and a proper fraction. It represents quantities greater than one but less than the next whole number. In this case, since ( \frac{7}{4} ) is greater than ( 1 ) and less than ( 2 ), it can be expressed as ( 1 \frac{3}{4} ).
This conversion is particularly useful in various mathematical contexts, such as measurements in cooking or construction, where mixed numbers can often make it easier to understand and visualize quantities.
Additionally, improper fractions like ( \frac{7}{4} ) can be less intuitive for some people, as they represent a quantity where the numerator exceeds the denominator. Converting them into mixed numbers makes it easier to grasp the value, as it clearly indicates the whole number and the additional fraction that completes it. Thus, ( 1 \frac{3}{4} ) effectively communicates that you have one whole part and three-quarters of another.