Write 4 4/7as an improper fraction.
The Correct Answer and Explanation is:
To convert the mixed number (4 \frac{4}{7}) into an improper fraction, follow these steps:
- Understand Mixed Numbers and Improper Fractions: A mixed number consists of a whole number and a proper fraction. An improper fraction, on the other hand, is a fraction where the numerator is greater than or equal to the denominator.
- Multiply the Whole Number by the Denominator: In the mixed number (4 \frac{4}{7}), the whole number is (4) and the fraction is (\frac{4}{7}). First, we multiply the whole number (4) by the denominator (7):
[
4 \times 7 = 28
] - Add the Numerator: Next, add the numerator (4) from the fraction (\frac{4}{7}) to the result obtained from the previous step:
[
28 + 4 = 32
] - Write the Improper Fraction: Now, we take the sum obtained in the previous step and place it over the original denominator:
[
\frac{32}{7}
]
Thus, the mixed number (4 \frac{4}{7}) can be expressed as the improper fraction (\frac{32}{7}).
Summary
Converting a mixed number to an improper fraction is a straightforward process involving multiplication and addition. This technique is essential in various mathematical operations, such as addition, subtraction, and simplification of fractions. Mixed numbers are often used in everyday situations, such as cooking or measuring, while improper fractions are typically preferred in algebra and higher mathematics because they simplify calculations.
Understanding how to convert between these forms allows for greater flexibility in mathematical problem-solving. It also aids in comprehending the relationship between whole numbers and fractions, which is a fundamental concept in mathematics. In summary, (4 \frac{4}{7}) as an improper fraction is (\frac{32}{7}).