Write three and two fourths as an improper fraction.

Write three and two fourths as an improper fraction.
Give your answer in its lowest terms.

The Correct Answer and Explanation is:

To write the mixed number three and two fourths (3 2/4) as an improper fraction in its lowest terms, we’ll first convert the mixed number to an improper fraction and then simplify it.

Step 1: Convert the Mixed Number to an Improper Fraction

A mixed number consists of a whole number and a fraction. To convert it to an improper fraction:

1. Multiply the whole number by the denominator of the fraction part.
2. Add the result to the numerator of the fraction part.
3. Place this sum over the original denominator.

For 3 2/4:

1. Multiply the whole number (3) by the denominator (4):
   [
   3 \times 4 = 12
   ]
2. Add the result (12) to the numerator (2):
   [
   12 + 2 = 14
   ]
3. Write this sum over the original denominator (4):
   [
   3 \frac{2}{4} = \frac{14}{4}
   ]

Step 2: Simplify the Fraction

To express (\frac{14}{4}) in its simplest form, we need to find the greatest common divisor (GCD) of 14 and 4, which is 2.

1. Divide both the numerator and the denominator by 2:
   [
   \frac{14 \div 2}{4 \div 2} = \frac{7}{2}
   ]

So, the improper fraction form of three and two fourths, in its lowest terms, is:
[
\frac{7}{2}
]

Explanation

Converting mixed numbers to improper fractions allows for easier calculations in operations like addition, subtraction, multiplication, and division. Here, we first transformed the whole part into a fraction by multiplying it by the fraction’s denominator, then combined it with the existing fraction. Simplifying fractions is an essential final step that ensures clarity and reduces the fraction to its simplest form for easier interpretation and calculation.