Write 1.75 as a mixed number and as an improper fraction

Write 1.75 as a mixed number and as an improper fraction. Write your answers in simplest form.

The Correct Answer and Explanation is :

Converting 1.75 to a Mixed Number and Improper Fraction

Mixed Number:

1.75 as a mixed number is 1 and 3/4.

• The whole number part is 1.
• The decimal part, 0.75, is equivalent to 3/4 because ( 0.75 = \frac{75}{100} ) and simplifies to 3/4.

So, 1.75 = 1 \frac{3}{4} as a mixed number.

Improper Fraction:

To convert the mixed number to an improper fraction:

1. Take the whole number part (1) and multiply it by the denominator of the fractional part (4).
   [
   1 \times 4 = 4
   ]
2. Add the result to the numerator of the fractional part (3).
   [
   4 + 3 = 7
   ]
3. Place this sum over the original denominator (4).
   [
   \frac{7}{4}
   ]
   Thus, 1.75 = \frac{7}{4} as an improper fraction.

Explanation:

A mixed number consists of a whole number and a fraction. To convert a decimal like 1.75 into a mixed number, you first identify the whole number part (which is 1) and then convert the decimal part (0.75) into a fraction. Since 0.75 means 75 out of 100, it simplifies to 3/4.

For converting the mixed number into an improper fraction, you multiply the whole number by the denominator of the fraction, then add the numerator. This step turns the whole number and fraction into a single fraction, where the numerator is larger than the denominator.

Both representations—mixed numbers and improper fractions—are different ways of expressing the same value.