Write 3.75 as a mixed number and as an improper fraction. Write vour answers in
The Correct answer and Explanation is:
To write 3.75 as a mixed number and as an improper fraction:
- Mixed Number:
The number 3.75 consists of the whole number 3 and the decimal 0.75. The decimal 0.75 can be written as a fraction:0.75=751000.75 = \frac{75}{100}0.75=10075Simplifying this fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 25:75÷25100÷25=34\frac{75 \div 25}{100 \div 25} = \frac{3}{4}100÷2575÷25=43So, 3.75 can be written as the mixed number 3 \frac{3}{4}. - Improper Fraction:
To convert the mixed number 3343 \frac{3}{4}343 to an improper fraction, you first multiply the whole number by the denominator of the fraction and then add the numerator. The denominator stays the same:(3×4)+3=12+3=15(3 \times 4) + 3 = 12 + 3 = 15(3×4)+3=12+3=15So, the improper fraction is:154\frac{15}{4}415
Explanation:
Mixed Numbers represent a whole number and a fraction. In 3.75, the whole number is 3, and the decimal 0.75 can be converted into the fraction 3/4.
Improper Fractions are fractions where the numerator is greater than the denominator. To convert a mixed number into an improper fraction, multiply the whole number by the denominator (in this case, 3 × 4 = 12) and add the numerator (3). This gives a new numerator of 15, while the denominator remains 4, making the improper fraction 15/4.
Both forms are useful depending on the context: mixed numbers for everyday use and improper fractions for mathematical operations.