What is 2.75 in fraction form in simplest form
The Correct Answer and Explanation is:
To convert 2.75 into a fraction, follow these steps:
- Separate the whole number and the decimal:
- The whole number is 2, and the decimal part is 0.75.
- Convert the decimal part (0.75) into a fraction:
- 0.75 is the same as 75/100. To simplify this, find the greatest common divisor (GCD) of 75 and 100. The GCD of 75 and 100 is 25.
- Now, divide both the numerator and the denominator by 25: 75100=75÷25100÷25=34\frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4}10075=100÷2575÷25=43
- Combine the whole number and the fraction:
- The whole number part is 2, so write it as a fraction with a denominator of 1: 2=212 = \frac{2}{1}2=12
- Now, combine the whole number fraction and the fraction from the decimal: 234=21+342 \frac{3}{4} = \frac{2}{1} + \frac{3}{4}243=12+43 To add these fractions, you need a common denominator. The least common denominator (LCD) of 1 and 4 is 4.
- Rewrite the fractions with the common denominator:
- Convert 21\frac{2}{1}12 to 84\frac{8}{4}48 because: 21=2×41×4=84\frac{2}{1} = \frac{2 \times 4}{1 \times 4} = \frac{8}{4}12=1×42×4=48
- Add the fractions: 84+34=8+34=114\frac{8}{4} + \frac{3}{4} = \frac{8 + 3}{4} = \frac{11}{4}48+43=48+3=411
Thus, the decimal 2.75 is equivalent to the fraction 11/4 in simplest form.
Explanation:
- We first dealt with the whole number and the decimal part separately. The decimal part 0.75 was converted into a fraction (75/100), and by simplifying it, we got 3/4.
- Then, we combined the fraction with the whole number. By finding a common denominator, we were able to add the two fractions to get the final result of 11/4.
