Convert the following to mixed fractions and simplify: 11_ 8.1 = 12 50.45 = 13 17.084 = 14.10.75 =13.33 =
The Correct Answer and Explanation is:
Here are the correct answers, with each decimal converted to a mixed number and simplified:
11. 8.1 =
➡️ 8 1/10
Explanation:
The whole number is 8. The decimal part is 0.1, which is 1/10. So, 8.1 = 8 1/10.
12. 50.45 =
➡️ 50 9/20
Explanation:
The whole number is 50. The decimal part is 0.45.
To write 0.45 as a fraction:
0.45 = 45/100
Simplify 45/100 by dividing both numerator and denominator by 5:
45 ÷ 5 = 9, 100 ÷ 5 = 20
So, 0.45 = 9/20.
Therefore, 50.45 = 50 9/20.
13. 17.084 =
➡️ 17 21/250
Explanation:
The whole number is 17. The decimal part is 0.084.
0.084 = 84/1000
Simplify 84/1000: Divide both by 4
84 ÷ 4 = 21, 1000 ÷ 4 = 250
So, 0.084 = 21/250
Therefore, 17.084 = 17 21/250
14. 10.75 – 13.33 =
First, do the subtraction:
10.75 – 13.33 = –2.58
Convert –2.58 to a mixed number:
➡️ –2 29/50
Explanation:
–2.58 = –(2 + 0.58)
0.58 = 58/100 → Simplify by dividing by 2:
58 ÷ 2 = 29, 100 ÷ 2 = 50
So, 0.58 = 29/50
Therefore, –2.58 = –2 29/50
Summary of Answers:
- 8.1 = 8 1/10
- 50.45 = 50 9/20
- 17.084 = 17 21/250
- 10.75 – 13.33 = –2 29/50
General Process Explanation
To convert a decimal to a mixed number, start by separating the whole number part from the decimal part. For example, in 8.1, the whole number is 8, and the decimal is 0.1. The decimal portion is then converted into a fraction by writing it over a power of 10. For instance, 0.1 becomes 1/10 because the digit is in the tenths place. If the decimal has two digits, like 0.45, you write it over 100, making 45/100, and then simplify by dividing the numerator and denominator by their greatest common factor. This step ensures the resulting fraction is in its simplest form.
The same applies to decimals with three places, such as 0.084, which becomes 84/1000. Again, reduce it to the lowest terms by finding the greatest common factor of 84 and 1000, giving 21/250.
If the decimal operation involves subtraction, like 10.75 – 13.33, perform the arithmetic first. In this case, it results in –2.58. Then convert 0.58 to a fraction (58/100), simplify to 29/50, and finally write the result as a negative mixed number: –2 29/50.
This approach ensures accuracy in converting decimal numbers to simplified mixed numbers, a valuable skill in both basic arithmetic and practical measurement tasks.
