27 5.37 16.49 rite the following mixed decimals as mixed numbers and reduce to lowe rms. 17.45 92.004 4.2 157.43
The Correct Answer and Explanation is:
Correct Answers (Mixed Decimals → Mixed Numbers in Lowest Terms)
- 27.5 = 27 ¹/₂
- 5.37 = 5 37/100 (already in lowest terms)
- 16.49 = 16 49/100 (already in lowest terms)
- 17.45 = 17 9/20
- 92.004 = 92 1/250
- 4.2 = 4 ¹/₅
- 157.43 = 157 43/100 (already in lowest terms)
Explanation (Without Using the Word “We”)
A mixed decimal consists of a whole number and a decimal fraction. To convert such a value into a mixed number, first separate the whole number from the decimal. For example, in 27.5, the whole number is 27 and the decimal part is 0.5. The decimal portion is then expressed as a fraction. Here, 0.5 equals ½, making the mixed number 27 ½.
For more complex decimals like 5.37, the number is split into 5 and 0.37. The decimal 0.37 is equivalent to 37/100. Since 37 is a prime number and shares no common factors with 100, the fraction remains 37/100.
In another example, 17.45 becomes 17 and 0.45. The decimal 0.45 converts to 45/100. Both numerator and denominator share a common factor of 5, simplifying the fraction to 9/20. This produces the mixed number 17 9/20.
In cases such as 92.004, the decimal 0.004 becomes 4/1000, which simplifies to 1/250 after dividing both terms by 4. Thus, the full mixed number reads 92 1/250.
For 4.2, the decimal part 0.2 becomes 2/10, which simplifies to 1/5.
Each conversion follows the same logic: isolate the decimal, convert it into a fraction by placing it over the appropriate power of 10, then reduce the fraction to lowest terms by dividing both numerator and denominator by their greatest common divisor.
This process ensures accurate transformation of mixed decimals into proper mixed numbers.
