The Correct Answer and Explanation is:
Correct Answer: -3 21/50
To convert the decimal -3.42 into a mixed number, we first identify the whole number part and the decimal part. The whole number is -3, and the decimal part is 0.42. The negative sign will be part of the final mixed number.
Next, we convert the decimal portion, 0.42, into a fraction. The decimal 0.42 means “forty-two hundredths,” which can be written as the fraction 42/100. This is because the last digit, 2, is in the hundredths place.
After converting the decimal to a fraction, the next step is to simplify the fraction 42/100 to its lowest terms. To do this, we find the greatest common divisor (GCD) of the numerator (42) and the denominator (100). We can see that both numbers are even, so they are divisible by 2.
Let’s divide both the numerator and the denominator by 2:
42 ÷ 2 = 21
100 ÷ 2 = 50
The resulting fraction is 21/50. We check if this fraction can be simplified further. The factors of 21 are 1, 3, 7, and 21. The factors of 50 are 1, 2, 5, 10, 25, and 50. Since the only common factor is 1, the fraction 21/50 is in its simplest form.
Finally, we combine the whole number part (-3) with the simplified fraction (21/50) to create the mixed number. Therefore, -3.42 written as a mixed number is -3 21/50.
