The Correct Answer and Explanation is:
-30.475
To convert the mixed number -30 19/40 into a decimal, we need to handle the whole number part and the fractional part separately. The negative sign applies to the entire number, so we will first find the decimal for 30 19/40 and then apply the negative sign to the final result.
The number consists of the whole number 30 and the fraction 19/40. The whole number 30 will be the part of the decimal number to the left of the decimal point. Our main task is to convert the fractional part, 19/40, into its decimal equivalent.
To convert a fraction to a decimal, you divide the numerator by the denominator. In this case, we need to perform the division 19 ÷ 40.
We can set up a long division:
- Since 19 is smaller than 40, the result will be less than 1. We place a decimal point and add a zero to 19, making it 190.
- We ask how many times 40 goes into 190. It goes in 4 times (4 × 40 = 160). We write down “4” as the first digit after the decimal point. The remainder is 190 – 160 = 30.
- We bring down another zero to our remainder, making it 300. Now we ask how many times 40 goes into 300. It goes in 7 times (7 × 40 = 280). We write down “7” as the next digit. The remainder is 300 – 280 = 20.
- We bring down a final zero, making the number 200. We ask how many times 40 goes into 200. It goes in exactly 5 times (5 × 40 = 200). We write down “5” as the last digit. The remainder is now 0, so the division is complete.
So, the fraction 19/40 is equal to the decimal 0.475.
Now, we combine the whole number part (30) with the decimal part (0.475). This gives us 30.475.
Finally, we reapply the negative sign from the original mixed number. Therefore, -30 19/40 as a decimal is -30.475.
