A lottery has a grand prize of 23 1/2 million dollars. There are 4 people who have winning tickets and they share this prize equally. How many millions of dollars does each person get? Express the answer as a mixed number.
23 1/2 = 23 + 1 / 2 = 46 / 2 + 1 / 2 = 47 / 2
23 1/2 / 4 = 47 / 2 / 2 = 47 / 2 ∙ 2 = 47 / 4 = 40 / 4 + 7 / 4 = 10 7/4
My typo:
23 1/2 / 4 = 47 / 2 / 2 = 47 / 2 ∙ 2 = 47 / 4 = 44 / 4 + 3 / 4 = 11 3/4
By the way 7/4 = 1 3/4
Write answer as:
23 1/2 / 4 = 47 / 2 / 2 = 47 / 2 ∙ 2 = 47 / 4 = 44 / 4 + 3 / 4 = 11 3/4
To find the amount of money each person gets, we need to divide the total grand prize by the number of people who have winning tickets.
The total grand prize is 23 1/2 million dollars. To express this as an improper fraction, we need to multiply the whole number part (23) by the denominator of the fraction (2) and add the numerator (1) to get the numerator of the improper fraction. This gives us (23 * 2) + 1 = 46 + 1 = 47.
Therefore, the total grand prize in fraction form is 47/2 million dollars.
Now, we need to divide this amount equally among the 4 people who have winning tickets. To do this, we divide the fraction by the number of people:
47/2 million dollars ÷ 4 = 47/2 ÷ 4 = (47 ÷ 2) / 4 = 23 1/2 ÷ 4.
To divide a mixed number by a whole number, we multiply the whole number part by the divisor (4) and add the remainder (1) to get the new numerator. This gives us (23 * 4) + 1 = 92 + 1 = 93.
Therefore, each person gets 93/4 million dollars. To express this as a mixed number, we divide the numerator (93) by the denominator (4) and have the remainder as the new numerator. This gives us 93 ÷ 4 = 23 with a remainder of 1.
Therefore, each person gets 23 1/4 million dollars.