describe a real-world situation that is modeled by dividing two fractions or mixed numbers
half of the kids ate 3/4 of the pie.
A real-world situation that can be modeled by dividing two fractions or mixed numbers is the scenario of sharing food among a group of people.
For example, let's say you have 3/4 of a pizza and you want to divide it equally among 2 friends. You can model this situation using division of fractions.
To find out how much pizza each friend will get, you divide the amount of pizza you have (3/4) by the number of friends (2). This can be expressed as the division problem:
(3/4) ÷ 2
To solve this problem, we can convert the mixed number 3/4 into an improper fraction. Multiplying the whole number (3) by the denominator (4) and adding the numerator (3), we get 12/4. So 3/4 is equal to 12/4.
Now let's rewrite the division problem using the improper fraction:
(12/4) ÷ 2
To divide fractions, you actually multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 2 is 1/2.
So, our division problem becomes:
(12/4) * (1/2)
To multiply fractions, you multiply the numerators and the denominators separately. Therefore:
12 * 1 = 12
4 * 2 = 8
So, the result of our multiplication is 12/8.
Now, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
12 ÷ 4 = 3
8 ÷ 4 = 2
Therefore, 12/8 simplifies to 3/2.
This means that each friend will get 3/2 (or 1 1/2) of the pizza.