Carly is making cookies from a premade roll of cookie dough. She cuts the roll into slices that are inches thick. If the roll is 12 inches long, how many cookies would Carly be able to make?
Your older brother just purchased a car with a loan that has a 51% interest rate. What is the interest rate converted into a fraction in its simplest form?
Answer (1)
To find the number of cookies, divide the total length of the dough by the thickness of each slice: 8 1 12 = 12 × 8 .
Calculate the number of cookies: 12 × 8 = 96 .
Convert the percentage to a fraction by dividing by 100: 51% = 100 51 .
The number of cookies Carly can make is 96 and the interest rate as a fraction is 100 51 .
Explanation
Problem Analysis We are given two separate problems. The first problem involves calculating how many cookies Carly can make from a roll of dough. The second problem requires converting a percentage into a simplified fraction. We will address each problem individually.
Solving the Cookie Problem For the cookie problem:
The total length of the cookie dough roll is 12 inches.
The thickness of each cookie slice is 8 1 inches.
To find the number of cookies, we divide the total length of the roll by the thickness of each cookie: Number of cookies = Thickness of each cookie Total length = 8 1 12 To divide by a fraction, we multiply by its reciprocal: 8 1 12 = 12 × 8 = 96 Therefore, Carly can make 96 cookies.
Solving the Interest Rate Problem For the interest rate problem:
The interest rate is 51%.
To convert a percentage to a fraction, we divide by 100: 51% = 100 51 Now, we need to check if this fraction can be simplified. The prime factorization of 51 is 3 × 17 , and the prime factorization of 100 is 2 2 × 5 2 . Since they have no common factors, the fraction is already in its simplest form.
Final Answer Therefore, Carly can make 96 cookies, and the interest rate as a fraction in its simplest form is 100 51 .
Examples
Imagine you're planning a pizza party. You have a 24-inch long baguette to make mini pizzas, and you want each pizza to be 1/4 inch thick. Using the same math as Carly's cookie problem, you can calculate how many mini pizzas you can make: 24 / (1/4) = 24 * 4 = 96 mini pizzas! Similarly, understanding percentages and fractions is crucial when calculating discounts at a store. If an item is 25% off, you know you're paying 75/100 or 3/4 of the original price.
