At Mariah's birthday party, 9 of her friends ate 3/4 of her chocolate cake. How much of the cake did each friend eat?
To find out how much each friend ate, we need to divide the amount of cake eaten by the number of friends.
9 friends ate 3/4 of the cake.
This means each friend ate 3/4 divided by 9.
To divide fractions, we can multiply by the reciprocal of the divisor.
So, 3/4 ÷ 9 is the same as 3/4 * 1/9.
Multiplying these fractions gives us 3/36, which simplifies to 1/12.
Therefore, each friend ate 1/12 of the cake.
The product of 9 and the sum of a number and 8 is 180. What is the number?
Let's let the number we are looking for be represented by "x".
The sum of the number and 8 can be expressed as x + 8.
According to the problem, the product of 9 and the sum of the number and 8 is 180. This can be written as:
9(x + 8) = 180.
To solve for x, we will first distribute the 9 to the terms inside the parentheses:
9x + 72 = 180.
Next, we can isolate the variable by subtracting 72 from both sides of the equation:
9x = 180 - 72.
Simplifying the right side gives us:
9x = 108.
Finally, we can solve for x by dividing both sides of the equation by 9:
x = 108/9.
Simplifying the right side gives us the solution:
x = 12.
Therefore, the number we are looking for is 12.
To find out how much of the cake each friend ate, we need to divide the total amount eaten by the number of friends who ate it.
In this case, 9 friends ate 3/4 of the cake. To calculate how much each friend ate, we can divide 3/4 by 9.
To divide a fraction by a whole number, follow these steps:
1. Invert the whole number and turn it into a fraction. In this case, the whole number is 9, so we will convert it to the fraction 9/1.
2. Multiply the inverted whole number fraction by the fraction you want to divide it by. In this case, we will multiply (3/4) by (1/9).
Let's now calculate this:
(3/4) ÷ (9/1) = (3/4) * (1/9)
To simplify the multiplication, we multiply the numerators (top numbers) together and the denominators (bottom numbers) together:
(3 * 1) / (4 * 9) = 3/36
Finally, we can reduce the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, both 3 and 36 can be divided by 3:
3/36 = 1/12
Therefore, each friend ate 1/12 of the chocolate cake.