zoey made 5 1/2 cups of trail mix for a camping trip. she wants to divide the trail mix into 3/4 cup servings. if zoey decides to us the 3/4 cup servings how much more trail mix will she need.explain
5 1/2/(3/4) = 5 1/2 * 4/3 = 11/2 * 4/3 = 44/6 = 22/3 = 7 1/3 servings.
2/3 of a serving needed:
2/3 * (3/4)cup = 6/12 = 1/2 cup needed.
To solve this problem, we need to calculate the total number of 3/4 cup servings in 5 1/2 cups of trail mix.
Step 1: Convert 5 1/2 cups to an improper fraction.
To simplify the calculation, we convert the mixed number to an improper fraction.
5 1/2 = (2 * 5) + 1 = 10/2 + 1/2 = 11/2
Step 2: Divide the total amount of trail mix by the serving size.
To find the number of 3/4 cup servings, we divide the total amount of trail mix (11/2 cups) by the serving size (3/4 cup).
(11/2) ÷ (3/4)
Step 3: Invert the second fraction and multiply.
When dividing fractions, we take the reciprocal of the second fraction and multiply.
(11/2) * (4/3) = (11 * 4) / (2 * 3) = 44/6 = 22/3
Step 4: Simplify the fraction.
We simplify the fraction 22/3 to mixed number form to see how many 3/4 cup servings we can get.
22/3 = (3 * 7) + 1 = 21/3 + 1/3 = 7 1/3
Therefore, if Zoey decides to use 3/4 cup servings, she would need 7 1/3 more cups of trail mix.
To solve this problem, we need to find two things:
1. The total number of 3/4 cup servings that can be made from 5 1/2 cups of trail mix.
2. The amount of trail mix remaining after making those servings.
Let's start with finding the total number of 3/4 cup servings that can be made from 5 1/2 cups of trail mix:
To convert mixed numbers to improper fractions, we multiply the whole number by the denominator of the fraction and add the numerator. So, 5 1/2 is equivalent to (5 x 2) + 1 = 11/2.
Now, we can divide the 5 1/2 cups by 3/4 cup per serving:
(11/2) / (3/4) = (11/2) x (4/3) = (11 x 4) / (2 x 3) = 44/6 = 22/3
So, Zoey can make a total of 22/3 or 7 1/3 servings from 5 1/2 cups of trail mix. However, since she cannot have a fraction of a serving, she can only make 7 servings (as 22 ÷ 3 = 7 remainder 1).
Next, we need to determine the amount of trail mix remaining after making those servings:
To find out how much trail mix was used for the servings, we need to multiply the number of servings by the serving size (3/4 cup):
7 servings x (3/4 cup/serving) = 7(3/4) = (7/1)(3/4) = (7 x 3) / (1 x 4) = 21/4 = 5 1/4 cups
Now, we subtract the amount used (5 1/4 cups) from the original amount (5 1/2 cups) to find how much more trail mix Zoey will need:
5 1/2 cups - 5 1/4 cups = (11/2) - (5/4) = (22/4) - (5/4) = (22 - 5)/4 = 17/4 = 4 1/4 cups
Therefore, Zoey will need 4 1/4 cups more trail mix to have enough for the desired 3/4 cup servings.