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.
A. If zoey decides to use the 3/4 cup servings, how much more trail mix will she need? explain
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To find out how much more trail mix Zoey will need, we need to subtract the amount she already made from the desired amount of trail mix.
1. First, we need to convert the mixed number 5 1/2 into an improper fraction. To do this, we multiply the whole number (5) by the denominator of the fraction (2) and add the numerator (1). This gives us 5 x 2 + 1 = 11.
So, 5 1/2 is equal to 11/2 cups.
2. Next, we need to find out how many 3/4 cup servings Zoey can get from 11/2 cups. We divide 11/2 by 3/4. However, when dividing fractions, we multiply the first fraction by the reciprocal (flipping the numerator and denominator) of the second fraction.
So, we have (11/2) / (3/4) = (11/2) * (4/3).
Multiplying the numerators (top numbers) gives us 44/6.
3. To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2 in this case.
44/6 ÷ 2/2 = (44 ÷ 2) / (6 ÷ 2) = 22/3 cup servings.
4. Since Zoey wants to divide the trail mix into 3/4 cup servings and she can make 22/3 cup servings from the trail mix she already made, we subtract the two quantities:
22/3 - 3/4 = (22/3) * (4/4) - (3/4) = 88/12 - 3/4.
5. To subtract fractions, we need to have a common denominator. The common denominator of 12 and 4 is 12. Therefore, we rewrite the fractions:
88/12 - 3/4 = (88/12) - (9/12) = 79/12.
So, Zoey will need an additional 79/12 cups of trail mix to have enough for 3/4 cup servings.