Question
Evan bought 3 pints of vegetable soup. 1 Serving is 3/4 of a pint. How many servings of vegetable soup can Evan make?
Answers
Answered by
GPT-4o
To determine how many servings of vegetable soup Evan can make, we need to find out how many 3/4-pint servings can be derived from 3 pints.
Here's the step-by-step calculation:
1. Start by determining the total amount of soup Evan has:
\[
3 \text{ pints}
\]
2. Each serving is 3/4 of a pint. So, we need to figure out how many 3/4-pint servings fit into 3 pints. This is essentially dividing 3 pints by 3/4 pint per serving:
\[
\text{Number of servings} = \frac{3 \text{ pints}}{\frac{3}{4} \text{ pint/serving}}
\]
3. To divide by a fraction, you can multiply by its reciprocal. The reciprocal of 3/4 is 4/3. Hence:
\[
\text{Number of servings} = 3 \times \frac{4}{3}
\]
4. Simplify the multiplication:
\[
3 \times \frac{4}{3} = \frac{3 \times 4}{3} = \frac{12}{3} = 4
\]
Therefore, Evan can make \( \boxed{4} \) servings of vegetable soup.
Here's the step-by-step calculation:
1. Start by determining the total amount of soup Evan has:
\[
3 \text{ pints}
\]
2. Each serving is 3/4 of a pint. So, we need to figure out how many 3/4-pint servings fit into 3 pints. This is essentially dividing 3 pints by 3/4 pint per serving:
\[
\text{Number of servings} = \frac{3 \text{ pints}}{\frac{3}{4} \text{ pint/serving}}
\]
3. To divide by a fraction, you can multiply by its reciprocal. The reciprocal of 3/4 is 4/3. Hence:
\[
\text{Number of servings} = 3 \times \frac{4}{3}
\]
4. Simplify the multiplication:
\[
3 \times \frac{4}{3} = \frac{3 \times 4}{3} = \frac{12}{3} = 4
\]
Therefore, Evan can make \( \boxed{4} \) servings of vegetable soup.
Answer
Allison is making bibs for her baby cousin. She has 2 1/4 yards of fabric in each bib uses 3/8 of a yard of fabric. How many bibs can Allison make?
Answered by
GPT-4o
To determine how many bibs Allison can make, we need to find out how many 3/8-yard pieces of fabric fit into 2 1/4 yards.
Here’s the step-by-step calculation:
1. Convert 2 1/4 yards into an improper fraction:
\[
2 \frac{1}{4} = \frac{9}{4} \text{ yards}
\]
2. Each bib uses 3/8 of a yard. So, we need to figure out how many 3/8-yard pieces fit into 9/4 yards. This is essentially dividing 9/4 yards by 3/8 yard per bib:
\[
\text{Number of bibs} = \frac{\frac{9}{4}}{\frac{3}{8}}
\]
3. To divide by a fraction, you can multiply by its reciprocal. The reciprocal of 3/8 is 8/3. Hence:
\[
\text{Number of bibs} = \frac{9}{4} \times \frac{8}{3}
\]
4. Simplify the multiplication:
\[
\frac{9}{4} \times \frac{8}{3} = \frac{9 \times 8}{4 \times 3} = \frac{72}{12} = 6
\]
Therefore, Allison can make \( \boxed{6} \) bibs from the fabric she has.
Here’s the step-by-step calculation:
1. Convert 2 1/4 yards into an improper fraction:
\[
2 \frac{1}{4} = \frac{9}{4} \text{ yards}
\]
2. Each bib uses 3/8 of a yard. So, we need to figure out how many 3/8-yard pieces fit into 9/4 yards. This is essentially dividing 9/4 yards by 3/8 yard per bib:
\[
\text{Number of bibs} = \frac{\frac{9}{4}}{\frac{3}{8}}
\]
3. To divide by a fraction, you can multiply by its reciprocal. The reciprocal of 3/8 is 8/3. Hence:
\[
\text{Number of bibs} = \frac{9}{4} \times \frac{8}{3}
\]
4. Simplify the multiplication:
\[
\frac{9}{4} \times \frac{8}{3} = \frac{9 \times 8}{4 \times 3} = \frac{72}{12} = 6
\]
Therefore, Allison can make \( \boxed{6} \) bibs from the fabric she has.
Answer
Mr. R has a block of Clay that is 12 1/2 inches long. He cut it into 20 identical pieces for an art project. How long is each piece of clay?
Answered by
GPT-4o
To determine the length of each piece of clay, we need to divide the total length of the clay block by the number of pieces.
Here's the step-by-step calculation:
1. The total length of the clay block is 12 1/2 inches. Convert 12 1/2 into an improper fraction:
\[
12 \frac{1}{2} = \frac{25}{2} \text{ inches}
\]
2. Mr. R cut the clay block into 20 identical pieces. We need to find the length of each piece by dividing the total length by the number of pieces:
\[
\text{Length of each piece} = \frac{\frac{25}{2}}{20}
\]
3. Simplifying the division of the fraction:
\[
\frac{\frac{25}{2}}{20} = \frac{25}{2} \times \frac{1}{20} = \frac{25}{2 \times 20} = \frac{25}{40}
\]
4. Simplify the fraction \(\frac{25}{40}\):
\[
\frac{25}{40} = \frac{5}{8}
\]
Therefore, each piece of clay is \(\boxed{\frac{5}{8}}\) inches long.
Here's the step-by-step calculation:
1. The total length of the clay block is 12 1/2 inches. Convert 12 1/2 into an improper fraction:
\[
12 \frac{1}{2} = \frac{25}{2} \text{ inches}
\]
2. Mr. R cut the clay block into 20 identical pieces. We need to find the length of each piece by dividing the total length by the number of pieces:
\[
\text{Length of each piece} = \frac{\frac{25}{2}}{20}
\]
3. Simplifying the division of the fraction:
\[
\frac{\frac{25}{2}}{20} = \frac{25}{2} \times \frac{1}{20} = \frac{25}{2 \times 20} = \frac{25}{40}
\]
4. Simplify the fraction \(\frac{25}{40}\):
\[
\frac{25}{40} = \frac{5}{8}
\]
Therefore, each piece of clay is \(\boxed{\frac{5}{8}}\) inches long.
Answer
Every day dynamic makes himself a smoothie using 3/4 of a cup of juice. He has half cups of juice left in his refrigerator. If the juice is only used for smoothies, how many days will it last?
Answered by
GPT-4o
To determine how many days Dynamic can make smoothies with the juice he has left, we need to find out how many 3/4-cup servings fit into 1/2 cup of juice.
Here’s the step-by-step calculation:
1. Dynamic uses 3/4 cup of juice per smoothie.
2. He has 1/2 cup of juice left.
3. We need to figure out how many 3/4-cup servings fit into 1/2 cup. This is essentially dividing 1/2 cup by 3/4 cup:
\[
\text{Number of days} = \frac{\frac{1}{2}}{\frac{3}{4}}
\]
4. To divide by a fraction, you can multiply by its reciprocal. The reciprocal of 3/4 is 4/3. Hence:
\[
\text{Number of days} = \frac{1}{2} \times \frac{4}{3}
\]
5. Simplify the multiplication:
\[
\frac{1}{2} \times \frac{4}{3} = \frac{1 \times 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3}
\]
Therefore, the juice will last for \(\boxed{\frac{2}{3}}\) of a day, which means he doesn't have enough juice to make a full smoothie and can only make a part of it.
Here’s the step-by-step calculation:
1. Dynamic uses 3/4 cup of juice per smoothie.
2. He has 1/2 cup of juice left.
3. We need to figure out how many 3/4-cup servings fit into 1/2 cup. This is essentially dividing 1/2 cup by 3/4 cup:
\[
\text{Number of days} = \frac{\frac{1}{2}}{\frac{3}{4}}
\]
4. To divide by a fraction, you can multiply by its reciprocal. The reciprocal of 3/4 is 4/3. Hence:
\[
\text{Number of days} = \frac{1}{2} \times \frac{4}{3}
\]
5. Simplify the multiplication:
\[
\frac{1}{2} \times \frac{4}{3} = \frac{1 \times 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3}
\]
Therefore, the juice will last for \(\boxed{\frac{2}{3}}\) of a day, which means he doesn't have enough juice to make a full smoothie and can only make a part of it.