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.
Evan bought 3 pints of vegetable soup. 1 Serving is 3/4 of a pint. How many servings of vegetable soup can Evan make?
7 answers
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?
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.
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?
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.
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?
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.