short response

1. mrs. abbate wishes to make a dozen towels. if each towel is to be $\frac{3}{4}$ yard long, how many yards of material should mrs. abbate buy?
answer _______

2. jose spent 6 hours in school. each school period is $\frac{3}{4}$ hour long. how many periods did jose spend in school?
answer _______

3. ava made 100 paper cranes, and brittany made $\frac{3}{4}$ of the number of the paper cranes that ava made. ava gave $\frac{9}{20}$ of her cranes to brittany. then, brittany gave $\frac{1}{4}$ of her paper cranes to ava. how many more cranes did brittany have than ava in the end?
answer: _______

4. at intermission, xavier sold refreshments. of the items he had, $\frac{1}{5}$ were granola bars and $\frac{1}{2}$ the remaining items were containers of popcorn. the rest were divided equally among apples, rice cakes, and containers of yogurt. xavier sold the 8 apples he had. how many items did he originally have?
answer: _______

Question

short response

1. mrs. abbate wishes to make a dozen towels. if each towel is to be $\frac{3}{4}$ yard long, how many yards of material should mrs. abbate buy?
answer _______

2. jose spent 6 hours in school. each school period is $\frac{3}{4}$ hour long. how many periods did jose spend in school?
answer _______

3. ava made 100 paper cranes, and brittany made $\frac{3}{4}$ of the number of the paper cranes that ava made. ava gave $\frac{9}{20}$ of her cranes to brittany. then, brittany gave $\frac{1}{4}$ of her paper cranes to ava. how many more cranes did brittany have than ava in the end?
answer: _______

4. at intermission, xavier sold refreshments. of the items he had, $\frac{1}{5}$ were granola bars and $\frac{1}{2}$ the remaining items were containers of popcorn. the rest were divided equally among apples, rice cakes, and containers of yogurt. xavier sold the 8 apples he had. how many items did he originally have?
answer: _______

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Fraction Word Problems", "Fraction Addition", "Fraction Division" ], "new_concepts": [], "current_concepts": [ "Fraction Word Problems", "Fraction Addition", "Fraction Division" ] } ## Solve Question 1 $$ \begin{aligned} &\text{Total towels} = 12\ &\text{Length per towel} = \frac{3}{4}\text{ yard}\ &\text{Total material} = 12 \times \frac{3}{4} = 9\text{ yards} \end{aligned} $$ ## Solve Question 2 $$ \begin{aligned} &\text{Total hours} = 6\ &\text{Period length} = \frac{3}{4}\text{ hour}\ &\text{Number of periods} = 6 \div \frac{3}{4} = 6 \times \frac{4}{3} = 8\text{ periods} \end{aligned} $$ ## Solve Question 3 $$ \begin{aligned} &\text{Initial Ava} = 100,\quad \text{Initial Brittany} = 100 \times \frac{3}{4} = 75\ &\text{Ava gives to Brittany} = 100 \times \frac{9}{20} = 45\ &\text{Ava after first trade} = 100 - 45 = 55,\quad \text{Brittany after first trade} = 75 + 45 = 120\ &\text{Brittany gives to Ava} = 120 \times \frac{1}{4} = 30\ &\text{Final Ava} = 55 + 30 = 85,\quad \text{Final Brittany} = 120 - 30 = 90\ &\text{Difference} = 90 - 85 = 5 \end{aligned} $$ ## Solve Question 4 $$ \begin{aligned} &\text{Granola bars} = \frac{1}{5}\ &\text{Remaining} = 1 - \frac{1}{5} = \frac{4}{5}\ &\text{Popcorn} = \frac{1}{2} \times \frac{4}{5} = \frac{2}{5}\ &\text{Rest} = \frac{4}{5} - \frac{2}{5} = \frac{2}{5}\ &\text{Apples fraction} = \frac{2}{5} \div 3 = \frac{2}{15}\ &\text{Total items } (x) \implies \frac{2}{15}x = 8 \implies x = 8 \times \frac{15}{2} = 60 \end{aligned} $$ ## Question 1 9 yards ## Question 2 8 periods ## Question 3 5 more cranes ## Question 4 60 items { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Arithmetic", "Fraction Word Problems" ] }

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