13. michelle spent $\frac{1}{2}$ of her summer vacation at camp, $\frac{1}{5}$ of her vacation babysitting, and $\frac{1}{4}$ visiting her grandmother. what part of her vacation was left to relax at home?
(a) $\frac{4}{5}$
(b) $\frac{1}{20}$
(c) $\frac{1}{3}$
(d) $\frac{3}{20}$

14. 800 employees work for the metropolitan transportation company. $\frac{1}{4}$ of these are college graduates, while $\frac{5}{6}$ of the remainder are high school graduates. what part of the employees never graduated from high school?
(a) $\frac{1}{6}$
(b) $\frac{1}{8}$
(c) $\frac{7}{8}$
(d) $\frac{3}{4}$

15. subtract $62\frac{2}{3}$ from 100.
(a) $37\frac{1}{3}$
(b) $38\frac{1}{3}$
(c) $37\frac{2}{3}$
(d) $38\frac{2}{3}$

16. divide $2\frac{2}{5}$ by $4\frac{8}{10}$.
(a) 2
(b) $\frac{1}{2}$
(c) $\frac{288}{25}$
(d) $\frac{25}{288}$

17. which of the following fractions is the smallest?
(a) $\frac{7}{12}$
(b) $\frac{8}{15}$
(c) $\frac{11}{20}$
(d) $\frac{5}{6}$

18. on monday evening, channel 2 scheduled 2 hours of situation comedy, 1 hour of news, and 3 hours of movies. what part of the evenings programming was devoted to situation comedy?
(a) $\frac{1}{3}$
(b) $\frac{2}{3}$
(c) $\frac{1}{2}$
(d) $\frac{1}{6}$

Question

13. michelle spent $\frac{1}{2}$ of her summer vacation at camp, $\frac{1}{5}$ of her vacation babysitting, and $\frac{1}{4}$ visiting her grandmother. what part of her vacation was left to relax at home?
(a) $\frac{4}{5}$
(b) $\frac{1}{20}$
(c) $\frac{1}{3}$
(d) $\frac{3}{20}$

14. 800 employees work for the metropolitan transportation company. $\frac{1}{4}$ of these are college graduates, while $\frac{5}{6}$ of the remainder are high school graduates. what part of the employees never graduated from high school?
(a) $\frac{1}{6}$
(b) $\frac{1}{8}$
(c) $\frac{7}{8}$
(d) $\frac{3}{4}$

15. subtract $62\frac{2}{3}$ from 100.
(a) $37\frac{1}{3}$
(b) $38\frac{1}{3}$
(c) $37\frac{2}{3}$
(d) $38\frac{2}{3}$

16. divide $2\frac{2}{5}$ by $4\frac{8}{10}$.
(a) 2
(b) $\frac{1}{2}$
(c) $\frac{288}{25}$
(d) $\frac{25}{288}$

17. which of the following fractions is the smallest?
(a) $\frac{7}{12}$
(b) $\frac{8}{15}$
(c) $\frac{11}{20}$
(d) $\frac{5}{6}$

18. on monday evening, channel 2 scheduled 2 hours of situation comedy, 1 hour of news, and 3 hours of movies. what part of the evenings programming was devoted to situation comedy?
(a) $\frac{1}{3}$
(b) $\frac{2}{3}$
(c) $\frac{1}{2}$
(d) $\frac{1}{6}$

Accepted Answer

{ "quality": "clear", "question_count": 6, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Fraction Word Problems", "Mixed Number Subtraction", "Fraction Division" ], "current_concepts": [ "Fraction Word Problems", "Mixed Number Subtraction", "Fraction Division", "Fraction Comparison" ] } ## Question 13: Calculate the remaining fraction of vacation $$ \begin{aligned} &\text{Total fraction spent} = \frac{1}{2} + \frac{1}{5} + \frac{1}{4} = \frac{10}{20} + \frac{4}{20} + \frac{5}{20} = \frac{19}{20}\ &\text{Fraction left} = 1 - \frac{19}{20} = \frac{1}{20} \end{aligned} $$ ## Question 14: Calculate the fraction of employees who never graduated from high school $$ \begin{aligned} &\text{Fraction of college graduates} = \frac{1}{4}\ &\text{Remainder fraction} = 1 - \frac{1}{4} = \frac{3}{4}\ &\text{Fraction of high school graduates from remainder} = \frac{5}{6} \times \frac{3}{4} = \frac{5}{8}\ &\text{Fraction never graduated from high school} = \frac{3}{4} - \frac{5}{8} = \frac{6}{8} - \frac{5}{8} = \frac{1}{8} \end{aligned} $$ ## Question 15: Subtract the mixed number from 100 $$ \begin{aligned} 100 - 62\frac{2}{3} = 99\frac{3}{3} - 62\frac{2}{3} = 37\frac{1}{3} \end{aligned} $$ ## Question 16: Divide the mixed numbers $$ \begin{aligned} &2\frac{2}{5} \div 4\frac{8}{10} = \frac{12}{5} \div \frac{48}{10}\ &\frac{12}{5} \times \frac{10}{48} = \frac{12}{48} \times \frac{10}{5} = \frac{1}{4} \times 2 = \frac{1}{2} \end{aligned} $$ ## Question 17: Compare the fractions to find the smallest $$ \begin{aligned} &\text{Common denominator for } \frac{7}{12}, \frac{8}{15}, \frac{11}{20}, \frac{5}{6} \text{ is } 60\ &\frac{7}{12} = \frac{35}{60},\quad \frac{8}{15} = \frac{32}{60},\quad \frac{11}{20} = \frac{33}{60},\quad \frac{5}{6} = \frac{50}{60}\ &\text{Smallest fraction is } \frac{32}{60} = \frac{8}{15} \end{aligned} $$ ## Question 18: Calculate the fraction of programming devoted to situation comedy $$ \begin{aligned} &\text{Total hours} = 2 + 1 + 3 = 6\ &\text{Fraction for situation comedy} = \frac{2}{6} = \frac{1}{3} \end{aligned} $$ ## Question 13 (A) $\frac{1}{5}$

(B) $\frac{1}{20}$

(C) $\frac{1}{3}$

(D) $\frac{3}{20}$ ## Question 14 (A) $\frac{1}{6}$

(B) $\frac{1}{8}$

(C) $\frac{7}{8}$

(D) $\frac{3}{4}$ ## Question 15 (A) $37\frac{1}{3}$

(B) $38\frac{1}{3}$

(C) $37\frac{2}{3}$

(D) $38\frac{2}{3}$ ## Question 16 (A) $2$

(B) $\frac{1}{2}$

(C) $\frac{288}{25}$

(D) $\frac{25}{288}$ ## Question 17 (A) $\frac{7}{12}$

(B) $\frac{8}{15}$

(C) $\frac{11}{20}$

(D) $\frac{5}{6}$ ## Question 18 (A) $\frac{1}{3}$

(B) $\frac{2}{3}$

(C) $\frac{1}{2}$

(D) $\frac{1}{6}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Arithmetic", "Fractions" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 13: Calculate the remaining fraction of vacation

Question 14: Calculate the fraction of employees who never graduated from high school

Question 15: Subtract the mixed number from 100

Question 16: Divide the mixed numbers

Question 17: Compare the fractions to find the smallest

Question 18: Calculate the fraction of programming devoted to situation comedy

Answer:

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18