19. what part of a gallon is 2 qt? (there are 4 quarts to a gallon)
(a) $\frac{1}{4}$
(b) $\frac{3}{10}$
(c) $\frac{1}{2}$
(d) $\frac{5}{8}$

20. in which arrangement are the fractions listed from least to greatest?
(a) $\frac{9}{19}, \frac{1}{2}, \frac{8}{15}$
(b) $\frac{1}{2}, \frac{8}{15}, \frac{9}{19}$
(c) $\frac{9}{19}, \frac{8}{15}, \frac{1}{2}$
(d) $\frac{1}{2}, \frac{9}{19}, \frac{8}{15}$

21. find the value of $(4\frac{5}{8} - 2\frac{3}{4}) \div \frac{5}{4}$
(a) 1
(b) 2
(c) $1\frac{7}{10}$
(d) $1\frac{1}{2}$

22. mrs. brown owns $x$ books. $\frac{1}{3}$ of these are novels, $\frac{2}{5}$ of the remainder are poetry, and the rest are nonfiction. how many nonfiction books does mrs. brown own?
(a) $\frac{4}{15} x$
(b) $\frac{2}{5} x$
(c) $\frac{2}{3} x$
(d) $\frac{3}{8} x$

23. $(\frac{3}{5} + \frac{1}{4}) + \frac{34}{15}$ is equal to
(a) $\frac{925}{300}$
(b) $\frac{187}{50}$
(c) $\frac{187}{60}$
(d) $\frac{915}{300}$

24. the annual income of a family is budgeted as follows: $\frac{1}{10}$ for clothing, $\frac{1}{3}$ for food, and $\frac{1}{5}$ for rent. this leaves $\$1,320$ for other expenses and savings. find the annual income.
(a) $\$2,156$
(b) $\$3,600$
(c) $\$23,760$
(d) $\$6,600$

Question

19. what part of a gallon is 2 qt? (there are 4 quarts to a gallon)
(a) $\frac{1}{4}$
(b) $\frac{3}{10}$
(c) $\frac{1}{2}$
(d) $\frac{5}{8}$

20. in which arrangement are the fractions listed from least to greatest?
(a) $\frac{9}{19}, \frac{1}{2}, \frac{8}{15}$
(b) $\frac{1}{2}, \frac{8}{15}, \frac{9}{19}$
(c) $\frac{9}{19}, \frac{8}{15}, \frac{1}{2}$
(d) $\frac{1}{2}, \frac{9}{19}, \frac{8}{15}$

21. find the value of $(4\frac{5}{8} - 2\frac{3}{4}) \div \frac{5}{4}$
(a) 1
(b) 2
(c) $1\frac{7}{10}$
(d) $1\frac{1}{2}$

22. mrs. brown owns $x$ books. $\frac{1}{3}$ of these are novels, $\frac{2}{5}$ of the remainder are poetry, and the rest are nonfiction. how many nonfiction books does mrs. brown own?
(a) $\frac{4}{15} x$
(b) $\frac{2}{5} x$
(c) $\frac{2}{3} x$
(d) $\frac{3}{8} x$

23. $(\frac{3}{5} + \frac{1}{4}) + \frac{34}{15}$ is equal to
(a) $\frac{925}{300}$
(b) $\frac{187}{50}$
(c) $\frac{187}{60}$
(d) $\frac{915}{300}$

24. the annual income of a family is budgeted as follows: $\frac{1}{10}$ for clothing, $\frac{1}{3}$ for food, and $\frac{1}{5}$ for rent. this leaves $\$1,320$ for other expenses and savings. find the annual income.
(a) $\$2,156$
(b) $\$3,600$
(c) $\$23,760$
(d) $\$6,600$

Accepted Answer

{ "quality": "clear", "question_count": 6, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Fraction Word Problems", "Fraction Addition", "Fraction Division", "Simplifying Fractions", "Fraction Comparison", "Mixed Number Subtraction" ], "new_concepts": [ "Fractional Remainder Word Problems", "Fractional Budgeting" ], "current_concepts": [ "Fraction Word Problems", "Fraction Addition", "Fraction Division", "Simplifying Fractions", "Fraction Comparison", "Mixed Number Subtraction", "Fractional Remainder Word Problems", "Fractional Budgeting" ] } ## Question 19: Convert quarts to gallons $$ \frac{2\text{ qt}}{4\text{ qt/gallon}} = \frac{2}{4} = \frac{1}{2} $$ ## Question 20: Compare and order fractions $$ \begin{aligned} &\frac{9}{19} \approx 0.4737\ &\frac{1}{2} = 0.5\ &\frac{8}{15} \approx 0.5333\ &\frac{9}{19} < \frac{1}{2} < \frac{8}{15} \end{aligned} $$ ## Question 21: Evaluate the mixed number expression $$ \begin{aligned} &4\frac{5}{8} - 2\frac{3}{4} = \frac{37}{8} - \frac{22}{8} = \frac{15}{8}\ &\frac{15}{8} \div \frac{5}{4} = \frac{15}{8} \times \frac{4}{5} = \frac{3}{2} = 1\frac{1}{2} \end{aligned} $$ ## Question 22: Determine the fraction of nonfiction books $$ \begin{aligned} &\text{Remainder} = 1 - \frac{1}{3} = \frac{2}{3}\ &\text{Poetry} = \frac{2}{5} \times \frac{2}{3} = \frac{4}{15}\ &\text{Nonfiction} = \frac{2}{3} - \frac{4}{15} = \frac{10}{15} - \frac{4}{15} = \frac{6}{15}X = \frac{2}{3}X \end{aligned} $$ ## Question 23: Evaluate the fraction sum $$ \begin{aligned} &\frac{3}{5} + \frac{1}{4} = \frac{12}{20} + \frac{5}{20} = \frac{17}{20}\ &\frac{17}{20} + \frac{34}{15} = \frac{51}{60} + \frac{136}{60} = \frac{187}{60} \end{aligned} $$ ## Question 24: Solve the budgeting word problem $$ \begin{aligned} &\text{Total Fraction Spent} = \frac{1}{10} + \frac{1}{3} + \frac{1}{5} = \frac{3}{30} + \frac{10}{30} + \frac{6}{30} = \frac{19}{30}\ &\text{Remaining Fraction} = 1 - \frac{19}{30} = \frac{11}{30}\ &\text{Annual Income} = \$1,320 \div \frac{11}{30} = \$1,320 \times \frac{30}{11} = \$120 \times 30 = \$3,600 \end{aligned} $$ ## Question 19 (C) $\frac{1}{2}$

(A) $\frac{1}{4}$

(B) $\frac{3}{10}$

(D) $\frac{5}{8}$ ## Question 20 (A) $\frac{9}{19}, \frac{1}{2}, \frac{8}{15}$

(B) $\frac{1}{2}, \frac{8}{15}, \frac{9}{19}$

(C) $\frac{9}{19}, \frac{8}{15}, \frac{1}{2}$

(D) $\frac{1}{2}, \frac{9}{19}, \frac{8}{15}$ ## Question 21 (D) $1\frac{1}{2}$

(A) 1

(B) 2

(C) $1\frac{7}{10}$ ## Question 22 (C) $\frac{2}{3}X$

(A) $\frac{4}{15}X$

(B) $\frac{2}{5}X$

(D) $\frac{3}{8}X$ ## Question 23 (C) $\frac{187}{60}$

(A) $\frac{925}{300}$

(B) $\frac{187}{50}$

(D) $\frac{915}{300}$ ## Question 24 (B) \$3,600

(A) \$2,156

(C) \$23,760

(D) \$6,600

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Fraction Word Problems" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 19: Convert quarts to gallons

Question 20: Compare and order fractions

Question 21: Evaluate the mixed number expression

Question 22: Determine the fraction of nonfiction books

Question 23: Evaluate the fraction sum

Question 24: Solve the budgeting word problem

Answer:

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24