Number, NAPX-E4-CA17

Question

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Worked Solution

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Variant 0

DifficultyLevel

636

Question

Vanessa has a basket of fruit that contains plums, oranges and peaches.

13\dfrac{1}{3} of the basket of fruit are oranges and 15\dfrac{1}{5} are peaches.

What fraction of the fruit are plums?

Worked Solution
Plums
 = 1 −- (13+15)\bigg( \dfrac{1}{3} + \dfrac{1}{5} \bigg)
= 1 −- (515+315)\bigg( \dfrac{5}{15} + \dfrac{3}{15} \bigg)
= 715\dfrac{7}{15}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Vanessa has a basket of fruit that contains plums, oranges and peaches. $\dfrac{1}{3}$ of the basket of fruit are oranges and $\dfrac{1}{5}$ are peaches. What fraction of the fruit are plums?
workedSolution
| | | | --------------------- | -------------- | |
Plums
| \= 1 $-$ $\bigg( \dfrac{1}{3} + \dfrac{1}{5} \bigg)$ | | | \= 1 $-$ $\bigg( \dfrac{5}{15} + \dfrac{3}{15} \bigg)$ | || \= {{{correctAnswer}}}|
correctAnswer
$\dfrac{7}{15}$

Answers

Is Correct?Answer
x

38\dfrac{3}{8}

x

710\dfrac{7}{10}

✓

715\dfrac{7}{15}

x

810\dfrac{8}{10}

x

815\dfrac{8}{15}

Variant 1

DifficultyLevel

638

Question

A pet shop has fish, guinea pigs and rabbits for sale.

16\dfrac{1}{6} of the animals are guinea pigs and 18\dfrac{1}{8} are rabbits.

What fraction of the animals are fish?

Worked Solution
Fish
 = 1 −- (16+18)\bigg( \dfrac{1}{6} + \dfrac{1}{8} \bigg)
= 1 −- (424+324)\bigg( \dfrac{4}{24} + \dfrac{3}{24} \bigg)
= 1724\dfrac{17}{24}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A pet shop has fish, guinea pigs and rabbits for sale. $\dfrac{1}{6}$ of the animals are guinea pigs and $\dfrac{1}{8}$ are rabbits. What fraction of the animals are fish?
workedSolution
| | | | --------------------- | -------------- | |
Fish
| \= 1 $-$ $\bigg( \dfrac{1}{6} + \dfrac{1}{8} \bigg)$ | | | \= 1 $-$ $\bigg( \dfrac{4}{24} + \dfrac{3}{24} \bigg)$ | || \= {{{correctAnswer}}}|
correctAnswer
$\dfrac{17}{24}$

Answers

Is Correct?Answer
x

17\dfrac{1}{7}

x

67\dfrac{6}{7}

x

724\dfrac{7}{24}

✓

1724\dfrac{17}{24}

x

4748\dfrac{47}{48}

Variant 2

DifficultyLevel

636

Question

A kitchen utensils draw contains knives, forks and spoons.

13\dfrac{1}{3} of the utensils are knives and 18\dfrac{1}{8} are forks.

What fraction of the utensils are spoons?

Worked Solution
Spoons
 = 1 −- (13+18)\bigg( \dfrac{1}{3} + \dfrac{1}{8} \bigg)
= 1 −- (824+324)\bigg( \dfrac{8}{24} + \dfrac{3}{24} \bigg)
= 1324\dfrac{13}{24}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A kitchen utensils draw contains knives, forks and spoons. $\dfrac{1}{3}$ of the utensils are knives and $\dfrac{1}{8}$ are forks. What fraction of the utensils are spoons?
workedSolution
| | | | --------------------- | -------------- | |
Spoons
| \= 1 $-$ $\bigg( \dfrac{1}{3} + \dfrac{1}{8} \bigg)$ | | | \= 1 $-$ $\bigg( \dfrac{8}{24} + \dfrac{3}{24} \bigg)$ | | | = {{correctAnswer}} |
correctAnswer
$\dfrac{13}{24}$

Answers

Is Correct?Answer
x

211\dfrac{2}{11}

x

1924\dfrac{19}{24}

x

911\dfrac{9}{11}

x

1124\dfrac{11}{24}

✓

1324\dfrac{13}{24}

Variant 3

DifficultyLevel

630

Question

A bag contains red, orange and blue coloured discs.

13\dfrac{1}{3} of the discs are red and 25\dfrac{2}{5} are orange.

What fraction of the discs are blue?

Worked Solution
Blue discs
 = 1 −- (13+25)\bigg( \dfrac{1}{3} + \dfrac{2}{5} \bigg)
= 1 −- (515+615)\bigg( \dfrac{5}{15} + \dfrac{6}{15} \bigg)
= 415\dfrac{4}{15}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A bag contains red, orange and blue coloured discs. $\dfrac{1}{3}$ of the discs are red and $\dfrac{2}{5}$ are orange. What fraction of the discs are blue?
workedSolution
| | | | --------------------- | -------------- | |
Blue discs
| \= 1 $-$ $\bigg( \dfrac{1}{3} + \dfrac{2}{5} \bigg)$ | | | \= 1 $-$ $\bigg( \dfrac{5}{15} + \dfrac{6}{15} \bigg)$ | | | = {{correctAnswer}} |
correctAnswer
$\dfrac{4}{15}$

Answers

Is Correct?Answer
✓

415\dfrac{4}{15}

x

1115\dfrac{11}{15}

x

38\dfrac{3}{8}

x

58\dfrac{5}{8}

x

1130\dfrac{11}{30}

Variant 4

DifficultyLevel

639

Question

Jonas has a hobby farm consisting of goats, sheep and cows.

37\dfrac{3}{7} of the animals are goats and 25\dfrac{2}{5} are cows.

What fraction of the animals are sheep?

Worked Solution
Sheep
 = 1 −- (37+25)\bigg( \dfrac{3}{7} + \dfrac{2}{5} \bigg)
= 1 −- (1535+1435)\bigg( \dfrac{15}{35} + \dfrac{14}{35} \bigg)
= 635\dfrac{6}{35}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Jonas has a hobby farm consisting of goats, sheep and cows. $\dfrac{3}{7}$ of the animals are goats and $\dfrac{2}{5}$ are cows. What fraction of the animals are sheep?
workedSolution
| | | | --------------------- | -------------- | |
Sheep
| \= 1 $-$ $\bigg( \dfrac{3}{7} + \dfrac{2}{5} \bigg)$ | | | \= 1 $-$ $\bigg( \dfrac{15}{35} + \dfrac{14}{35} \bigg)$ | | | = {{correctAnswer}} |
correctAnswer
$\dfrac{6}{35}$

Answers

Is Correct?Answer
x

512\dfrac{5}{12}

✓

635\dfrac{6}{35}

x

712\dfrac{7}{12}

x

2935\dfrac{29}{35}

x

2335\dfrac{23}{35}

Variant 5

DifficultyLevel

625

Question

Bailey watches Netflix most nights of the week.

He watches a mixture of movies, cartoons and documentaries.

Last week, 18\dfrac{1}{8} of the shows he watched were cartoons and 23\dfrac{2}{3} were documentaries.

What fraction of shows that he watched were movies?

Worked Solution
Movies
 = 1 −- (18+23)\bigg( \dfrac{1}{8} + \dfrac{2}{3} \bigg)
= 1 −- (324+1624)\bigg( \dfrac{3}{24} + \dfrac{16}{24} \bigg)
= 524\dfrac{5}{24}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Bailey watches Netflix most nights of the week. He watches a mixture of movies, cartoons and documentaries. Last week, $\dfrac{1}{8}$ of the shows he watched were cartoons and $\dfrac{2}{3}$ were documentaries. What fraction of shows that he watched were movies?
workedSolution
| | | | --------------------- | -------------- | |
Movies
| \= 1 $-$ $\bigg( \dfrac{1}{8} + \dfrac{2}{3} \bigg)$ | | | \= 1 $-$ $\bigg( \dfrac{3}{24} + \dfrac{16}{24} \bigg)$ | | | = {{correctAnswer}} |
correctAnswer
$\dfrac{5}{24}$

Answers

Is Correct?Answer
x

2124\dfrac{21}{24}

x

1924\dfrac{19}{24}

x

811\dfrac{8}{11}

x

311\dfrac{3}{11}

✓

524\dfrac{5}{24}

Tags