20136

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

629

Question

Ali has a bag of marbles. The marbles are either blue, black or orange.

16\dfrac{1}{6} of her marbles are blue and 14\dfrac{1}{4} are black.

What fraction of her marbles are orange?

Worked Solution

Fraction of orange marbles
= 1−(16+14)1 - \bigg( \dfrac{1}{6} + \dfrac{1}{4} \bigg)
= 1−(212+312)1 - \bigg( \dfrac{2}{12} + \dfrac{3}{12} \bigg)
= 1−5121 - \dfrac{5}{12}
= 712\dfrac{7}{12}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Ali has a bag of marbles. The marbles are either blue, black or orange. $\dfrac{1}{6}$ of her marbles are blue and $\dfrac{1}{4}$ are black. What fraction of her marbles are orange?
workedSolution
sm_nogap Fraction of orange marbles
> > | | | > > | --- | ----------------------------------------------------- | > > | | \= $1 - \bigg( \dfrac{1}{6} + \dfrac{1}{4} \bigg)$ | > > | | \= $1 - \bigg( \dfrac{2}{12} + \dfrac{3}{12} \bigg)$ | > > | | \= $1 - \dfrac{5}{12}$ | > > | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{7}{12}$

Answers

Is Correct?Answer
x

512\dfrac{5}{12}

x

310\dfrac{3}{10}

✓

712\dfrac{7}{12}

x

710\dfrac{7}{10}

Variant 1

DifficultyLevel

640

Question

Julius has a bag of sweets. The sweets are either pink, white or green.

27\dfrac{2}{7} of his sweets are pink and 13\dfrac{1}{3} are white.

What fraction of his sweets are green?

Worked Solution

Fraction of green sweets
= 1−(27+13)1 - \bigg( \dfrac{2}{7} + \dfrac{1}{3} \bigg)
= 1−(621+721)1 - \bigg( \dfrac{6}{21} + \dfrac{7}{21} \bigg)
= 1−13211 - \dfrac{13}{21}
= 821\dfrac{8}{21}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Julius has a bag of sweets. The sweets are either pink, white or green. $\dfrac{2}{7}$ of his sweets are pink and $\dfrac{1}{3}$ are white. What fraction of his sweets are green?
workedSolution
sm_nogap Fraction of green sweets
> > | | | > > | --- | ----------------------------------------------------- | > > | | \= $1 - \bigg( \dfrac{2}{7} + \dfrac{1}{3} \bigg)$ | > > | | \= $1 - \bigg( \dfrac{6}{21} + \dfrac{7}{21} \bigg)$ | > > | | \= $1 - \dfrac{13}{21}$ | > > | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{8}{21}$

Answers

Is Correct?Answer
✓

821\dfrac{8}{21}

x

1321\dfrac{13}{21}

x

710\dfrac{7}{10}

x

810\dfrac{8}{10}

Variant 2

DifficultyLevel

628

Question

Kurt has an esky containing cans of drink. The drinks are either sparkling water, cola or lemonade.

34\dfrac{3}{4} of the cans are sparkling water and 16\dfrac{1}{6} are cola.

What fraction of the cans are lemonade?

Worked Solution

Fraction of cans of lemonade
= 1−(34+16)1 - \bigg( \dfrac{3}{4} + \dfrac{1}{6} \bigg)
= 1−(912+212)1 - \bigg( \dfrac{9}{12} + \dfrac{2}{12} \bigg)
= 1−11121 - \dfrac{11}{12}
= 112\dfrac{1}{12}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Kurt has an esky containing cans of drink. The drinks are either sparkling water, cola or lemonade. $\dfrac{3}{4}$ of the cans are sparkling water and $\dfrac{1}{6}$ are cola. What fraction of the cans are lemonade?
workedSolution
sm_nogap Fraction of cans of lemonade
> > | | | > > | --- | ----------------------------------------------------- | > > | | \= $1 - \bigg( \dfrac{3}{4} + \dfrac{1}{6} \bigg)$ | > > | | \= $1 - \bigg( \dfrac{9}{12} + \dfrac{2}{12} \bigg)$ | > > | | \= $1 - \dfrac{11}{12}$ | > > | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{1}{12}$

Answers

Is Correct?Answer
x

78\dfrac{7}{8}

x

610\dfrac{6}{10}

x

310\dfrac{3}{10}

✓

112\dfrac{1}{12}

Variant 3

DifficultyLevel

643

Question

Andrew and Rory went fishing and returned home with a bag of fish.

The fish in the bag are either bream, flathead or snapper.

38\dfrac{3}{8} of their fish are flathead and 15\dfrac{1}{5} are snapper.

What fraction of their fish are bream?

Worked Solution

Fraction of bream
= 1−(38+15)1 - \bigg( \dfrac{3}{8} + \dfrac{1}{5} \bigg)
= 1−(1540+840)1 - \bigg( \dfrac{15}{40} + \dfrac{8}{40} \bigg)
= 1−23401 - \dfrac{23}{40}
= 1740\dfrac{17}{40}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Andrew and Rory went fishing and returned home with a bag of fish. The fish in the bag are either bream, flathead or snapper. $\dfrac{3}{8}$ of their fish are flathead and $\dfrac{1}{5}$ are snapper. What fraction of their fish are bream?
workedSolution
sm_nogap Fraction of bream
> > | | | > > | --- | ----------------------------------------------------- | > > | | \= $1 - \bigg( \dfrac{3}{8} + \dfrac{1}{5} \bigg)$ | > > | | \= $1 - \bigg( \dfrac{15}{40} + \dfrac{8}{40} \bigg)$ | > > | | \= $1 - \dfrac{23}{40}$ | > > | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{17}{40}$

Answers

Is Correct?Answer
x

340\dfrac{3}{40}

x

410\dfrac{4}{10}

✓

1740\dfrac{17}{40}

x

610\dfrac{6}{10}

Variant 4

DifficultyLevel

631

Question

Homer has a bag of doughnuts for Bart's birthday party.

The doughnuts are either cinnamon, choc hazelnut or strawberry jam.

310\dfrac{3}{10} of the doughnuts are strawberry jam and 15\dfrac{1}{5} are cinnamon.

What fraction of the doughnuts are choc hazelnut?

Worked Solution

Fraction of choc hazelnut doughnuts
= 1−(310+15)1 - \bigg( \dfrac{3}{10} + \dfrac{1}{5} \bigg)
= 1−(310+210)1 - \bigg( \dfrac{3}{10} + \dfrac{2}{10} \bigg)
= 1−5101 - \dfrac{5}{10}
= 12\dfrac{1}{2}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Homer has a bag of doughnuts for Bart's birthday party. The doughnuts are either cinnamon, choc hazelnut or strawberry jam. $\dfrac{3}{10}$ of the doughnuts are strawberry jam and $\dfrac{1}{5}$ are cinnamon. What fraction of the doughnuts are choc hazelnut?
workedSolution
sm_nogap Fraction of choc hazelnut doughnuts
> > | | | > > | --- | ----------------------------------------------------- | > > | | \= $1 - \bigg( \dfrac{3}{10} + \dfrac{1}{5} \bigg)$ | > > | | \= $1 - \bigg( \dfrac{3}{10} + \dfrac{2}{10} \bigg)$ | > > | | \= $1 - \dfrac{5}{10}$ | > > | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{1}{2}$

Answers

Is Correct?Answer
✓

12\dfrac{1}{2}

x

310\dfrac{3}{10}

x

415\dfrac{4}{15}

x

1115\dfrac{11}{15}

Variant 5

DifficultyLevel

637

Question

Indigo has a selection of dyes.

The dyes are either blue, red or green.

110\dfrac{1}{10} of her dyes are red and 34\dfrac{3}{4} are blue.

What fraction of her dyes are green?

Worked Solution

Fraction of green dyes
= 1−(110+34)1 - \bigg( \dfrac{1}{10} + \dfrac{3}{4} \bigg)
= 1−(220+1520)1 - \bigg( \dfrac{2}{20} + \dfrac{15}{20} \bigg)
= 1−17201 - \dfrac{17}{20}
= 320\dfrac{3}{20}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Indigo has a selection of dyes. The dyes are either blue, red or green. $\dfrac{1}{10}$ of her dyes are red and $\dfrac{3}{4}$ are blue. What fraction of her dyes are green?
workedSolution
sm_nogap Fraction of green dyes
> > | | | > > | --- | ----------------------------------------------------- | > > | | \= $1 - \bigg( \dfrac{1}{10} + \dfrac{3}{4} \bigg)$ | > > | | \= $1 - \bigg( \dfrac{2}{20} + \dfrac{15}{20} \bigg)$ | > > | | \= $1 - \dfrac{17}{20}$ | > > | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{3}{20}$

Answers

Is Correct?Answer
x

3740\dfrac{37}{40}

x

3440\dfrac{34}{40}

x

57\dfrac{5}{7}

✓

320\dfrac{3}{20}

Tags