20179

Question

{{{question}}}

Worked Solution

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Variant 0

DifficultyLevel

655

Question

A garden centre sells a potting mix made up of soil, manure and sand.

Soil makes up 34\dfrac{3}{4} of the mix and manure makes up 16\dfrac{1}{6} of the mix.

What fraction of the potting mix is sand?

Worked Solution
Sand
 = 1−(34+16)1 - \bigg( \dfrac{3}{4} + \dfrac{1}{6} \bigg)
= 1−(912+212)1 - \bigg( \dfrac{9}{12} + \dfrac{2}{12} \bigg)
= 112\dfrac{1}{12}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A garden centre sells a potting mix made up of soil, manure and sand. Soil makes up $\dfrac{3}{4}$ of the mix and manure makes up $\dfrac{1}{6}$ of the mix. What fraction of the potting mix is sand?
workedSolution
| | | | ---------------------: | -------------------------------------------- | |
Sand
| \= $1 - \bigg( \dfrac{3}{4} + \dfrac{1}{6} \bigg)$ | | | \= $1 - \bigg( \dfrac{9}{12} + \dfrac{2}{12} \bigg)$ | | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{1}{12}$

Answers

Is Correct?Answer
✓

112\dfrac{1}{12}

x

410\dfrac{4}{10}

x

412\dfrac{4}{12}

x

37\dfrac{3}{7}

Variant 1

DifficultyLevel

653

Question

A landscaper's concrete mix is made up of sand, cement and gravel.

Cement makes up 16\dfrac{1}{6} of the mix and gravel makes up 12\dfrac{1}{2} of the mix.

What fraction of the concrete mix is sand?

Worked Solution
Sand
 = 1−(16+12)1 - \bigg( \dfrac{1}{6} + \dfrac{1}{2} \bigg)
= 1−(16+36)1 - \bigg( \dfrac{1}{6} + \dfrac{3}{6} \bigg)
= 26\dfrac{2}{6}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A landscaper's concrete mix is made up of sand, cement and gravel. Cement makes up $\dfrac{1}{6}$ of the mix and gravel makes up $\dfrac{1}{2}$ of the mix. What fraction of the concrete mix is sand?
workedSolution
| | | | ---------------------: | -------------------------------------------- | |
Sand
| \= $1 - \bigg( \dfrac{1}{6} + \dfrac{1}{2} \bigg)$ | | | \= $1 - \bigg( \dfrac{1}{6} + \dfrac{3}{6} \bigg)$ | | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{2}{6}$

Answers

Is Correct?Answer
x

14\dfrac{1}{4}

✓

26\dfrac{2}{6}

x

23\dfrac{2}{3}

x

56\dfrac{5}{6}

Variant 2

DifficultyLevel

658

Question

A patchwork quilt is constructed using red, white and blue material.

Red material makes up 25\dfrac{2}{5} of the quilt and blue material makes up 37\dfrac{3}{7} of the quilt.

What fraction of the quilt material is white?

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

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A patchwork quilt is constructed using red, white and blue material. Red material makes up $\dfrac{2}{5}$ of the quilt and blue material makes up $\dfrac{3}{7}$ of the quilt. What fraction of the quilt material is white?
workedSolution
| | | | ---------------------: | -------------------------------------------- | |
White
| \= $1 - \bigg( \dfrac{2}{5} + \dfrac{3}{7} \bigg)$ | | | \= $1 - \bigg( \dfrac{14}{35} + \dfrac{15}{35} \bigg)$ | | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{6}{35}$

Answers

Is Correct?Answer
x

512\dfrac{5}{12}

x

712\dfrac{7}{12}

✓

635\dfrac{6}{35}

x

2935\dfrac{29}{35}

Variant 3

DifficultyLevel

674

Question

Students either walk to school or travel by bus or car.

38\dfrac{3}{8} of the students catch a bus and 37\dfrac{3}{7} of the students walk.

What fraction of the students travel by car?

Worked Solution
Car
 = 1−(38+37)1 - \bigg( \dfrac{3}{8} + \dfrac{3}{7} \bigg)
= 1−(2156+2456)1 - \bigg( \dfrac{21}{56} + \dfrac{24}{56} \bigg)
= 1156\dfrac{11}{56}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Students either walk to school or travel by bus or car. $\dfrac{3}{8}$ of the students catch a bus and $\dfrac{3}{7}$ of the students walk. What fraction of the students travel by car?
workedSolution
| | | | ---------------------: | -------------------------------------------- | |
Car
| \= $1 - \bigg( \dfrac{3}{8} + \dfrac{3}{7} \bigg)$ | | | \= $1 - \bigg( \dfrac{21}{56} + \dfrac{24}{56} \bigg)$ | | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{11}{56}$

Answers

Is Correct?Answer
x

25\dfrac{2}{5}

x

35\dfrac{3}{5}

x

956\dfrac{9}{56}

✓

1156\dfrac{11}{56}

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