Number_gap-2026_695

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

697

Question

Two-thirds of a number is 24.

What is three-quarters of twice the number?

Worked Solution
The number = 24 ÷\div 23\dfrac{2}{3}
= 24 ×\times 32\dfrac{3}{2}
= 36

Twice the number = 2 ×\times 36 = 72

Three-quarters of 72 = 34\dfrac{3}{4} ×\times 72
= 34\dfrac{3}{4} ×\times 4 ×\times 18
= 3 ×\times 18
= 54

Question Type

Answer Box

Variables

Variable nameVariable value
question
Two-thirds of a number is 24. What is three-quarters of twice the number?
workedSolution
| | | | ----------------------:| -------------------------------------------- | | The number | \= 24 $\div$ $\dfrac{2}{3}$ | | | \= 24 $\times$ $\dfrac{3}{2}$ | | | \= 36 |

| | | | ----------------------:| -------------------------------------------- | | Twice the number | \= 2 $\times$ 36 = 72 |

| | | | ----------------------:| -------------------------------------------- | | Three-quarters of 72 | \= $\dfrac{3}{4}$ $\times$ 72 | | | \= $\dfrac{3}{4}$ $\times$ 4 $\times$ 18 | | | \= 3 $\times$ 18 | | | \= {{{correctAnswer0}}} |
correctAnswer0
54
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer054

Variant 1

DifficultyLevel

699

Question

Three-fifths of a number is 45.

What is two-thirds of three times the number?

Worked Solution
The number = 45 ÷\div 35\dfrac{3}{5}
= 45 ×\times 53\dfrac{5}{3}
= 53\dfrac{5}{3} ×\times 3 ×\times 15
= 5 ×\times 15 = 75

Three times the number = 3 ×\times 75 = 225

Two-thirds of 225 = 23\dfrac{2}{3} ×\times 225
= 23\dfrac{2}{3} ×\times 3 ×\times 75
= 2 ×\times 75
= 150

Question Type

Answer Box

Variables

Variable nameVariable value
question
Three-fifths of a number is 45. What is two-thirds of three times the number?
workedSolution
| | | | ----------------------:| -------------------------------------------- | | The number | \= 45 $\div$ $\dfrac{3}{5}$ | | | \= 45 $\times$ $\dfrac{5}{3}$ | | | \= $\dfrac{5}{3}$ $\times$ 3 $\times$ 15 | | | \= 5 $\times$ 15 = 75 |

| | | | ----------------------:| -------------------------------------------- | | Three times the number | \= 3 $\times$ 75 = 225 |

| | | | ----------------------:| -------------------------------------------- | | Two-thirds of 225 | \= $\dfrac{2}{3}$ $\times$ 225 | | | \= $\dfrac{2}{3}$ $\times$ 3 $\times$ 75 | | | \= 2 $\times$ 75 | | | \= {{{correctAnswer0}}} |
correctAnswer0
150
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0150

Variant 2

DifficultyLevel

701

Question

Four-sevenths of a number is 48.

What is five-sixths of half the number?

Worked Solution
The number = 48 ÷\div 47\dfrac{4}{7}
= 48 ×\times 74\dfrac{7}{4}
= 74\dfrac{7}{4} ×\times 4 ×\times 12
= 7 ×\times 12 = 84

Half the number = 84 ÷\div 2 = 42

Five-sixths of 42 = 56\dfrac{5}{6} ×\times 42
= 56\dfrac{5}{6} ×\times 6 ×\times 7
= 5 ×\times 7
= 35

Question Type

Answer Box

Variables

Variable nameVariable value
question
Four-sevenths of a number is 48. What is five-sixths of half the number?
workedSolution
| | | | ----------------------:| -------------------------------------------- | | The number | \= 48 $\div$ $\dfrac{4}{7}$ | | | \= 48 $\times$ $\dfrac{7}{4}$ | | | \= $\dfrac{7}{4}$ $\times$ 4 $\times$ 12 | | | \= 7 $\times$ 12 = 84 |

| | | | ----------------------:| -------------------------------------------- | | Half the number | \= 84 $\div$ 2 = 42 |

| | | | ----------------------:| -------------------------------------------- | | Five-sixths of 42 | \= $\dfrac{5}{6}$ $\times$ 42 | | | \= $\dfrac{5}{6}$ $\times$ 6 $\times$ 7 | | | \= 5 $\times$ 7 | | | \= {{{correctAnswer0}}} |
correctAnswer0
35
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer035

Variant 3

DifficultyLevel

703

Question

Five-ninths of a number is 60.

What is seven-eighths of twice the number?

Worked Solution
The number = 60 ÷\div 59\dfrac{5}{9}
= 60 ×\times 95\dfrac{9}{5}
= 95\dfrac{9}{5} ×\times 5 ×\times 12
= 9 ×\times 12 = 108

Twice the number = 2 ×\times 108 = 216

Seven-eighths of 216 = 78\dfrac{7}{8} ×\times 216
= 78\dfrac{7}{8} ×\times 8 ×\times 27
= 7 ×\times 27
= 189

Question Type

Answer Box

Variables

Variable nameVariable value
question
Five-ninths of a number is 60. What is seven-eighths of twice the number?
workedSolution
| | | | ----------------------:| -------------------------------------------- | | The number | \= 60 $\div$ $\dfrac{5}{9}$ | | | \= 60 $\times$ $\dfrac{9}{5}$ | | | \= $\dfrac{9}{5}$ $\times$ 5 $\times$ 12 | | | \= 9 $\times$ 12 = 108 |

| | | | ----------------------:| -------------------------------------------- | | Twice the number | \= 2 $\times$ 108 = 216 |

| | | | ----------------------:| -------------------------------------------- | | Seven-eighths of 216 | \= $\dfrac{7}{8}$ $\times$ 216 | | | \= $\dfrac{7}{8}$ $\times$ 8 $\times$ 27 | | | \= 7 $\times$ 27 | | | \= {{{correctAnswer0}}} |
correctAnswer0
189
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0189

Variant 4

DifficultyLevel

705

Question

Three-eighths of a number is 42.

What is five-sevenths of three times the number?

Worked Solution
The number = 42 ÷\div 38\dfrac{3}{8}
= 42 ×\times 83\dfrac{8}{3}
= 83\dfrac{8}{3} ×\times 3 ×\times 14
= 8 ×\times 14 = 112

Three times the number = 3 ×\times 112 = 336

Five-sevenths of 336 = 57\dfrac{5}{7} ×\times 336
= 57\dfrac{5}{7} ×\times 7 ×\times 48
= 5 ×\times 48
= 240

Question Type

Answer Box

Variables

Variable nameVariable value
question
Three-eighths of a number is 42. What is five-sevenths of three times the number?
workedSolution
| | | | ----------------------:| -------------------------------------------- | | The number | \= 42 $\div$ $\dfrac{3}{8}$ | | | \= 42 $\times$ $\dfrac{8}{3}$ | | | \= $\dfrac{8}{3}$ $\times$ 3 $\times$ 14 | | | \= 8 $\times$ 14 = 112 |

| | | | ----------------------:| -------------------------------------------- | | Three times the number | \= 3 $\times$ 112 = 336 |

| | | | ----------------------:| -------------------------------------------- | | Five-sevenths of 336 | \= $\dfrac{5}{7}$ $\times$ 336 | | | \= $\dfrac{5}{7}$ $\times$ 7 $\times$ 48 | | | \= 5 $\times$ 48 | | | \= {{{correctAnswer0}}} |
correctAnswer0
240
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0240