Fraction Lines

Sort the fractions in order from smallest to largest.

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Click on these fractions in order from smallest to largest.

Loco Bogey Bogey Bogey Bogey Bogey Bogey Bogey Bogey Bogey Bogey

Not so fast with the clicking!

That is not the next smallest number.

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Cheese and Onion Pies

Cheese and Onion Pies

Arrange the fractions in order from smallest to largest.

The short web address is:

Transum.org/go/?to=cheese

Well Done!

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A Challenge

Vinculum

Vinculum

Find fractions larger than the previous fraction but less than one.

The short web address is:

Transum.org/go/?to=vinculum

This is Fraction Lines level 3. You can also try:
Level 1 Level 2 Level 4 Level 5 Level 6 Level 7

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Description of Levels

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Level 1 - Fractions represented as pie charts

Level 2 - Tenths represented as a grid of squares

Level 3 - Decimal fractions some with hundredths

Level 4 - Twelfths represented as a grid of squares

Level 5 - Vulgar fractions simplified twelfths

Level 6 - Mixed fraction pictures

Level 7 - Mixed fractions and decimals

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Example

Order these fractions from smallest to largest

$$ \frac{3}{4} , \frac{7}{8} , \frac{1}{2} , \frac{1}{4} , \frac{3}{8} $$

Method 1: Write each of the fractions with a common denominator. The lowest common multiple of the five denominators is 8 so the five fractions become:

$$ \frac{6}{8} , \frac{7}{8} , \frac{4}{8} , \frac{2}{8} , \frac{3}{8} $$

It is now easy to order the fractions in order of their denominators:

$$ \frac{2}{8} , \frac{3}{8} , \frac{4}{8} , \frac{6}{8} , \frac{7}{8} $$

Now write each of these fractions in the way they were written in the question:

$$ \bbox[yellow,5px,border:2px solid red]{ \frac{1}{4} ,\quad \frac{3}{8} ,\quad \frac{1}{2} ,\quad \frac{3}{4} ,\quad \frac{7}{8} }$$

Method 2: Convert each of the fractions to decimals (to three decimal places for this example) by dividing the numerators by the denominators:

$$ \require{enclose} \begin{array}{r} 0.750 \\[-3pt] 4 \enclose{longdiv}{3.000} \\[-3pt] \end{array} , \require{enclose} \begin{array}{r} 0.875 \\[-3pt] 8 \enclose{longdiv}{7.000} \\[-3pt] \end{array} , \require{enclose} \begin{array}{r} 0.500 \\[-3pt] 2 \enclose{longdiv}{1.000} \\[-3pt] \end{array} , \require{enclose} \begin{array}{r} 0.250 \\[-3pt] 4 \enclose{longdiv}{1.000} \\[-3pt] \end{array} , \require{enclose} \begin{array}{r} 0.375 \\[-3pt] 8 \enclose{longdiv}{3.000} \\[-3pt] \end{array} $$

The decimal equivalents can more easily be ordered then writen in the way they were written in the question to give the same answer as method 1.

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