Fraction Lines

Sort the fractions in order from smallest to largest.

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Click on the red fractions in order from smallest to largest.

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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 1. You can also try:
Level 2 Level 3 Level 4 Level 5 Level 6 Level 7

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

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Featured Activity

Lemon Law

Lemon Law

A fascinating digit changing challenge. Change the numbers on the apples so that the number on the lemon is the given total. Can you figure out, by understanding place value, how this works?

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Scan the QR code below to visit the online version of this activity.

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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.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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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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