Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm trying to understand fractions more by using a visual representation, and I having a hard time making a visual representation of the 1/6 of 4/5 and getting a visual understandable representation of the answer 4/30.

I'd appreciate If somebody could represent it for me.

share|cite|improve this question
up vote 18 down vote accepted

Look at the following grid:enter image description here

Suppose you want to take $\frac{1}{6}$ of it, then just take one of the rows, as shown in the following drawing:

enter image description here

Now, suppose we only want $\frac{4}{5}$ of that $\frac{1}{6}$. Then just take $4$ of the $5$ squares that make up that row:

enter image description here

At the end we ended up with $4$ squares, while the entire grid has a total of $30$. therefore $\frac{1}{6}\cdot\frac{4}{5}=\frac{4}{30}$

share|cite|improve this answer
How can I make the images smaller? – dREaM Jun 3 '14 at 21:35
You could do something without graphics, like $$\begin{array}{ccccc} X&X&X&X&O\\O&O&O&O&O\\O&O&O&O&O\\O&O&O&O&O\\O&O&O&O&O\\O&O&O&O&O\end{array}$$ – MPW Jun 3 '14 at 21:46
Or, even better, $$\begin{array}{ccccc} \blacksquare&\blacksquare&\blacksquare&\blacksquare&\square\\ \square&\square&\square&\square&\square\\ \square&\square&\square&\square&\square\\ \square&\square&\square&\square&\square\\ \square&\square&\square&\square&\square\\ \square&\square&\square&\square&\square\end{array}$$ – MPW Jun 3 '14 at 21:50
Now all that's left is to explain why the word "of" translates into multiplication. – Mehrdad Jun 4 '14 at 11:04
Right-click and select "Show as LaTeX commands", you can see it. Its basically an array filled with \square and \blacksquare items – MPW Jun 5 '14 at 1:11

Divide a cake into $30$ equal slices. $\frac45$ of the cake is represented by $\frac45\times 30=24$ slices. $\frac16$ of these $24$ slices is $\frac16\times 24=4$ slices, which is also $\frac{4}{30}$ of the whole cake.

share|cite|improve this answer
Jasper Loy is a curious individual. In every 30-day month, he eats a hamburger every day, except when the day is divisible by 5. Every 6th time he eats a hamburger, he adds cheese. At the end of the month, he will have eaten 4 hamburgers with cheese. – Arkamis Jun 3 '14 at 21:36
Good job people - now you have me hungry :( – Dason Jun 4 '14 at 1:47

Take 15 squares and shade 12 of them. Then you have shaded 4/5 of the squares. Now divide the 12 shaded squares into 6 equal pieces. Then each piece consists of two squares. So two squares represents 1/6 of 4/5 and two squares out of 15 squares equals 4/30.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.