Need to know the official name of these type of fraction problems

[rrbrisbo89]

Hi,
I need to know the official name of these type of fraction problems?

This is what I wrote on a flash card I couldn't upload the flashcard because of file size.

Example problem -

4/3 times x = 6/7

These are the instructions I wrote on the flash card.

1. Divide sides by left (least) (4/3) number.

2. Cross out left number (4/3).

3. Multiply reciprocal (3/4).

Thank you.

 

[Jameson]

Hi BR89,

Welcome to MHB! :)

I'm not aware of an official name for this kind of problem, but I would say the main idea used is dividing fractions. Dividing fractions uses the idea that if you divide by that fraction, it's the same as multiplying by the reciprocal. For example:
$$\frac{3}{\frac{2}{5}}=3 \cdot \frac{5}{2}=\frac{15}{2} $$
Or your example,
$$\frac{\frac{6}{7}}{\frac{4}{3}} = \frac{6}{7} \cdot \frac{3}{4}=\frac{18}{28}=? $$
You already had this main idea written down. Can you finish simplifying the above fraction?

 

[rrbrisbo89]

Do you know if there are any guides to display the problem like you did in the previous post?

Thanks.

 

[topsquark]

Do you know if there are any guides to display the problem like you did in the previous post?

Thanks.

We have a LaTeX help forum on the main page (almost all the way down.) http://mathhelpboards.com/latex-help-discussion-26/. You'll pick up the basics pretty quickly.

-Dan

 

[rrbrisbo89]

Hi BR89,

Welcome to MHB! :)

I'm not aware of an official name for this kind of problem, but I would say the main idea used is dividing fractions. Dividing fractions uses the idea that if you divide by that fraction, it's the same as multiplying by the reciprocal. For example:
$$\frac{3}{\frac{2}{5}}=3 \cdot \frac{5}{2}=\frac{15}{2} $$
Or your example,
$$\frac{\frac{6}{7}}{\frac{4}{3}} = \frac{6}{7} \cdot \frac{3}{4}=\frac{18}{28}=? $$
You already had this main idea written down. Can you finish simplifying the above fraction?

[math]
\frac {6}{7} \times \frac {3} {4} = \frac {18} {28} = \frac {9} {14}\
[/math]