What are equivalent fractions?  As you may have worked out by the name, equivalent fractions are fractions which have the same value.  Now that sounds a bit strange, but as you known fractions may look different because they have different denominators yet are the same fraction (in disguise you might say).  Have a look at this one ...

Can you see what I mean know?  All these are equivalent fractions because they are all equal to three-quarters.  Even though the denominator is different, we can see that the numerator is multiplied by the same amount.

and

What if we were given a problem like ...

and we have to find the value that the square represents?  Our amazing slide rule makes finding equivalent fractions very easy.

Do you remember how we divided two number?

We lined up the first number on the D scale with the second number on the C scale.  Of course our problem was written a bit differently, it was written with the division sign, but the vinculum means the same thing.

So this is our first step, we line up 5 (on the D scale, D5) with 7 on the C scale (C7).  Remember, numerator on the D scale and denominator on the C scale.  In our problem, we need to find the new numerator. Since our numerator is on the D scale, this means that our answer will also be on the D scale.  Our denominators are on the C scale, so slide the cursor to 21 on the C scale.  What do you notice?

We have the value 15 underneath on the D scale!  There it is!  Too easy, so the square represents the number 15!

Sometimes though, the value we are trying to find is off scale, that is, the slider is too far to the left or right.  Let's look at an example and how we can get around this problem.  What value does the triangle represent in this problem?

When we set C7 above D2, we see that our slider is too far to the left to move the cursor to C21, no matter how hard we try!  Now with a bit of nifty slider and using the CI scale we can still find the answer to our problem.

1. Move the slider so that C1 is above D2.
2. Now move the cursor to CI7.  Remember we said that the CI scale was an inverse scale, so doing this we are multiplying by the inverse or 7 or one-seventh.
   
3. Without moving the cursor, move the slider so that CI21 is under the hairline.
4. You will now read the answer on the D scale below C10.
   

What do you get? 6! So the triangle represents the number 6.

Let's try another one, but this time with the unknown value in the denominator.

What number does the rectangle represent in the following problem?

Remember, the numerator goes on the D scale and the denominator goes on the C scale.

1. Line up D2 with C3.
2. Move the cursor to D6.
3. Now read the answer on the C scale at C9.

So the rectangle represents the number 9.

Now it's your turn to try some problems, click here to do some practice questions.