Before we buy any ribbon material, let's convert what the sister is asking for into the right unit. Sarah needs  in order to make the ribbon, so to convert that to  we need to multiply  by . We do this because .

So we can see that Sarah needs to buy  of ribbon material in order to make a ribbon that is exactly  long.

Our answer is .

In order to convert  into , let's first convert our  into , since  is the unit in between the two.

, so in order to convert this we need to multiply our number of , , with the number of  it takes to make , .

We now have , so converting this to  should make it easier. 

, so in order to convert what we have we need to multiply our  by  for the same reasons above.

We can conclude that .

Our answer is .

Since the conversion we are asking for is from two different metric systems, the conversion rate will not be a whole number.

While it differs slightly, the conversion we will use for  to  is 

We have , so in order to convert that to  we'll have to multiply our number by .

Our answer is 

While the conversion may vary, the one we will be using for this problem is .

Since we are at , we'll need to multiply this by  in order to convert it to .

Our answer is 

For this problem, it's important to know that . This conversion factor will allow you to convert twelve inches into centimeters. 

Aside from knowing the conversion factor, it's important to also know how to set up this kind of problem so you can be successful at solving the question. 

Often times, it's easier to solve/set up through the use of dimensional analysis. Begin by drawing a "t". In the top left corner of the t we will write in our original unit ( inches). We know that our final answer must me in centimeters - therefore, we need to be able to "cross out" the inches units. This can be done by placing  inch (the conversion factor) in the bottom right corner of the t. The inches will cancel out because think of them as being divided out. When you have one thing as the numerator of the fraction and the same thing is the denominator of the fraction, they will cancel out as . The same concept goes for dimensional analysis with units. 

In order to complete the t, we need to include the  in the top right corner to finish the conversion factor. This will leave us with an answer ending in centimeters. 

Now, we must multiply across the top and divide by the numbers on the bottom. 

To pattern uses the formula .

The pattern follows this equation:

The symbols show that if one number is equal to another,  the equality holds no matter the order of the two. This is the symmetric property of equality.

The symbols express the idea that any number is equal to itself. This is the reflexive property of equality.

The symbols express the idea that if three numbers are added, the same sum results regardless of which numbers are added first. This is the associative property of addition.