First, compute the new number of philosophy books.  This will be .  

The ratio of philosophy books to history books is thus:

This can be reduced by dividing the numerator and the denominator by :

Therefore, the ratio is .

27 of the 72 cars are 4-wheel drive, we can write this as a proportion.

The proportion of the 4-wheel drive cars to the total number of vehicles. 

Therefore, to find the proportion of 2-wheel drive cars is,

 Therefore the ratio of 2-wheel drive:4-wheel drive vehicles is 5:3.

One remote is defective for every 199 non-defective remotes.

Begin by making your life easier: presume that there are  papers on the desk. Immediately, we know that there are  paper clips. Now, if there are  papers, you know that there also must be  greeting cards. Technically you figure this out by using the ratio:

By cross-multiplying you get:

Solving for , you clearly get .

(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)

Now, this means that our desk has on it:

 papers

 paper clips

 greeting cards

Therefore, you have  total items.  Based on this, your ratio of paper clips to total items is:

, which is the same as .

To begin, you need to calculate how many students are taking Old Norse. This is:

Now, the ratio of students taking Old Norse to students taking Greek is the same thing as the fraction of students taking Old Norse to students taking Greek, or:

Next, just reduce this fraction to its lowest terms by dividing the numerator and denominator by their common factor of :

This is the same as .

To begin, you need to do a simple addition to find the total number of flowers in the garden:

Now, the ratio of petunias to the total number of flowers in the garden can be represented by a simple division of the number of petunias by . This is:

Next, reduce the fraction by dividing out the common  from the numerator and the denominator:

This is the same as .

A ratio is two numbers separated by a colon. When expressing fractions as a ratio, the numerator is the number to the left of the colon while the denominator is to the right of the colon. The answer is 

Let's convert the words into numbers. Since there are  girls and  boys, we need ratio of boys to girls. The ratio should be . 

Let's list a bunch of square numbers from  noninclusive.

 doesn,t count since it's not included HOWEVER:  count.

Let's list a bunch of cubic numbers from  noninclusive.

 doesn,t count since it's not included HOWEVER:  count.

There are four square numbers to two cubic numbers. The ratio becomes  or .

To get the apple to carrot ratio, we need to equal out the bananas. The least common denominator of  and  is . So if  apples equal  bananas, then  bananas equal  apples. Also, if  bananas equal  carrots, then  bananas equal  carrots. Since now the total bananas are equal, we can find the ratio of apples to carrots. We have  as the final answer.