The ratio of boys to girls is \(\displaystyle 25 \textrm{ to } 15\), but this is not in simplest form. Rewrite this as a fraction for simplicity, then divide both numbers by \(\displaystyle GCF (25,15) = 5\):

\(\displaystyle \frac{25}{15} = \frac{25\div 5}{15\div 5} = \frac{5}{3}\)

In simplest form, the ratio is \(\displaystyle 5 \textrm{ to }3\)

To find the children who preferred pancakes, subtract all the other children (cereal + yogurt) from the total:

\(\displaystyle 14\: cereal+7\: yogurt=21\)

\(\displaystyle 35\: total-21\: children=14\: pancakes\)

There are 2 green candies in the assortment out of a total of 12 candies. The proportion of green candies to total candies is \(\displaystyle \frac{2}{12}\), which simplifies to \(\displaystyle \frac{1}{6}\). This fraction describes a 1 in 6 chance, which is what we are looking for. 

Ratios represent how one number is related to another. These steps will help you determine the ratio of the numbers shown:

1) Divide both terms of the ratio by the GCF (greatest common factor). In this case, the GCF is 43 because 43 is the greatest number that goes into both numbers evenly. 

2) Show the ratio with a colon : and remember to keep the numbers in the same order!

Therefore, the ratio of 86 to 129 is \(\displaystyle 2:3\).

Multiply 18 miles per gallon by 24 gallons to get the distance the truck can travel on a full tank:

\(\displaystyle 18 \times 24 = 432\) miles

On one-half of a tank, this truck can travel 

\(\displaystyle 432 \times \frac{1}{2} = \frac{432}{2} = 216\ miles\)

Multiply 15 gallons by 29 miles per gallon to get the distance the car can travel on a full tank:

\(\displaystyle 15 \times 29 = 435\) miles.

Multiply this by three-fourths to get the distance it can travel on three-fourths of a tank.

\(\displaystyle 435 \times \frac{3}{4} = \frac{435 \times 3}{4}= \frac{1,305 }{4}\)

\(\displaystyle 1,305 \div 4 = 326 \textrm{ R }1\), so

\(\displaystyle \frac{1,305 }{4} = 326\frac{1 }{4}\) miles

The ratio needed is unsharpened to new box and it says there are 24 pencils in a new box.  It does not say how many are unsharpened but it does give the amount that has been sharpened already.

To find the unsharpened amount subtract the number of pencils sharpened from the number of pencils in the new box.  Therefore, it would be \(\displaystyle 24\, -\, 18= 6\) unsharpened pencils.

 The ratio of unsharpened to new box would be \(\displaystyle 6\: to\: 24\).

The question asked for the ratio of the students NOT ready for lab to the students in the science class.

There are 15 students that are not ready for the computer lab.

There are 30 students in the science class.

Therefore, the ratio is \(\displaystyle 15 \: to\: 30\).

Since 15 and 30 can be reduced by their greatest common factor of 15 the ratio is simplified to \(\displaystyle 1\: to \: 2\).   

\(\displaystyle [\frac{15}{15} = 1\)  \(\displaystyle and \: \: \frac{30}{15} = 2]\)

In order to solve this problem, we should set up a ratio.

The ratio of flour to sugar in the recipe is \(\displaystyle 4:1\)

If Sarah only has 2 cups of flour, the ratio would be \(\displaystyle 2:x\) where \(\displaystyle x\) is the sugar.

Looking at the first ratio, 2 cups is half of 4, so the sugar would also be half. So the answer is \(\displaystyle \frac{1}{2}\) cup of sugar.

The ratio of female-to-male students is 3:2 or:

\(\displaystyle \frac{3}{2}\)

Since we have 18 female students, we can set it up like this:

\(\displaystyle \frac{3}{2}=\frac{18}{x}\)

where \(\displaystyle x\) is the unknown number of male students.

Now multiply the fraction by whatever number so that the numerator (the female students) equals 18.

\(\displaystyle \frac{3\times 6}{2\times 6}=\frac{18}{12}\)

So the amount of male students is 12.