You can write out the multiples of each number, and find the first number that is common to all of them.

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

12: 12, 24, 36, 48, 60

15: 15, 30, 45, 60

The correct answer is 60.

To find the greatest common factor of three numbers, first factor each number as a product of prime numbers:

\(\displaystyle \dpi{100} 96: 2\times 2\times 2\times 2\times 2\times 3\)

\(\displaystyle \dpi{100} 24: 2\times 2\times 2\times 3\)

\(\displaystyle \dpi{100} 12: 2\times 2\times 3\)

Now take all of the factors that are in common between 12, 24 and 96.  In this case, that is 2, 2 and 3.

\(\displaystyle \dpi{100} 2\times 2\times 3=12\)

To solve:

First, find the number of answers completed by calculating:

\(\displaystyle \small 60\cdot 0.25=15\)

Then, find how long it would take him to complete the 60 question test if for every 20 minutes he answer 15 questions:

\(\displaystyle \small 60 \div 15=4\) (sets of 15 questions)

\(\displaystyle \small \small \small 4\cdot 20 =80\) minutes altogether to finish the test.

A ratio can be rewritten as a quotient; do this, and simplify it.

\(\displaystyle 13 \frac{1}{2} : 1 \frac{1}{2}\)

Rewrite as

 \(\displaystyle 13 \frac{1}{2} \div 1 \frac{1}{2} = \frac{27}{2} \div \frac{3}{2} = \frac{27}{2} \cdot \frac{2}{3} = \frac{9}{1} \cdot \frac{1}{1} = \frac{9}{1}\)

or \(\displaystyle 9:1\)

There are 5 white chocolates. There are a total of 12 milk and dark chocolates. The ratio of white to other chocolates is 5:12.

Identify the number of sunny days in February : \(\displaystyle 10\)

Then, creating a ratio,  show the number of sunny days compared to the total number of days in the month of February (28):

\(\displaystyle 10:28\)

Answer: \(\displaystyle 10:28\)

Rewrite this in fraction form for the sake of simplicity, and divide both numbers by \(\displaystyle GCF (140,60) = 20\):

\(\displaystyle \frac{140}{60}=\frac{140\div 20}{60\div 20} = \frac{7}{3}\)

The ratio, simplified, is \(\displaystyle 7:3\).

A ratio involving decimals can be simplified as follows:

First, move the decimal point over a common number of places in each number so that both numbers become whole. In this case, it would be two places:

\(\displaystyle 2.4 : 0.75 \Rightarrow 240 : 75\) (note the addition of a zero at the end of the first number)

Now, rewrite as a fraction and divide both numbers by \(\displaystyle GCF(240,75) = 15\):

\(\displaystyle \frac{240}{75} = \frac{240 \div 15}{75 \div 15} = \frac{16}{5}\)

The ratio, simplified, is \(\displaystyle 16:5\)

A ratio of fractions can best be solved by dividing the first number by the second. Rewrite the mixed fraction as an improper fraction, rewrite the problem as a multiplication by taking the reciprocal of the second fraction, and cross-cancel: 

\(\displaystyle 3 \frac{4}{7} \div \frac{5}{7} = \frac{25}{7} \div \frac{5}{7} = \frac{25}{7} \div \frac{7}{5} = \frac{5}{1} \div \frac{1}{1}=\frac{5}{1}\)

The ratio, simplified, is \(\displaystyle 5:1\).

Divide the number of words by the number of minutes to get words per minute:

\(\displaystyle 450 \div 25 = 18\) words per minute