To find a fraction of a whole number, we will multiply the fraction by the whole number. 

So, in the problem

one-third of 27

we will first write one-third as a fraction.  We know one-third can be written as \(\displaystyle \frac{1}{3}\).

So, we get

\(\displaystyle \frac{1}{3}\) of \(\displaystyle 27\)

Now, we can multiply them together.  So,

\(\displaystyle \frac{1}{3} \cdot 27\)

Now, we will write 27 as a fraction.  We know that whole numbers can be written as fractions over 1.  So,

\(\displaystyle \frac{1}{3} \cdot \frac{27}{1}\)

Now, we can multiply straight across.  We get

\(\displaystyle \frac{1 \cdot 27}{3 \cdot 1}\)

\(\displaystyle \frac{27}{3}\)

\(\displaystyle 9\)

Therefore, \(\displaystyle \frac{1}{3}\) of \(\displaystyle 27\) is \(\displaystyle 9\).

To find a fraction of a whole number, we will multiply the fraction by the whole number. So, in the problem

 \(\displaystyle \frac{2}{7}\) of \(\displaystyle 63\)

we can write it like this:

\(\displaystyle \frac{2}{7} \cdot 63\)

Now, we will write \(\displaystyle 63\) as a fraction.  We know that whole numbers can be written as fractions over 1.  So, we get

\(\displaystyle \frac{2}{7} \cdot \frac{63}{1}\)

Now, we will simplify before we multiply to make things easier.  The 7 and the 63 can both be divided by 7.  So, we get

\(\displaystyle \frac{2}{1} \cdot \frac{9}{1}\)

Now, we will multiply straight across.  We get

\(\displaystyle \frac{2 \cdot 9}{1 \cdot 1}\)

\(\displaystyle \frac{18}{1}\)

\(\displaystyle 18\)

Therefore,  \(\displaystyle \frac{2}{7}\) of \(\displaystyle 63\) is \(\displaystyle 18\).

Amanda has 3 more marbles than Jason and 5 fewer marbles than Kate. Together, they all have 17 marbles. 

To solve this problem, we should experiment by picking a number for Amanda. We can pick the number 4. 

If Amanda has 4 marbles, this means that Jason has 1 marble, since Amanda has 3 more. If she has 5 fewer marbles than Kate, that means that Kate must have 9 marbles. 

This leaves us with:

Amanda - 4 marbles 

Jason - 1 marble

Kate - 9 marbles

This adds up to a total of 14 marbles. However, we know that there are a total of 17 marbles. Thus, each child must have 1 more marble than what is stated above. The correct information would be below:

Amanda - 5 marbles 

Jason - 2 marble

Kate - 10 marbles

Here, the sum of the marbles is 17 and Amanda still has 3 more marbles that Jason and 5 fewer marbles that Kate. 

Thus, the correct answer is that Amanda has 5 marbles.

To find a fraction of a whole number, we will multiply the fraction by the whole number.  First, given the problem,

a third of 42

we know that a third can be written as \(\displaystyle \frac{1}{3}\).  So, we can re-write it as

\(\displaystyle \frac{1}{3}\) of \(\displaystyle 42\)

Now, we will multiply the fraction by the whole number.  We get

\(\displaystyle \frac{1}{3} \cdot 42\)

Now, we need to write 42 as a fraction.  We know that whole numbers can be written as fractions over 1.  So,

\(\displaystyle \frac{1}{3} \cdot \frac{42}{1}\)

Now, we can multiply straight across.  We get

\(\displaystyle \frac{1 \cdot 42}{3 \cdot 1}\)

\(\displaystyle \frac{42}{3}\)

\(\displaystyle 14\)

Therefore, a third of 42 is 14.

To find a fraction of a whole number, we will multiply the fraction by the whole number.

So, we know a third is the same as \(\displaystyle \frac{1}{3}\).  Now, we can multiply.

\(\displaystyle \frac{1}{3} \cdot 336\)

We will write 336 as a fraction.  We know whole numbers can be written as fractions over 1.  So, we get

\(\displaystyle \frac{1}{3} \cdot \frac{336}{1}\)

Now, we can multiply straight across.  We get

\(\displaystyle \frac{1 \cdot 336}{3 \cdot 1}\)

\(\displaystyle \frac{336}{3}\)

\(\displaystyle 112\)

Therefore, a third of 336 is 112.

To find a fraction of a whole number, we will multiply the fraction by the whole number.

So, in the problem

\(\displaystyle \frac{3}{4}\) of \(\displaystyle 52\)

We can re-write it as

\(\displaystyle \frac{3}{4} \cdot 52\)

Now, we will write 52 as a fraction.  We know that whole numbers can be written as fractions over 1.  So, we get

\(\displaystyle \frac{3}{4} \cdot \frac{52}{1}\)

Now, we can simplify before we multiply.  The 4 and the 52 can both be divided by 4.  We get

\(\displaystyle \frac{3}{1} \cdot \frac{13}{1}\)

Now, we multiply straight across.

\(\displaystyle \frac{3 \cdot 13}{1 \cdot 1}\)

\(\displaystyle \frac{39}{1}\)

\(\displaystyle 39\)

Therefore, \(\displaystyle \frac{3}{4}\) of \(\displaystyle 52\) is \(\displaystyle 39\).

To find a fraction of a whole number, we will multiply the fraction by the whole number.  We get

\(\displaystyle \frac{3}{4} \cdot 100\)

\(\displaystyle \frac{3}{4} \cdot \frac{100}{1}\)

Now, we can simplify.  The 4 and the 100 can both be divided by 4.  We get

\(\displaystyle \frac{3}{1} \cdot \frac{25}{1}\)

\(\displaystyle \frac{3 \cdot 25}{1 \cdot 1}\)

\(\displaystyle \frac{75}{1}\)

\(\displaystyle 75\)

Therefore, \(\displaystyle \frac{3}{4}\) of \(\displaystyle 100\) is \(\displaystyle 75\).

To find a fraction of a whole, we will multiply the fraction by the whole number.  So, we get

\(\displaystyle \frac{1}{5} \cdot 100\)

\(\displaystyle \frac{1}{5} \cdot \frac{100}{1}\)

\(\displaystyle \frac{1 \cdot 100}{5 \cdot 1}\)

\(\displaystyle \frac{100}{5}\)

\(\displaystyle 20\)

Therefore, \(\displaystyle \frac{1}{5}\) of \(\displaystyle 100\) is \(\displaystyle 20\).

To find a fraction of a whole number, we will multiply the fraction by the whole number.  So, we get

\(\displaystyle \frac{1}{4} \cdot 280\)

\(\displaystyle \frac{1}{4} \cdot \frac{280}{1}\)

\(\displaystyle \frac{1 \cdot 280}{4 \cdot 1}\)

\(\displaystyle \frac{280}{4}\)

\(\displaystyle 70\)

Therefore, \(\displaystyle \frac{1}{4}\) of \(\displaystyle 280\) is \(\displaystyle 70\).

To find a fraction of a whole number, we will multiply the fraction by the whole number. 

We know that "a quarter" is the same as \(\displaystyle \frac{1}{4}\).  So, we get

\(\displaystyle \frac{1}{4} \cdot 96\)

\(\displaystyle \frac{1}{4} \cdot \frac{96}{1}\)

\(\displaystyle \frac{1 \cdot 96}{4 \cdot 1}\)

\(\displaystyle \frac{96}{4}\)

\(\displaystyle 24\)