## What are fractions?

Fractions refer to the number of parts that equal the whole.

Suppose we have a cake divided into equal portions, the fraction comes to represent each of the portions into which we have cut the cake. Thus, if we have four equal portions, each of them represents a quarter of the pie. This is expressed numerically as follows: $1 \over 4$.

The number $1$ refers to the specific slice of the total pie set. We can look at it in the following way: we are talking about one slice and, therefore, we express it with a $1$. If we were talking about two slices, instead of $1$ we would write $2$.

The number $4$ refers to all equal portions of the pie. Since we have divided the pie into four equal portions, the number that should represent this division is $4$.

## Examples with solutions for Simple Fractions

### Exercise #1

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$5:6=$

### Step-by-Step Solution

Note that the numerator is smaller than the denominator:

5 < 6

As a result, we can claim that:

\frac{5}{6} < 1

Therefore, the quotient in the division problem is indeed less than 1

Yes

### Exercise #2

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$7:11$

### Step-by-Step Solution

Note that the numerator is smaller than the denominator:

7 < 11

As a result, we can claim that:

\frac{7}{11}<1

Therefore, the quotient in the division problem is indeed less than 1

Yes

### Exercise #3

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$1:2=$

### Step-by-Step Solution

Note that the numerator is smaller than the denominator:

1 < 2

As a result, we can claim that:

\frac{1}{2}<1

Therefore, the fraction in the division problem is indeed less than 1

Yes

### Exercise #4

Without calculating, determine whether the quotient in the following division is less than 1 or not:

$11:8$

### Step-by-Step Solution

Note that the numerator is smaller than the denominator:

11 > 8

As a result, we can claim that:

\frac{11}{8} > 1

Therefore, the quotient in the division problem is not less than 1

No.

### Exercise #5

Solve the following:

$\frac{29}{29}=$

### Step-by-Step Solution

We will divide the numerator and denominator by the highest number that both are divisible by.

In this case, the number is 29

We will divide the fraction as follows:

$\frac{29:29}{29:29}=\frac{1}{1}=1$

### Answer

$1$

### Exercise #6

Solve the following:

$\frac{13}{13}=$

### Step-by-Step Solution

We will divide the numerator and denominator by the highest number that both are divisible by.

In this case, the number is 13

We will divide the fraction as follows:

$\frac{13:13}{13:13}=\frac{1}{1}=1$

### Answer

$1$

### Exercise #7

What fraction results from dividing 8 by 13?

### Step-by-Step Solution

Let's write the division exercise:

$8:13$

Now let's write it as a simple fraction, remembering that the numerator is on top and the denominator is on the bottom:

$\frac{8}{13}$

### Answer

$\frac{8}{13}$

### Exercise #8

Solve the following:

$\frac{2}{18}=$

### Step-by-Step Solution

We will divide the numerator and denominator by the highest number that both are divisible by.

In this case, the number is 2

We will divide the fraction as follows:

$\frac{2:2}{18:2}=\frac{1}{9}$

### Answer

$\frac{1}{9}$

### Exercise #9

My numerator is 6 and my denominator is 7.

Which am I?

### Step-by-Step Solution

Remember that the numerator of the fraction is the top half, whilst the denominator of the fraction is the bottom half.

If we position them accordingly we should obtain the following:

$\frac{6}{7}$

### Answer

$\frac{6}{7}$

### Exercise #10

What is the marked part?

### Step-by-Step Solution

We can see that there are three shaded parts out of six parts in total,

that is - 3/6

But this is not the final answer yet!

Let'snotice that this fraction can be reduced,

meaning, it is possible to divide both the numerator and the denominator by the same number,

so that the fraction does not lose its value. In this case, the number is 3.

3:3=1
6:3=2

And so we get 1/2, or one half.
And if we look at the original drawing, we can see that half of it is colored.

### Answer

$\frac{1}{2}$

### Exercise #11

Solve the following:

$\frac{10}{5}=$

### Step-by-Step Solution

We will divide the numerator and denominator by the highest number that both are divisible by.

In this case, the number is 5

We will divide the fraction as follows:

$\frac{10:5}{5:5}=\frac{2}{1}=2$

### Answer

$2$

### Exercise #12

My numerator is 3 and my denominator is 8.

Which am I?

### Step-by-Step Solution

Let's remember that the numerator of the fraction is on top, while the denominator of the fraction is on the bottom.

Now we'll place them accordingly and get:

$\frac{3}{8}$

### Answer

$\frac{3}{8}$

### Exercise #13

Solve the following:

$\frac{64}{8}=$

### Step-by-Step Solution

We will divide the numerator and denominator by the highest number that both are divisible by.

In this case, the number is 8

We will divide the fraction as follows:

$\frac{64:8}{8:8}=\frac{8}{1}=8$

### Answer

$8$

### Exercise #14

Solve the following:

$\frac{56}{7}=$

### Step-by-Step Solution

We will divide the numerator and denominator by the highest number that both are divisible by.

In this case, the number is 7

We will divide the fraction as follows:

$\frac{56:7}{7:7}=\frac{8}{1}=8$

### Answer

$8$

### Exercise #15

What fraction results from dividing 5 by 9?

### Step-by-Step Solution

Let's write the division exercise:

$5:9$

Now let's write it as a simple fraction, remembering that the numerator is on top and the denominator is on the bottom:

$\frac{5}{9}$

### Answer

$\frac{5}{9}$