# What is the extension of 1 + x 2

## Calculator: Expand fractions

### 1. Expand fraction with number

A fraction is given as well as an expansion number. In this case, the numerator and denominator of the fraction must each be multiplied by the expansion number. As an example we take the extension number 3:

\$\$ \ frac {1} {5} = \ frac {1 · \ textcolor {# 00F} {3}} {5 · \ textcolor {# 00F} {3}} = \ frac {3} {15} \$\$

### 2. Determine the enlargement number

In this case we are given a fraction and an expanded fraction. We now need to determine what the expansion number was. We can do this by dividing the two numerators or the two denominators. Example exercise (the x is the unknown expansion number):

\$\$ \ frac {3} {5} = \ frac {3 · \ textcolor {# 00F} {x}} {5 · \ textcolor {# 00F} {x}} = \ frac {12} {20} \$\$

Now we can either use the numerators with: x = 12: 3 = 4. Or we consider the denominators: x = 20: 5 = 4. In both cases the same number must come out, in this example it is x = 4.

The sample is right:

\$\$ \ frac {3} {5} = \ frac {3 · \ textcolor {# 00F} {4}} {5 · \ textcolor {# 00F} {4}} = \ frac {12} {20} \$\$

### 3. Determine the numerator or denominator of the expanded fraction

It can happen that we have not given either a numerator or a denominator and that the expansion number is also missing. For a missing counter it would look like this:

\$\$ \ frac {3} {7} = \ frac {3 · \ textcolor {# 00F} {x}} {7 · \ textcolor {# 00F} {x}} = \ frac {\ textcolor {# F00} { y}} {14} \$\$

The original denominator is given with 7 and the expanded denominator with 14. With this we can determine the expansion number with: x = 14: 7 = 2. In the next step we use the calculated expansion number to determine the numerator: 3 · 2 = 6 In summary, we hold the solution:

\$\$ \ frac {3} {7} = \ frac {3 · \ textcolor {# 00F} {2}} {7 · \ textcolor {# 00F} {2}} = \ frac {\ textcolor {# F00} { 6}} {14} \$\$

We proceed in the same way with the determination of a missing denominator. First determine the expansion number from numerators, then calculate the missing denominator.

\$\$ \ frac {4} {11} = \ frac {4 · \ textcolor {# 00F} {x}} {11 · \ textcolor {# 00F} {x}} = \ frac {20} {\ textcolor {# F00} {y}} \ quad \ rightarrow \ textcolor {# 00F} {x} = 20: 4 \ textcolor {# 00F} {= 5} \ quad \ rightarrow \ textcolor {# F00} {y} = 11 · \ textcolor {# 00F} {5} = \ textcolor {# F00} {55} \$\$

Solution:

\$\$ \ frac {4} {11} = \ frac {4 · \ textcolor {# 00F} {5}} {11 · \ textcolor {# 00F} {5}} = \ frac {20} {\ textcolor {# F00} {55}} \$\$