# Adding, subtracting and finding the least common multiple

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This solution deals with adding, subtracting and finding the least common multiple.

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- Adding, subtracting and finding the least common multiple

## Step by Step Solution

## Step 1 :

```
4
Simplify —
9
```

#### Equation at the end of step 1 :

```
11 4
—— - —
12 9
```

## Step 2 :

```
11
Simplify ——
12
```

#### Equation at the end of step 2 :

```
11 4
—— - —
12 9
```

## Step 3 :

#### Calculating the Least Common Multiple :

3.1 Find the Least Common Multiple

The left denominator is : 12

The right denominator is : 9

Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
---|---|---|---|

2 | 2 | 0 | 2 |

3 | 1 | 2 | 2 |

Product of all Prime Factors | 12 | 9 | 36 |

Least Common Multiple:

36

#### Calculating Multipliers :

3.2 Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 3

Right_M = L.C.M / R_Deno = 4

#### Making Equivalent Fractions :

3.3 Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)^{2} and (y^{2}+y)/(y+1)^{3} are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. 11 • 3 —————————————————— = —————— L.C.M 36 R. Mult. • R. Num. 4 • 4 —————————————————— = ————— L.C.M 36

#### Adding fractions that have a common denominator :

3.4 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

```
11 • 3 - (4 • 4) 17
———————————————— = ——
36 36
```

## Final result :

```
17
—— = 0.47222
36
```