# 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

### Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.48" was replaced by "(148/100)". 3 more similar replacement(s)

### Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

(58/10)-(32/100)*x-(-(148/100))=0

## Step by step solution :

## Step 1 :

```
37
Simplify ——
25
```

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

```
58 32 37
(——-(———•x))-(0-——) = 0
10 100 25
```

## Step 2 :

```
8
Simplify ——
25
```

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

```
58 8 -37
(—— - (—— • x)) - ——— = 0
10 25 25
```

## Step 3 :

```
29
Simplify ——
5
```

#### Equation at the end of step 3 :

```
29 8x -37
(—— - ——) - ——— = 0
5 25 25
```

## Step 4 :

#### Calculating the Least Common Multiple :

4.1 Find the Least Common Multiple

The left denominator is : 5

The right denominator is : 25

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

5 | 1 | 2 | 2 |

Product of all Prime Factors | 5 | 25 | 25 |

Least Common Multiple:

25

#### Calculating Multipliers :

4.2 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 = 5

Right_M = L.C.M / R_Deno = 1

#### Making Equivalent Fractions :

4.3 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. 29 • 5 —————————————————— = —————— L.C.M 25 R. Mult. • R. Num. 8x —————————————————— = —— L.C.M 25

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

4.4 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:

```
29 • 5 - (8x) 145 - 8x
————————————— = ————————
25 25
```

#### Equation at the end of step 4 :

```
(145 - 8x) -37
—————————— - ——— = 0
25 25
```

## Step 5 :

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

5.1 Adding fractions which have a common denominator

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

```
(145-8x) - (-37) 182 - 8x
———————————————— = ————————
25 25
```

## Step 6 :

#### Pulling out like terms :

6.1 Pull out like factors :

182 - 8x = -2 • (4x - 91)

#### Equation at the end of step 6 :

```
-2 • (4x - 91)
—————————————— = 0
25
```

## Step 7 :

#### When a fraction equals zero :

` 7.1 When a fraction equals zero ...`

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

```
-2•(4x-91)
—————————— • 25 = 0 • 25
25
```

Now, on the left hand side, the 25 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

-2 • (4x-91) = 0

#### Equations which are never true :

7.2 Solve : -2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

#### Solving a Single Variable Equation :

7.3 Solve : 4x-91 = 0

Add 91 to both sides of the equation :

4x = 91

Divide both sides of the equation by 4:

x = 91/4 = 22.750