# (1 - 15%) × 700 = ? Number 700 decreased by 15% (15 percent) of its value (percentage decrease) and calculated absolute change (actual difference)

## Decrease 700 by 15% of its value

## Detailed calculations & verification

### Introduction. Percent, p%

#### 'Percent (%)' means 'out of one hundred':

#### p% = p 'out of one hundred',

#### p% is read p 'percent',

#### p% = ^{p}/_{100} = p ÷ 100.

#### 15% = ^{15}/_{100} = 15 ÷ 100 = 0.15.

#### 100% = ^{100}/_{100} = 100 ÷ 100 = 1.

### Decrease number by 15% of its value.

#### Percentage decrease = 15% × 700

#### New value = 700 - Percentage decrease

### Calculate the New Value

#### New value =

#### 700 - Percentage decrease =

#### 700 - (15% × 700) =

#### 700 - 15% × 700 =

#### (1 - 15%) × 700 =

#### (100% - 15%) × 700 =

#### 85% × 700 =

#### 85 ÷ 100 × 700 =

#### 85 × 700 ÷ 100 =

#### 59,500 ÷ 100 =

#### 595

### Calculate absolute change (actual difference)

#### Absolute change (actual difference) =

#### New value - 700 =

#### 595 - 700 =

#### - 105

## Proof.

### Calculate percentage increase...

#### ... And see if we get as a result

the absolute change (actual difference).

#### Percentage decrease =

#### 15% × 700 =

#### 15 ÷ 100 × 700 =

#### 15 × 700 ÷ 100 =

#### 10,500 ÷ 100 =

#### 105

### So we have proven that the calculations are correct.

#### For positive numbers

#### Absolute change (actual difference) =

#### - 1 × Percentage decrease

## Answer:

700 decreased by 15% = 595

Absolute change (actual difference):

595 - 700 = - 105

#### Signs: % percent, ÷ divide, × multiply, = equal, ≈ approximately equal, / fraction bar;

#### Writing numbers: comma ',' as thousands separator; point '.' as a decimal mark;

## More operations of this kind:

## Decrease number by percentage of value, calculate percentage decrease

## Latest numbers decreased by percentage of value

** 700, percentage decreased by 15% (percent) of its value = 595 ** | * May 17 14:52 UTC (GMT)* |

** 30,500, percentage decreased by 27% (percent) of its value = 22,265 ** | * May 17 14:52 UTC (GMT)* |

** 2,160,000, percentage decreased by 15% (percent) of its value = 1,836,000 ** | * May 17 14:52 UTC (GMT)* |

** 220, percentage decreased by 15% (percent) of its value = 187 ** | * May 17 14:52 UTC (GMT)* |

** 296, percentage decreased by 56% (percent) of its value = 130.24 ** | * May 17 14:52 UTC (GMT)* |

** 10.92, percentage decreased by 21% (percent) of its value = 8.6268 ** | * May 17 14:51 UTC (GMT)* |

** 237, percentage decreased by 50% (percent) of its value = 118.5 ** | * May 17 14:51 UTC (GMT)* |

** 721.45, percentage decreased by 9.2% (percent) of its value = 655.0766 ** | * May 17 14:51 UTC (GMT)* |

** 3,929, percentage decreased by 4% (percent) of its value = 3,771.84 ** | * May 17 14:51 UTC (GMT)* |

** 110, percentage decreased by 50% (percent) of its value = 55 ** | * May 17 14:51 UTC (GMT)* |

** 67,530, percentage decreased by - 1% (percent) of its value = 68,205.3 ** | * May 17 14:51 UTC (GMT)* |

** 65.7, percentage decreased by - 7% (percent) of its value = 70.299 ** | * May 17 14:51 UTC (GMT)* |

** 420, percentage decreased by 750% (percent) of its value = - 2,730 ** | * May 17 14:50 UTC (GMT)* |

** All the numbers decreased by percentage of value ** |

## Decrease numbers by percentages of their values and calculate the absolute percentage change (difference)

### How to calculate the new value of a number by decreasing it by percentage of its value and the absolute percentage change (difference)

- Percentage decreased number = Initial value - Absolute percentage change (difference)
- Absolute percentage change (difference) = Percentage decrease % × Initial value
- Percentage decreased number = Initial value - Percentage decrease % × Initial value = (1 - Percentage decrease %) × Initial value
- In conclusion:
#### Percentage decreased number = (1 - Percentage decrease %) × Initial value

#### Initial value = ^{Percentage decreased number} / _{(1 - Percentage decrease %)}

#### Absolute percentage change (difference) = Percentage decrease % × Initial value = New value - Initial value

### Examples of calculations on how to decrease a number by percentage of its value and calculate the absolute percentage change:

- If Percentage decrease % = 20%, (1 - Percentage decrease %) = 1 - 20% = 100/100 - 20/100 = 80/100 = 0.8 =>
**Percentage decreased number** = 0.8 × Initial value, and **Initial value** = Percentage decreased number / 0.8; **Absolute percentage change (difference)** = New value - Initial value; - If Percentage decrease % = 5%, (1 - Percentage decrease %) = 1 - 5% = 100/100 - 5/100 = 95/100 = 0.95 =>
**Percentage decreased number** = 0.95 × Initial value, and **Initial value** = Percentage decreased number / 0.95; **Absolute percentage change (difference)** = New value - Initial value; - If Percentage decrease % = 120%, (1 - Percentage decrease %) = 1 - 120% = 100/100 - 120/100 = -20/100 = -0.2 =>
**Percentage decreased number** = -0.2 × Initial value, and **Initial value** = Percentage decreased number / -0.2; **Absolute percentage change (difference)** = New value - Initial value; - If Percentage decrease % = -30%, (1 - Percentage decrease %) = 1 - (-30%) = 1 + 30% = 100/100 + 30/100 = 130/100 = 1.3 =>
**Percentage decreased number** = 1.3 × Initial value, and **Initial value** = Percentage decreased number / 1.3; this is in fact a percentage increase of the initial number; **Absolute percentage change (difference)** = New value - Initial value.