Fractions

Portions of a whole

𝑧 = 𝑥/𝑦
⇕
𝑥 = 𝑦 × 𝑧

𝑥∈ℤ
𝑦∈ℕ⁺
⇒ 𝑧∈ℚ

Adding and substracting

𝑧₁ + 𝑧₂ =

  𝑥₁𝑦₂ + 𝑥₂𝑦₁
______________
     𝑦₁𝑦₂

Multiplying

𝑧₁ × 𝑧₂ =

  𝑥₁𝑥₂
_______
  𝑦₁𝑦₂

Ratios

Fraction : Decimal : Percent

⅓  :  0,3333…  :  33,3%



Gold carats:
24:  pure gold
18:  18∕24 ,3∕4, 75%


Half an hour
Quarter to

Photography:  Shutter speed  in fractions of a second.

PERCENT  RATE OF   CHANGE

We use PERCENT RATE OF CHANGE to show how much an amount has changed in relation to the original amount. Another way to think about it is simply as the rate of change expressed as a percent.

When the original
amount goes up ,
we calculate percent
increase .

When the original amount goes down , we calculate percent decrease .

To calculate the percent rate of change: First , set up this ratio : CHANGE IN QUANTITY ORIGINAL QUANTITY (The “change in quantity” is the difference between the original and new quantity.)

Second , divide. Last , move the decimal two spaces to the right and add your % symbol.

EXAMPLE: A store purchases T-shirts from a factory for $20 each and sells them to customers for $23 . What is the percent increase in price?

23 - 20
________
20
= 
3/20 = 0.15 = 15% increase

EXAMPLE: On your first history test, you get 14 questions correct. On your second test, you don’t study as much, so you get only 10 questions are correct. What is the per cent decrease from your first to your second test?

14-10 
______
14
= 4/14
= 0.29 = 29%

Remember to reduce fractions whenever possible to make your calculations easier. 156 decrease

FOR PERCENTAGES, ROUND TO THE NEAREST HUNDREDTH PLACE.

Remember to reduce fractions whenever possible to make your calculations easier.

Tricks for Mental Arithmetics

𝐴𝐵 = (2𝐴)(B∕2)

2.5*6 = 5*3

𝑛² = (𝑛+𝑑)(𝑛-𝑑)+𝑑²

17² = 20*14+3²=280+9=289
99² = 100*98+1 = 9801