PEMDAS

MATH

ORDER OF OPERATIONS
KLALI QDIMUT
"כללי קדימות" 

PEMDAS(please excuse my dear aunt Sally)
Parentheses, exponents multiplication, division, addition, subtraction

Hebrew: סחםחחח Xacamccc (talking warm lol)

Xograyim(), cezqah ^, kefel ×, ciluq ÷, cibur +, cixur -

GREATER THAN

MATH

MATH

before we begin let's get in some relevant Hebrew vocabulary so that we are advancing our Hebraic education in every circumstance

Greater than
GaDoL Me גדול מ

Less than
Qa9aN Me קטן מ

The alligator on the left is greater than any

The tail on the left is less than an inch

SQUARE ROOTS

MATH

Square root
5oRe5 MRuBa7 שורש מרובע

RADICALS
The square root of a positive number x is the number that, when squared, equals x.

For example:

The square root of 16 equals 4 because 4 × 4 = 16.
The square root of 9 equals 3 because 3 × 3 = 9.
The square root of 4 equals 2 because 2 × 2 = 4.

The symbol for a positive square root is √, also called a radical.

√16=4
√9=3

EXPONENT

MATH

Exponent
Ma7aRi2 מעריך

4 Rules of exponents
An exponent is shorthand for multiplication. The large number is called the base, and the little number is called the exponent.

*When you multiply numbers that have the same base, you simply add the exponents.
*When you divide numbers that have the same base, you simply subtract the bottom exponent from the top exponent.
*Anything to the zero power is 1.
*anything to the first power equals that number.

HOW BIG IS A BILLION YOUTUBE

A milliard is 1,000^3 think of a yard having 3 feet
A million is 1,000^2 thus it has six zeros

RATE

MATH

before we begin let's get in some relevant Hebrew vocabulary so that we are advancing our Hebraic education in every circumstance

Rate
5i7uR שיעור

Distance is 50 in the photo

Speed(rate)
50 ÷ .5 = 100

Time
50 ÷ 100 = .5

Distance
100 × .5 = 50

EXAMPLE

A train traveled at a speed of 120 kilometers per hour for 2.5 hours. How many kilometers did the train travel?

R × T = D
120 x 2.5 = 300

In summary: when you are talking about rate it's all about dividing distance

CROSS MULTIPLICATION

MATH

When two fractions have the same exact value, multiplying the numerators by the denominators will give the same answer.

for example:
8/12= 2/3
-these two fractions have the same exact value

8×3=24
12×2=24

This proves they are identical in value

To cross multiply is to go from this:
a/b = c/d

To this:
ad = bc

Knowing this simple fact is useful. With this we can use a technique called 'cross multiplication'. Cross multiplication has two uses
1. It can tell us which of two fractions is larger
2. It can help us solve variables or the missing piece of information in an equation

WHICH IS THE GREATER FRACTION?

Cross-multiplication is a handy math skill to know. You can use it for a few different purposes. For example, you can compare fractions and find out which is greater.

For example, suppose you want to find out which of the following three fractions is the greatest:

3/5   5/9   6/11

Cross-multiplication works only with two fractions at a time, so pick the first two:

3/5 cross multiply with 5/9

3×9=27
5×5=25

Because 27 is greater than 25, you know now that 3/5 is greater than 5/9. So you can throw out 5/9.

Now do the same thing for 3/5 and 6/11:

3/5 cross multiply with 6/11

3×11=33
6×5=30

Because 33 is greater than 30, 3/5 is greater than 6/11. Pretty straightforward, right?

SOLVING VARIABLES

If a 4ft tree cast an 8ft shadow, how long of a shadow does an 8ft tree cast?

4:8 = 8:x

4x = 8×8
4x = 64
x= 16

Remember the formula?
a:b = c:d

Which is:
ad = bc


KNOWN AS THE RULE OF THREE, WAS UNDERSTOOD BY HEBREWS IN THE 15TH CENTURY

 

Weighted mean

MATH

before we begin let's get in some relevant Hebrew vocabulary so that we are advancing our Hebraic education in every circumstance

Weighted Mean
MMu3a7 M5uQLaL ממוצע משוקלל

The weighted mean is used when numbers in a set are not all equally important. Those with more importance are given more weight when calculating the mean, or average. Here's how.

Let's say there are 4 tests in total for a certain class: Exam A, the Midterm Exam, Exam B, and the final Exam. Exam A and B may be worth only 20% each of your final grade, while the Midterm and Final Exams may each be worth 30% of your final grade. You happen to score the following on each:

Exam A-95
Midterm Exam-90
Exam B-92
Final Exam-87

To calculate your final grade for the class, you can't just take the mean (average), since the Midterm and Final exams have more weight than Exams A and B. So you must find the weighted mean. Start by writing the weights next to each corresponding item.

Exam A-95             20%
Midterm Exam-90 30%
Exam B-92              20%
Final Exam-87        30%

Now multiply each score by its weight and write that new value off to the right.

Exam A-95             20% = 1,900
Midterm Exam-90 30% = 2,700
Exam B-92              20& = 1,840
Final Exam-87        30% = 2,610

Add up both the final column and the weights column.

Exam A-95              20% = 1,900
Midterm Exam-90 30% = 2,700
Exam B-92              20& = 1,840
Final Exam-87        30% = 2,610
                                 100%   9,050

Now divide the total value by the total of the weights to get the weighted average.

9050÷100=90.5

Your final grade in class would be 90.5

In summary, you can calculate the weighted mean by following these steps:

STEP 1. Multiply your values by their respective weights
STEP 2. Add all your weights together and all your new values together
STEP 3. Divide the total new value by the total weight.

Not that it's real important but:

For converting percentages into decimals click here
For multiplying decimals click here