Mathematics

For money 3.3 is

$3.30 because there needs to be at least 2 decimal places after the decimal to represent cents. This isn't the case for percentage

what is $60 @ 15 cookies mean?

$60 for 1 cookie

In the ordinary decimal system 5623 means

(5x1000) + (6x100) + (2x10) + (3x1) or 5×10³ + 6x10² + 2x10¹ + 3x10⁰

0 x 2-¹ is and 1x2-¹ is

0 , 0.2

Divisible by 5 if it ends in

0 or 5, 130, 1345, 2460

whole numbers W

0, 1, 2, 3... same as natural Numbers but start from 0

A number is divisible by 2 if it ends in

0,2,4,6,8

when converting a percentage to a decimal put 2.5% as

0.025, because when there is a % it means to divide by 100 or you move the decimal place to the left twice.

what is 2/10 as a decimal

0.2

anything to the power of 0 even by 0 is

1

@ means

1 each item. so $50 @ 12 bun means $50 for 1 bun

If you add 0 to any number the answer will not change so

1+0 =1

Natural Numbers (Counting Numbers) N

1, 2, 3, 4, 5, 6, 7, 8, 9, etc. Whole numbers that are not negative and start from 1 and does not include decimals

write 156000 in standard form/scientific notation

1.56 x 10⁵ because you always put the decimal infront of the first non zero digit then count to the end and put the exponent by the number of times you counted.

decimal/Binary

10 digits below ten

to find rate RIPT

100 I/ PT when letters and numbers are beside eachother it means to multiply them

to find Principal PIRT

100 T/RT when letters and numbers are beside eachother it means to multiply them

Any number to the power of 0 = 1 so 2 to the power of 0 = 1

1034053459334 to the power of 0 = 1

what is 1010.01 in base 19

11.02 base 10

12 patties cost 2400. What is the cost of one patty?

12 patties cost 24000 So 1 patty costs 2400÷12=200 divide total cost by number of items to find cost of 1 item.

A number is divisible by 4 if the right last 2 digits are divisible by 4

12,312,516,7328,58736

find the square root of 144 and cube root of 27

12x12 3x3x3

6420 is divisible by 15?

15 is the product of the prime factors 3 and 5, so you need too test to see if 6420 is divisible by both 3 and 5. 6420 is divisible by 5 since it ends in 0, 6420 is divisible by 3 since 6+4+2+0=12 which is divisible by 3. 6420 is therefore divisible by 3 and 5. I.e it is divisible by 3x5 or 15

A donut costs 150. what is the total cost of 10 donuts?

150x10=1500 so 10 donuts cost 1500

Fill in spaces with either ∈ or ∉ 1999 ________________ (numbers divisible by 4)

1999 ∉ (numbers divisible by 4) Since 1999 is not divisible by 4 without leaving a remainder, you will put no element. If you could the answer would be ∈. So 1999 (numbers divisible by 4) = ∉

Ratio: A comparison of two quantities by division. The ratio can be written as a:b or a/b

1:2 = 1/2

in 2006 2 as fv is face value

2

binary

2 digits below 2

Divisible by 9;the sum of all digits should be divisible by 9

2+7=27=9x3 when adding numbers to find if they're divisible by 9, take away addition sign such as 3+6=36 and see if they add up to 9. 3+6 equals nine so 36 is divisible by 9. This goes with multiples of 9 as well. 2+7+9 = 18. 9x2=18

Even numbers are divisible by

2, if a number ends with 2,4,6,8 or 0, it's an even number. 12, 24, 36, 48, 50 ect.

round to decimal place, round 2.567 to 2 decimal places are

2.57 the 2 places after the decimal are 5 and 6, you see the number after 6 and if it's five or higher round it up and the answer is 2.57, if it was lower than 5 the answer would be 2.56

5 (2+3) is and what property is it called

25 because 5x2 = 10, + 5x3 =15 and ten plus 15 is 25. associative property.

when rounding a number, put place values over numbers starting from one's from right to left, so 2567 rounded to the nearest 10 would be

2570, because 7 is one's and 6 is tens, and you check if 67 is closer to 60 or 70 and round it up or down. so the answer is 2570

ternary

3 digits below 3

quaternary

4 digits below 4

The inverse of a number under addition combined with another number will result in the answer '0'

4+(-4)=0

To find the value of x in a fraction such as 1/15 = x/675, see what number can be put by x that if it was reduced it would give 1/15

45/675 reduced is 1/15 so 45 is x, 45 is the answer

quinary

5 digits below 5

what is 0.0000053 in standard form/scientific notation

5.3 to the power of -6

what are the significant figures in 0.0050830010

50830010 because the zeros are after the number

We count place value starting from right to left.

5327 Face value of 3=3 place value of 3=100 Value of 3=3x100

senary

6 digits below 6

7 over 1 equals

7

septenary

7 digits below 7

786 standard form into expanded notation

789 = 700 1+ 80 + 9

octal

8 digits below 8

nonary

9 digits below 9

0.3813 in the ordinary decimal system

= 3/10 + 8/100 + 1/100 + 3/1000 or 3x10-¹ + 8x10-² + 1x10-³ + 3x10-⁴ because fractions mean to divide . You count how many places to the left to count from infront of the number to decide what exponent to put it in. so 8 is two places from the decimal point and you're going backwards so 8 would be 8x10-² You can also put integers over the numbers, put 0 over 0 and-4 over 3 and you would know what exponent to multiply it by. only in this case before decimal is positive after decimal is negative

exponent

A mathematical notation indicating the number of times a quantity is multiplied by itself. 2³ 5³

squared

A number multiplied by itself. A small 2 at the right top side of the number

Formula for compound interest

A=P(1+r/100)^(n/t) n=T

What is inverse property?

Additive inverse- The inverse of a number under addition combines with another number will result in the answer '0' EG: 4+(-4) = 0

Real numbers R

All rational and irrational numbers, including natural, whole numbers, and integers

When converting percentages to decimals the decimals are in the front of the number for percentages before you convert, so for 50% the decimal is in front of 50 which is 50. and a decimal is in front of 50 as opposed to it being in front of the first non zero digit number like when you're doing standard form such as 5.0, the only time this isn't the case of conversion of percentage to decimal is if there is already a decimal on the number such as 5.5% then you would move the decimal instead of putting one in front of the number since the decimal already has a place.

Also when converting the percentage to decimal you move the decimal of the percentage, as stated before two places to the right since you are dividing by 100 to get a decimal. So 75% as a decimal is 75.=7.5=0.75 so 75% is 0.75 as a decimal. 7% as a fraction is 7.=0.7=0.07. 5.5% As a decimal (since it already has a decimal move it to the right) 5.5=0.55=0.055

What are irrational numbers?

An irrational number is a number that cannot be expressed as a fraction for any integers and. . Irrational numbers have decimal expansions that neither terminate nor become periodic. Such as square root 6, or square root 2. The answer to these would be decimal numbers with no detectable pattern such as 3344.338383, if it was a pattern such as 34.43434343 it would be rational. square root 64 is also rational because the answer would be 8. they are can be negative or can be expressed as a fraction as well. As long as the number isn't unending such as 7.4542, or has a pattern it's rational. If it's unending and doesn't have a pattern it's irrational. Numbers like 7/8 are rational as well because they have an ending. 0.875 Or 4/5. Can check on calculator. You can also multiply irrational numbers to get rational numbers such as square root 2 × square root 2 which is equal to 2

significant figures

Any number more than zero.

Rational numbers Q

Any number that can be expressed as a fraction -9/2,7/1, 10/2 2.5

E

Belongs to/elements belong to

Integers (Z or I)

Both positive and negative including 0 -3 -2 -1 0 1 2 3

Formula to find loss

CP - SP

What are coefficients?

Coefficients are numbers which are tied to (multiply) a letter. Such as 2A, 3x, and 4y. 2 and 3 are not coefficients because they are not tied to a letter. Think of it as a number and letter cooperating.

A1

Complement

Difference between compound and simple interest

Compound interest is rising the percentage at the amount of money you receive over time. Simple interest is gaining money but the percentage you gain that money is at a constant

What are constants?

Constante are numbers that stand alone, such as 4,8,25 and 33. 2A is or 33x or 329y are NOT constants because they don't stand alone while numbers like 377237 or 32 and 9 and 0 are. Think of it as numbers being Constantly alone

how to find loss

Cost price- Selling price = loss

To convert a decimal to a fraction

Count the number of place values and put the number of the place value of the number before the decimal. 0.3, ends at tens. omit decimal point. and divide by 10 for 0.351 divide by 1000 because the place value of 0 in this number is 1000. If it was a number such as 2.5, It would have to be 25/10 because 2 is the number before the decimal and the place value of 2 is ten. And into a fraction is 25/10 to 5/2 if reduced ​

when putting numbers in scientific notation such as 52314 or 602000,000 or 0000428

Determine the exponent by the number of places it takes to get infront of the first non zero digit. 5.2314 x 10⁴, 6.02 x 10⁸, 4.28 x 10‐⁵. If you're given a number like 3.2 and are told to put it into scientific notation, the exponent would be 0 because you don't need to move any places 3.2 x 10⁰

What is distributive property?

Distribute number outside of bracket to each number and multiply numbers. 5 (2+3) = 25

To find proportion such as 4/16=x/64 To find x you

Divide numerators, the answer would be 4 1/7=x/49 =7 (You don't divide? ._.)

Prime numbers

Divisible by themselves and 1. The first 6 prime numbers are 2,3 5,7,11,13 1 is not considered a prime number 2 is the only even prime number; all the other prime numbers are odd. Prime numbers are whole numbers with only 2 factors, 1 and itself. Basically numbers that can only have the equation 5x1, 4x1 ect because 1x5 can give you 5 and 5x1 can give you five 5 is a prime number ANSWER: BUT 6 has the factors of 1,2,3 and 6. 6 has more factors than 1 and itself so it isn't a prime number

Rate is a ratio that compares quantities with different units. When a rate expresses a quantity per one unit of another quantity, it is called a unit rate.

Eg: I bought 2lb of onion for $600. How much per lb were the onions sold for? 600/2 = $300 So 1 onion was sold for $300

Divisible by 6: Any even number divisible by 3 is also divisible by 6

Eg:24 is an even number which is divisible by 3, so it must be divisible by 6

HCF

Highest common factor 4-1,2,4=4

Formula for simple interest

I=prt/100

unitary method

If 12 apples cost 30 dollars, what is the cost of 28 apples. Find out how much is 1 apple first. so divide 30÷12=2.5 and multiply the answer by 28. which would give you 70. 28 apples cost 70

Difference between irrational and non irrational decimals

If a number is short like 0.5, has a pattern like 3434343434... or is repeating the same number like 0.66666 it's rational, but if is continuous with none of these like 0.31545673 it's irrational

What is identify property?

If you add any number by 0 the answer is the number itself and NOT 0

What is multiplicative identity?

If you multiply any number by one, the answer will not change. EG: 32x1

Difference between decimal placements in, trying to convert percentage to decimal, and doing scientific notation.

In percentage to decimal you put decimal at the end of the number and move it to the left two times, you're just dividing the number by 100 but aren't looking to make the number short. 25% = 0.25, 2.5% = 0.025 In scientific notation you're trying to make the number short so you put the number infront of the first non zero digit and times it by 10 and put the exponent by how many times it took to move the decimal to reach infront of the first non zero digit. 2.3 x 10¹

To find an unknown answer you most likely divide two numbers or numbers that are there.

In the question "Kim earns $600 in 5 hours. What is the unit of her pay?" Since we're trying to find the unknown answer we divide the two numbers that are there. We set it out as 600/5. The answer should be 120. So she gets $120 an hour.

square root 49

Is a natural number because 7 times 7 is 49, and 7 is a natural number. therefore squareroot 48 is not a irrational but natural number same with square root 144 ....12

how to find profit layout

Item (number of items) - cost of item =CP Unit price Mark up price Markup price x number of items =SP Profit =SP-CP =profit ALWAYS PUT DOLLAR SIGN

Lcm

Lowest common multiple 2-2,4,6,8,12.... 2

Multiple= Time tables of a number

Multiples of 12 are 12,24,36,48,60 and so on...

If a number is beside a bracket without any operations in-between such as 5 (10) you...

Multiply them, Distributive property is a bit different. So 5(10) = 5x10 = 50

Given that R = 9 Cat, Dog, Rabbit) state n (R)=

N (R)=3 n=NUMBER R=set name 3=number of things in set ALWAYS PUT n BEFORE, The set name will be given and you will have to find out the number

Ø

Null or empty set

n (A)

Number of elements in set A

Composite numbers

Numbers that can be expressed as the product (multiply) of 3 or more natural numbers; 6 is composite because 6=1x2x3 A composite number can also be expressed as the product of 2 or more prime numbers. Eg=6x3; both 2 and 3 are prime, so 6 is composite. 2=2x2x3; 30=2x3x5; 5=1x5 5 is prime, but 1 is not, so 5 is not composite. Any number greater than one is either prime or composite . ANSWER: Composite numbers are Whole numbers with more than 2 factors. While prime numbers are numbers with the factors of only 1 and itself

Factors

Numbers that can be multiplied to get that number without leaving a remainder. Factors of 2=1,2, Factors of 12=1,2,3,4,6,12

Odd numbers

Numbers that leave a remainder of one when divided by two. I.e a number that is not a multiple of two. If a number ends with 1,3,5,7,9 it is an odd number. 3,5,13,17,39,231. No number can be both even and odd

A

P+I=Amount

Interest =

PRT/100 principal x rate x time divided by 100 $40 x 15% x 4 years. Interest is how much you'll get at a certain time

Interest

Paid or earned amount, what other people, companies get.

PEMDAS "Order of Operations"

Parenthesis ( ) Exponents x2 Multiply x Division ➗ Addition + Subtraction -

What is the formula for profit%? How to find profit%?

Porift% = Profit divided by CP x 100

When converting percentage to decimal

Put number at the end of number and put it to the left 2 times. so 50% would be 0.5. Think of it as since it's percentage you're just dividing it by 100. It's Not Scientific notation where you're trying to make the number short.

how to find cost of all items for profit

Selling price - cost price

trailing zeros are

Significant, they are the zeros after the nunber such as 7800 in 0.007800

John imported a motor vehicle for $1,253,790 and was priced at $1,631,250 for sale. After two months the price was reduced by 20%. Determine whether the new price selling price represents a profit or loss and calculate same.

Since reduce was mentioned we already know it'll be a loss, the loss is 377,460

Distributive property: States that multiplication is distributive our addition and subtraction. For distributive property you multiply the number outside of the bracket by the numbers inside the bracket and add the answers. So after multiplying the number outside of the bracket by the closest one in the bracket, you skip the addition sign and multiply the other number beside the addition sign to the number outside the bracket then add the answers...

So 5 (2+3) = 5x2 + 5x3 = 25 and 5(10+5+3+6) =120

When subtracting a smaller number from a bigger number such as 3-4

Subtract the bigger number by the smaller number and add a negative sign. So 3-4 = 4-3=1 =-1 So 3-4 = -1

SAMD

Subtraction Addition = Find LCM Multiplication=Cross multiply Division=Keep fraction, flip division to multiplication, flip last fraction

to convert a mixed fraction to a percentage

Such as 12 1/2, turn it into a fraction and devide by numerator so 12 1/2% is 12.5% since 25/2 divided gives 12.5

To find Time (invest) (how long it'll take to get the money) TIPR

T = 100T/PR. when letters and numbers are beside eachother it means to multiply them

How to find the cost of one item

Take away markup price by unit price

whenever there is a fraction without a denominator

The denominator is 1

How to read numbers

The first , stands for thousand. The second stands for million The third stands for billion The fourth stands for billion So in the number 81,315,930 it's read as eighty-one million, 315 thousand, 930 1st comma= thousand 2nd comma=million 3rd billion 4th trillion Note= There is a comma after every 3 digits. ​

reciprocal

The flipping of a fraction, so the reciprocal of 8/7 is 7/8

Interest isn't all of what you'll get back but just what you didn't have before, so if you invest 2500 hoping to get an interest of 2700.

The interest would be $200 not 2700 because 200 is what you didn't have before not the 2500. (ALWAYS PUT DOLLAR SIGN)

What is multiplicative Inverse?

The inverse of a number under multiplication combines with another number gives the result '1' EG: 2 x 1/2 = 2/2 = 1

Two Jars of the same type of jam contain different amounts of jam and cost different amounts of money. You can find which of these jars is the better value for money (best buy)

The larger jar holds 500g and costs $700 so 1g cost $700 ÷ 500 = $1.40 The smaller jar holds 300g and costs 450 so 1g cost $450 ÷ 300 = $1.50 smaller jar:1.50 per gram larger har:1.40 per gram Therefore buying the larger jar is a better value for your money. Just divide ._. depending on the result you'll see which one is more or less, by the unit price that is. (Or how much grams is 1 Jam???)

irrational numbers P

The number that cannot be written as a fraction. A number that cannot be written as the ratio of one over another. square root 143

Simple interest

The princia is unchanged over the period of the loan or investment. Interest is usually added regularly yearly

if a question asks to take something off by the discount, but percentage isn't stated, use

VAT, which is 15%. Which is the cost of good. You can use this for either tax or discount

What are variables?

Variables are the unknown or letters (letters because it's unknown what they're suppose to represent.) Such as x, and y. Think of it as there are too many variables that it could just be one, so we don't know.

How to convert from base 10 to binary

When converting a number from base to binary, you divide it by 2 and put the remainder to the side, after everything put 0 and r 1 at the bottom, then put number from up up down and put base 2. practice, what is 40 in base 10 in binary, the answer should be 101000 base 2. If it says convert to binary divide by 2, but it can say convert to bases of other numbers such as 30 base 10 to base 4, and you would do the same thing but instead would divide by 4 and put base 4 along your answer.

improper fraction

a fraction whose numerator is larger than the denominator

proper fraction

a fraction with a numerator smaller than the denominator

Mixed number

a number made up of a whole number and a fraction

mixed number

a number made up of a whole number and a fraction 4 ¾

Factor

a number that is multiplied by another number to find a product

sum

addition

note if you're asked to convert a number such as 50% or 3837% to a decimal

always place the decimal at the end of the number and move it two places to the left. so 50 would be 50. then 5.0 and .5 then 0.5. It is NOT like scientific notation where you put it after the first non zero digit. like in 2.5¹.

Face value can only be zero to nine

anything after that is a place value. 01234 are 5 digits,0 counts as a digit.

do not leave improper fraction as a mixed number

because an improper fraction can be turned into a mixed number

Divisible

can be divided by a number without leaving a remainder

A fraction means to

divide, if a fraction is 3/5 it means to divide 5 by 3, so 5 (denominator) would be outside the box and 3 (numerator)would be in the box and the answer would be. denominator bottom numerator inside box. numerator has too much an ego so it deserves to go in the box, denominator is shy so he is forced to be put outside to get confident.

you get the unit price by

dividing the number of all items by the cp

when dealing with money

do not round up, only round up for percentage unless it's a grade (teachers usually round up percentage grades though but don't do it in work)

the decimal of an irrational number

does not end, irrational number of 2 is 1.41215362... 1.41215362. is also the answer because it's the closest number/decimal that can be multiplied by itself to get the closest number to 2, or 1.4 x 1.4

when finding x of a fraction

find a number that is divisible. so in 5/5 = x/5 x would be 5 since you divide it to get 1/1. 1/5 = x/675 x is 45 because 45 x 15 is 675 and 45 x one gives back the number.

When doing a pemdas equation

for math, division, addition and subtraction. do which ever one comes first for that section. so MD if multiplication comes first do it, if division comes first do it then multiplication Same thing with addition and subtraction

When converting percentage to decimal, with numbers that end with 0

get rid of the 0, so 50% as a decimal isn't 0.50 but it's 0.5 (isn't it the opposite?)

anything added by zero

gives back the same number so one plus 0 is 1.

cost price

how much the items were originally for

the check mark for division, the square root ICANT

if it has 144 under. the answer would be 12. whatever number multiplied by itself gets gets number

∩

intersection (all numbers that are members of exclusively both sets in question)

∈

is an element of

if it's money and the answer is something like 67.5

it should be $67.50 if it's for money,if it's for anything else leave it as 67.5

110011 binary to base 10

know how to do, add and calculate properly. 51 and base 10 bottom right.

0.00 in the number 0.0050830 are

leading zeros

How to find loss%

loss divided by cost price x 100

how to find percentage loss

loss/CP x 100 = percentage loss. Round answer up if needed after decimal

to find the markup price of an item

multiply markup percentage x cost of all items

squared

multiply the number by itself 2 times

cube

multiply the number by itself 3 times

cubed

multiply thr number by itself 3 times. number is at the top right

Elements in each Eg Elements of vowels would be set out as Set V=

n (V)=5 number of vowels=5 V = Set name or vowels N=NUMBER 5=number of things in set ALWAYS PUT n BEFORE, The set name will be given and you will have to find out the number

leading zeros

never significant, they are the zeros before a number with no significant number behind them 0.00 in 0.007809

C| ... close enough... but the line goes through the C

not a subject

∉

not an element of

Rectangular numbers

numbers that can be represented by a rectangular array of dots or squares. No prime number is rectangular, because a line of dots is not a rectangle.

Triangular numbers

numbers that can be represented by a triangular array of dots or squares.

percentage

out of 100

R is the

percentage rate, RATE IS ALWAYS IN PERCENTAGE. Rate of interest paid or charged . 15%

+

positive

P

principal, the amount borrowed or invested. $40 borrowed or invested

how to find percentage profit

profit/CP x 100 = percentage profit. Round number up if needed after decimal

what is profit

proft is the selling price subtracted by the cost price. it is how much money was gained

for standard form large and small numbers

put decimal infront of first non zero digit. so in 0309 the decimal point would be 03.09

ALWAYS REMEMBER TO

put dollar signs or else you'll get it wrong and show working

to convert decimal percentages to fractions

put place value over numbers and the put place value of the number before the decimal point under the whole number without a decimal. so 777.5 is 7775/10, 7.555 would be 7555 over 1000 and 7.55 percent would be 755 over 100

When doing interest after

putting P R T also put how long in months it will take them to get the money, so transfer year to months.

what is rate?

rate is a ratio that compares quantities with different units.

product

result

In binary numbers, anything multiplied by 0 is 0

so 0 x 2⁰ is 0 but 0 x 2³⁴⁷ will still be 0 no matter what.

when dividing decimals such as 5.76 ÷ 0.3, move the decimal to the right until kts at the end of the number then move the decimal of the dividend to the right the amount of times you moved it the divisor's decimal point to the right and divide them

so 0.3 divided by 5.76 is 3 divided by 57.6

when taking away decimals ect always put bigger number on top

so 1.2-0.3 would be 1.2 over 0.3 and you would take away after

If you multiply 0 to any number the answer will be 0 NO MATTER WHAT, if there is an exception ask a teacher (THERE IS NO OTHER EXCEPTION)

so 1x0 = 0 1.2x0 = 0 No matter the number anything multiplied 0 gives you 0

Even if a number can't round off it must always have a full amount of decimals,anything before the decimal must always be there

so 300.62 to 2sig fig would not be 30 but would be 300. Unless the number starts with zero

When changing a percentage to a fraction, after putting the number over 100, you reduce if possible

so 75% as a fraction isn't 75/100 but 3/4 since 3/4 is the completely reduced version of 75/100

When multiplying decimals, after you multiply them

start from the end of the answer/right of the answer and move the decimal place to the right to the amount of numbers to the left of number. So 2.6x1.8, the answer will be 46.8, put the decimal place to the right so the number is 468. and move the decimal to the left to number of numbers to the right of the decimal place of the equation. So it would be 468.=4.68=4.68 for 2.6x1.8

C

subject

difference means to

subtract

when a price is in bracket it means to

subtract.

When subtracting numbers when you're taking awaking a number

such as in 111 if you're taking away 1 and moving it to another number, the other number becomes 11 so the middle one would become 11. But in addition it would just be 3, because you added another number to it

tax

tax is what's given to the government, it means to add an amount of money to a certain amount of money, it's the same as discount but instead of subtracting by the original price you add by the original price when doing percentage.

try 20 in base 10 to binary

the answer should be 10100 to base 2, don't say base 2 but put base 2 since I can't type it here.

what is 30 base 10 to base 4, try it

the answer should be 132 base 4

quotient

the answer to a division problem

markup

the markup is additional money was added to the unit price to make a profit

markup vs markup price

the markup price is made by adding the markup to the unit price. the markup is what is added to the unit price to get the markup price. Markup is ONLY added to unit price?

divisor

the number you divide by

T

the period of time of the loan or investment. 4 years, days, months

note in profit

the selling price is ALWAYS larger than the cost price because you're gaining money.

note in loss

the selling price is ALWAYS less than the cost price because you're losing money, similar to discount.

to find thr discount of an item

times the percentage over 100 by the original price and subtract the answer by the original price. So the 25% discount of $1200 is $900.

0 after 3 in 0.0050830, or any zero after a number are

trailing zeros

If you're asked to find a discount or percentage of a number using a mixed number such as 12 1/2

turn it into a proper fraction = 25/2, divide it to make it 12.5 m, and divide it by 2 using the quick method, which will give 6.25. Don't know how to do with calculator.

in 2006 2 as pv is pv place value

two thousands

U

union The union of two sets A and B is defined as the set of all the elements which lie in set A and set B or both the elements in A and B altogether. The union of the set is denoted by the symbol '∪'.

VAT

value added tax, adding 15% percentage to the original price. the vat is ALWAYS 15%. so when they say add vat it means add 15% to the price. The only time VAT isn't q5 percent is if they state what percentage the VAT ism

selling price

what price the item is being sold at

blast discount

what's being taken away from all the items added together

discount

what's taken away by the original price to get what you have to pay for. so in the 25 percent discount of $1200 , even though we pay $900 the discount is $300 since we have to take away that by the original price to get 300 and that's what we take off the original price to get what we have to pay for.

what is unit rate?

when a rate expresses a quantity per one unit of another quantity. It is called unit rate.

In addition and subtraction

when adding an additional number put to the left side of a number would be for example 3 and number 1 to the top would be 4. but if it's subtraction 3 to the 1 at the top right it would now be 13

What is associative property?

when adding or multiplying you can group numbers in any order. Example, (3+5) + 7 = 3 + (5+7)

proper fraction

when the numerator is less than the denominator

In binary we can only multiply by 2 to get a regular number

which is why we use 2. In 1010111 since there isnno decimal we put positive numbers over it to determine what exponent to multiply each number by, the last 1 has an exponent of 9 and the first 1 has an exponent of 6. We then multiply the number by 2 and the exponent above that number. so since the first number represents a 6 exponent, it would be 1x2⁶, we do this for every one and calculate them and add them after and put base 10 along the answer

Square number

x2

cubed number

x3

to divide two numbers example 3.6 ÷ 2.6

you need to multiply each number by a hundred and divide after. Or move decimal two places two places to the right so it would be 360÷260 or 36÷26