Brain Dumping!

Divisibility Rules A number is divisible by: 2 if the number ends in 2,4,6,8,0 3 if the sum of the digits is divisible by 3 4 if the last to digits of the number is divisible by 4 5 if the number ends in 0 or 5 6 if the number is divisible by 2 AND 3 9 if the sum of the digits is divisible by 9 10 if the number ends in 0

PRIME, COMPOSITE or Neither Prime numbers have exactly two factors 1 and itself 2 x 1 = 2 13 x 1 = 13 19 x 1 = 19 Composite numbers have many factors 1x6=6, 2x3=6 or 1x12=12, 2x6=12, 3x4=12 The number 1 is NEITHER prime nor composite! 1x1=1 it only has ONE factor!

8 3 Exponents 8 is the base & the number you multiply 3 is the exponent and tells you how many times to multiply the base (or how many time to write the big number) 8x8x8= 512

Decimal Rule for Adding and Subtracting LINE UP THE DECIMAL and ADD or SUBTRACT 3.34 7.990 +2.333 - 1. 23 5.673 6.760 Add a zero To fill in blanks Add a zero To fill in blanks

Multiply Decimals Rule Multiply and forget the decimal. After you get the answer count the number of digits after the decimal in the problem and that will BE the number of digits after the decimal in the problem 2.01 X 3.8 1608 +603 7.638 2 digits after the decimal 1 digit after the decimal Total of 3 digits after the decimal Count 3 digits and add the decimal point Count 3,2,1

Dividing Decimals Rule You CANNOT divide by a DECIMAL! MOVE the Decimal to the Right UNTIL the number you are dividing by is a WHOLE # THEN do the same thing to the other NUMBER & DIVIDE! .8 6.4 change to 8 64

COMPARE FRACTIONS! CROSS MULTIPLY 3/4 < > = 2/3 3 2 4 3 3x3 2x4 9 > 8 3/4 > 2/3 CROSS MULTIPLY Compare the numbers

Compare Similar Figures SET UP A Proportion Height of 1 = length of 1 Height of 2 = length of 2 Divide the top by the bottom and compare.

RATE Rate = $ divide top by bottom to get rate unit Units are – gallons, meters, miles, hours, minutes, inches, feet, yards, etc Rate + $60 = 20 gallons = $3 per gallon

Write and READ fraction as: ___ : ___ or ___to___ 2/3 2 : 3 or 2 to 3 RATIO Write and READ fraction as: ___ : ___ or ___to___ 2/3 2 : 3 or 2 to 3

A proportion is an equation that shows two equivalent ratios. 2 1 __ 4 = 4 2 __ 8 = 2 1 __ 6 3 = Reading Math 2 1 __ 4 2 __ Read the proportion = as “two is to one as four is to two.”

Additional Example 1: Modeling Proportions Write a proportion for the model. First write the ratio of hearts to stars. number of hearts number of stars 4 8 __ = Next separate the hearts and stars into two equal groups.

Metric conversion Rules King Henry Died Over Drinking Chocolate Milk Kilo Hecto Deka Origin Deci Centi Milli RIGHT The direction and how many times the frog has to jump is the direction and number of times You move the decimal point. Change 3.888 kilometers to decimeters 38880. decimeters Origin = 1 liter, 1 meter, 1 gram

60 seconds = 1 minute 60 minutes = 1 hour 24 hours = 1 day 7 days = 1 week About 4 weeks = 1 month 12 months = 1 year 365 days = 1 year

G PP cc cc PP cc cc PP PP cc cc cc cc

Percent = per 100… place the percent over 100 and simplify. 45% = 45/100 = 9/20 2 % = 2/100 = 1/50 2 ½ % = 2.50 % = .025 = 25/1000 = 1/40 (you must change to a decimal then to a fraction and then simplify)   Decimal to percent – is in the correct alphabetic order D to P so you move to the Right ---- move the decimal 2 places to the right… .35 = 35 % .08 = 8 % .8 = 80 % Percent to Decimal – is not in the correct alphabetic order P to D so you move to the Left ---- move the decimal 2 places to the left… 5 % = .05 30 % = .30 or .3 2.5 % = .025

Decimals to fractions – use place values and simplify .03 OR .03 3 put a 0 for each number and a 1 where the decimal is 100 100 Fractions to decimals – divide bottom number into top number ¾ .75 3.00 -2 8 20 You will have a terminating decimal – with no remainder, or a repeating decimal – use a repeating bar…. 6 SIMPLIFY ALL FRACTIONS EVERY TIME!!!!

Fractions to Memorize ¼ = .25 1/8 = .125 1/5 = .2 ¼ = .25 1/8 = .125 1/5 = .2 ½ = .5 3/8 = .375 2/5 = .4 ¾ = .7 5/8 = .625 3/5 = .6 1/6 = .6

SQUARED2 when a number is squared it is multiplied times itself Memorize these squared numbers: 22 = 4 82 = 64 142 = 196 32 = 9 92 = 81 152 = 225 42 = 16 102 = 100 52 = 25 112 = 121 62 = 36 122 = 144 72 = 49 132 = 169

Variable letter that stands for a number To solve for a variable DO THE OPPOSITE OPERATION TO BOTH SIDES multiply 2x = 12 divide is opposite 2x/2 = 12/2 X = 6

A translation is the movement of a figure along a straight line. Only the location of the figure changes with a translation.

A rotation is the movement of a figure around a point A rotation is the movement of a figure around a point. A point of rotation can be on or outside a figure. The location and position of a figure can change with a rotation.

When a figure flips over a line, creating a mirror image, it is called a reflection. The line the figure is flipped over is called line of reflection. The location and position of a figure change with a reflection.

Additional Example 1A: Identifying Transformations Tell whether each is a translation, rotation, or reflection. The figure is flipped over a line. It is a reflection.

30 days hath September, April, June and November. All the rest have 31 days except February which have 28 or 29 on leap year.

How do you know which months have 30 or 31 days. Look at your knuckles How do you know which months have 30 or 31 days? Look at your knuckles! The peaks are 31 days the valleys are 30….except for Feb! Aug 31 Oct 31 Dec 31 May 31 Ju l 31 Jan 31 Mar31 No Peak or valley Sept 30 Jun 30 Apr 30 Nov 30 Feb 28

Time and Date 60 seconds in a minute 60 minutes in an hour 24 hours in a day 7 days a week 52 weeks in a year 365 days in a year

Simplify all fraction answers as Fraction Rules + and – fractions 1-You must find a common denominator (LCM) 2-Next add or subtract the top number only 3-Simplify 3 1 + 3 = 3 x3= 9 4 x3= 12 1 x4= 4 +3 x4= +12 13 12 LCM factor both numbers- all the couples and the ugly people go to the party 3= 3,1 4= 2,2 LCM = 3X2X2 LCM = 12 (use 12 as the common denominator) Simplify all fraction answers as the last step! Simplify to 1 112

multiplying fractions Simplify all fraction answers as Fraction Rules multiplying fractions 1-multiply the top with the top number 2-multiply the bottom with the bottom number 3-Simplify !! HINT !! If the problem has mixed numbers change to an improper fraction then follow the rules for multiplying fractions! HINT! If the problem has mixed numbers change to an mixed number then multiply! 3 1 3 x 3 = 12 3 1 12 divide top and bottom by 3 = 4 Simplify all fraction answers as the last step!

Simplify all fraction answers as Fraction Rules dividing fractions 1-flip the 2nd fraction (reciprocal) 2-change the sign to multiplication 3-multiply the top with the top & bottom with bottom 4-Simplify !! HINT !! If the problem has mixed numbers change to an improper fraction then follow the rules for dividing fractions! 3 1 ÷ 3 = 3 3 9 2 1 X 1 = 4 = (simplify) 2 Simplify all fraction answers as the last step!