Memory Aid Example PDF

# Place Value | Million | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones | |---|---|---|---|---|---|---| | 5 | 4 | 3 | 2 | 1 | 9 | 8 | Five million, four hundred thirty-two thousand, one hundred ninety-eight 5x1000000+4x100000+3x10000+2x1000+1x100+9x10+8x1 ## Order of Ope...

# Place Value | Million | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones | |---|---|---|---|---|---|---| | 5 | 4 | 3 | 2 | 1 | 9 | 8 | Five million, four hundred thirty-two thousand, one hundred ninety-eight 5x1000000+4x100000+3x10000+2x1000+1x100+9x10+8x1 ## Order of Operation 1. Brackets () [ ] √ 2. Exponents & Square root ^ √ 3. Multiplication & Division x ÷ 4. Addition & Subtraction + - 42+3x2^3 Invisible brackets 4x(3+2) = 16 + 3 x 8 = 4 x 5 = 16+24 = 40 = 20+22 = 42 = 20 ## Multiples Multiply to get multiples 6, 6, 12, 18, 24, 30... ## LCM (List method) 1. Make list of multiples 2. Choose lowest multiples on both lists LCM of 5 and 9 5, 10, 15, 20, 25, 30, 35, 40, 45 9, 18, 27, 36, 45 LCM is 45 # Prime 2 factors, 1 and itself Examples: 7, 11, 17 # Composite More than 2 factors Example: 10, 1, 2, 5, 10 9, 1, 3, 9 # Prime Factorization 504 Expanded: 2x252 2x2x2x3x3x7 2x126 2x63 3^2 x 1 3^1 x 7 Exponential: 2^3x3^2x7 # Exponents Value or Exponential Expanded Standard 2^5 2x2x2x2x2 32 (-2)^5 -2x2x2x2x2 -32 2^4 (-2)^4 (-2)x(-2)x(-2)x(-2) 16 6^1 6 6 (3/2)^4 (3/2)x(3/2)x(3/2)x(3/2) 81 4^2 4x4 16 # Square Root "What number times itself gives me..." √49 = 7 because 7x7=49 # Factors Factors are numbers that fit. They divide into a number. Factors of 12 are 1, 2, 3, 4, 6, 12 # GCF (List method) 1. Make list of factors 2. Choose greatest factor on both lists GCF of 10 and 15 10 1, 2, 5, 10 15 1, 3, 5, 15 GCF is 5 # LCM and GCF ## Prime factorization/Venn diagram Example of 126 and 270 Make trees 126 9x14 3x3 2x7 126 2x3x3x7 270 10 x27 2x5 3x9 270 2x3x3x3x5 ## LCM and GCF Word Problems ### LCM: When multiple events will happen again at the same time in the future. Ex: Blue light flashes every 126 seconds. Green light flashes every 270 seconds. When will lights flash again at the same time? 1890 seconds. ### GCF: Greatest number of identical groups. Ex: There are 126 roses and 270 daisies. How many equal bouquets can be made? How many of each flower in each? 18 bouquets and 126-18= 7 ROSES 270-18=15 DAISIES # Key Words - **Add**. Warm - **Sum** up. - **More**. Increase. - **Ascend**. - **Total**. - **Product**. Multiply. - **Times**. - **Double (x2)** - **Triple (x3)** - **Squared**. Square root. - **Cubed**. # Difference - **Less**. Cold. - **Decrease**. - **Loss**. Drop, withdrawal - **Space between**. - **Quotient**. Divide. - **Group**. Separate. # Proper: Less than 1 N <D 5/6 _ 5 hops _== _ 6 parts _ 3/8 _ 3 hops _==_ 8 hops # Improper: 1 or more N >= to D 19/9 _ 19 hops _==_ 9 hops # Numerator = Number of shaded or hops # Denominator=Number of 1 # Converting Fractions ## Mixed to Improper 5 1/4 5x4+1= 21 5 = 21/5 ## Improper to Mixed 21/5 21+5= 4 r1 5 = 4 1/5 (how many times 5 fits into 21) # Fraction Operations ## Place Whole numbers over 1 (Ex. 3= 3/1) ## Convert mixed to improper (ex. 2 1/4= 9/4) ## Add and Subtract ### COMMON DENOMINATOR 1. Keep Denominator 2. Add or subtract numerator Ex. 2/4 + 3/4 = 5/4 Ex. 2/3 + 3/4 = 8/12 + 9/12 = 17/12 Ex. 25/12 - 7/12 = 18/12 ## Multiply ### NUMERATOR x NUMERATOR ### DENOMINATOR x DENOMINATOR Ex. 1/3 x 3/5 = 3/15 Ex. 4/5 x 3/8 = 12/40 ## Divide ### KEEP 1st fraction ### CHANGE ÷ to x ### FLIP 2nd fraction Ex. 3/4 ÷ 5/4 = 3/4 x 4/5 = 12/20 _Keep, change, flip_ = 12/20 = 3/5 Ex. 5/6 ÷12/25 = 5/ 6 x 25/12 = 125/72 # Fraction Word Problems (*Reduce* *Convert to mixed*) Jim installed 3 1/2 meters of fence, then he did 2 1/2 meters. How much in all? 3 1/2 + 2 1/2 = 7/2 + 5/2 = 12/2 = 6 meters Jim ate 2/7 of pizza, then how much pizza is left? 1- 2/7 = 7/7 - 2/7 = 5/7 1/4 Eaten = 3/4 pizza left Jim took 4/9 m of ribbon and cut it into 1/6 m pieces. How many pieces? 4/9 ÷1/6 = 4/9 x 6/1 = 24/9 =8/3 =2 2/3 = 2+2/3 = 8/3 = 48/3 = 16 pieces # Add Integers ## SAME SIGN - Keep sign - Add values Ex. -2+(-3)=-5 Ex. 2+3=5 ## DIFFERENT SIGNS - Keep sign of LARGER value - Subtract values Ex. 7+(-2)=5 Ex. -7+2=-5 # Subtract Integers 1. Keep 1 integer 2. Flip the ADD to SUBTRACT 3. Change the sign of 2nd number 4. Follow rules of adding Ex. -4-6 =-40+(-6) = -10 # Cartesian Plane (+,+) 1st Quadrant X (-,+) 2nd Quadrant X (#,-) 3rd Quadrant # Exponents (-2)^2 = 4 (-2)^3 = -2x(-2)x(-2) = -8 (-2)^4 = -2x(-2)x(-2)x(-2) = 16 2^2 = 2 x 2 = 4