Foundations of Math I
Order of Operations (PEMDAS)
PEMDAS 1. 18/9x4= 2x4= 8 2. 5x4( exponent 2)= 5x16= 80
Place Value Chart & Comparing
Place Values- Hundreds:Tens:Ones(.)Tenths:Hundredths: Thousandths:Ten-Thousandths Comparing Fractions- 1. 7 Tenths= 0.7= 7/10 2. Nineteen thousandths= 0.019= 19/1000
Prime Factorization (T) Diagram *Choose factors on left side of the (T) chart
Prime factorization of 60: *Create "T"' diagram * 2x30 * 2x15 * 3x5 * 5x1 = 2 x 2 x 3 x 5 is the prime factorization of 60.
Fractions with Exponents
2/3 to the 4th power(exponent) =2/3*2/3*2/3*2/3= 2x2x2x2=16 = 3x3x3x3= 81 Answer: 16/81
Writing Whole Numbers in Expanded Form
26,429 is "20,000+6,000+400+20+9" is written in expanded form
Standard Form
35,789 is "thirthy-five thousand seven-hundred eight-nine" written in standard form
Commutative Property of Addition
4+8=12 8+4=12
Find LCM of 450 and 600. *Use the (T) diagram to figure out its multiples
450 Multiples: *2x225, 3x75, 3x25, 5x5, 5x1 600 Multiples: *2x300, 2x150, 2x75, 3x25, 5x5, 5x1 (T) Diagrams: 450: 2*(3*3)*(5*5) 600: (2*2*2)*3*5 = pick biggest equation in each column above = LCM: 2*2*2*3*3*5*5= 1800 Answer: 1800
Associative Prpoperty of Addition
(3+2)+4= 3+(2+4) 5+4=9 3+6=9
Multiplication of Decimals
* 53.46 -------> 2 #'s behind the decimal point X. 4 So move decimal twice to the ----------- left 213.84 * 3.892 x 10= 38.92 =Answer: 38.92 Reason: the tenths is one place to the right of the decimal. So move the decimal to the right once. * 3.892 x 10,000 ---------> four places over = 38920 -----> add zero
Multiply 3 3/8 x 4. (No LCM needed)
* Change 3 3/8 into an improper fraction = 27/8 x 4/1= (3*3*3)*2*2 (2*)2*2 *Cross out all matching numbers above = 3*3*3/ 2= 27/2 *27 divided by 2 = 13 1/2
Division of Fractions and Mixed Numbers (No LCM needed)
*The reciprocal of 2/3 is 3/2. 1. Divide 2/3 by 3/4= 2/3 by 4/3(reciprocal) *2/3 x 4/3= 8/9
Adding or Subratcing Mixed Numbers
*Turn mixed numbers into improper fractions first *Find the LCM for denominator *If results as an improper fraction, turn it into a mixed number
Divide 0.1344 by 0.032
- Make .032 a whole number by moving three to the right -Move 3 spaces over on the number .1344 - Divide 134.4 by 32 doing long division - Answer: 4.2
<, > or = to
0.02: 0.0135: 200/100 (>) 135/10,000 *look at its place value
Multiply Decimals
1. 0.3 x 5 - the 3 in the decimal is in the Tenths place *3/10 x 5/1= 15/10 * 10 divided by 15 turns fraction into decimal *Answer: 1.5 2. 0.3 x 0.05 * 3/10 x 5/100= 15/1,000 (always multiply denominator) *15/1,000= 0.015
Simplify.
1. 14/15-(1/2)exponent 2 X (2/3+4/5):10/15+12/15= 22/15 =14/15-(1/2)exponent 2 X 22/15 =exponent: 1/2 x 1/2= 1/4 =14/15 - 1/4 x 22/15 = 1/4 x 22/15= 22/60= 11/30 =14/15 - 11/30= 28/30 - 11/30 Answer: 17/30
Multiplication of Fractions (No LCM needed)
1. 2/3 x 4/5= 8/15 (multiply across) 2. 4/15 x 5/28 (find multiples of the numbers and list them for both numerators and denominators) 1.Numerators 4 & 5: 2*2*5 2. Denominators 15 & 28: (3)*5*2*2*(7) **Cross out all numbers that match each other** = 3*7= 21 Answer: 1/21
Division of Decimals
1. 3.25 divided by 15.275 * make 3.25 a whole # by moving to the right two spaces. *move the decimal on 15.275 over two places to the right so it is now, 1527.5 * Perform long division and carry decimal up *Answer: 4.7
Adding Whole numbers, mixed numbers and fractions
1. 5+ 3/8= 5/1+3/8 *Find LCM* = 40/8+ 3/8= 43/8: Make improper = 8/43= 5r3= 5 3/8 Answer: 5 3/8
Order Relations between 11/18 and 5/8.
1. The LCD is 72 2. 11/18= 44/72 3. 5/8= 45/72 Answer: 5/8 is bigger
Additions and Substraction of Decimals
Add 0.237+4.9+27.32 * 27.320 + 4.900 .237 ---------------------- 32.457 *Subtract the same way
Finding Factors
Factors of 42: 1x42, 2x21, 3x14, 6x7 = 1,2,3,6,7,21,42,14
Greatest Common Factor (GCF) * The largest factor
Find the GCF of 126 and 180. *Create (T) diagram for both numbers below (T) Diagram: 126: 2x63, 3x21, 3x7, 7x1 180: 2x90, 2x45, 3x15, 3x5, 5x1 ** Line up multiples in chart** 126: 2*3*3*7 (Don't use #s that are not similar) 180: 2*2*3*3*5 (pick the smallest equations) = GCF: 2*3*3= 18 Answer: 18
LCM (Least Common Multiple)
Multiples of 4: *4,8,(12),16,20,(24),28,32,(36) Multiples of 6: *6,(12),18,(24),30,(36) = LCM is 12
Adding Fractions with and without the same denominator
Same Denominator: * 2/7 + 3/7= 5/7 Different Denominator: *Find LCM first * 7/12 + 3/8= 14/24 + 9/24= 23/24 : 12x2=24 so you take 7x2 to get 14 : 8x3=24 so you take 3x3 to get 9
Subtraction of Fractions with and without the same denominators
Same Denominator: *11/18-7/18= 4/18= simplified to 2/9 Answer: 2/9 Different Denominator: *Find LCM * Do the same steps you would for adding fractions except you subtract at the end.
Decimals
Standard and Written Form: *Four and twenty-three hundredths= 4.23 Word Form: *0.9684: nine thousand six hundred eighty-!four ten-thousandths (Decimals mean "and" in word form) *Ninety-one and eight thousandths = 91.008 (Insert two zeros so that the eight is in the thousandths place)
Write improper fraction as a mixed number & Turning mixed numbers into improper
Write 13/5 as a mixed number. * divide numerator by denominator * 5 goes into 13; 2 times and 13 minus 10 equals 3 * So 13/5= 2 3/5 Write 2 3/5 into an improper fraction. * 2 3/5= 5*2= 10+3= 13/5
