Arithmetic and Fractions 1 Properties of Real Number

Arithmetic and Fractions

1. Properties of Real Number Symmetric Property )สมบตการสมมาตร Reflexive Property )สมบตการสะท อน( a = a Addition Property of Equality Properties of Equality ( Transitive Property )สมบตการถายทอด If a = b, then a + c = b + c If a = b, then b = a Multiplication Property of Equality )สมบตการบวกดวยจำนวนท เทากน ( ( If a = b and b = c, then a = c การคณดวย จำนวนท เทากน (

Division Property of Equality Subtraction Property of Equality )สมบต การลบดวย จำนวนท เทากน ( If a = b, then a - c = b - c Properties of Equality การหารดวย จำนวนท เทากน ( Substitution Property )สมบต การแทนท ( If a = b, then a may be substituted for b, or conversely

Closure Property of Multiplication Closure Property of Addition )สมบตปดการบวก )สมบตปด ( การคณ ( ab is a real number a + b is a real number Commutative Property of Addition )สมบตการสลบทการบ ( a + b = b + a วก Commutative Property of Multiplication )สมบตการสลบท การคณ a • b = b • a (

Associative Property of Addition )สมบต การเปลยนหม การบวก( Associative Property of Multiplication )สมบตการเปลยนหม การคณ ( a + (b + c) = (a + b) + c a(bc) = (ab)c Identity Property Additive Identity Property )สมบตการมเอกลกษณ การบวก( a + 0 = a = 0 + a Multiplicative Identity Property )สมบตการมเอกลกษณ การคณ ( a • 1 = a = 1 • a

Multiplication Property of Zero Division Property of Zero (สมบตการคณดว ยศนย ) 0 • a = 0 (สมบต Properties of Zero Division by Zero Is Undefined การหารดวย ศ นย )

Placement of Negative Signs Multiplication by -1 )การคณดวย (-1)a = -a (-1)(-a) = a -1( )ตำแหนงของเครองหม ายลบ( (-ab) = (-a)(b) = (a)(-b) Properties of Negation Product of Two Opposite (-a)(-b) = ab

2. Positive and Negative Number Vocabulary Integer Positive Integer Negative Integer Zero Number line จำนวนเต ม จำนวนเตม บวก จำนวนเตม ลบ ศน ย เสนจำน วน

Vocabulary Absolute Value คาสมบ รณ Opposite Number จำนวนตรงข าม Odd Number จำนวน ค Even Number จำนวน ค

3. Mental Math, Addition, and Subtraction Vocabulary Counting Estimation Strategy Double Minuend การน บ การประมาณค า กลยท ธ สองเท า ตวต ง

4. Order of Operations Vocabulary Bracket Exponent Rule Calculation วงเล บ เลขยกกำล ง กฎ การคำนว ณ Multiplication การค ณ Division การหาร Addition การบวก Subtraction การลบ

Example: Evaluate 3 + 6 x (5 + 4) ÷ 3 - 7 using the order of operations. Solution: Step 1: 3 + 6 x (5 + 4) ÷ 3 - 7 = 3 + 6 x 9 ÷ 3 – 7 Parentheses Step 2: 3 + 6 x 9 ÷ 3 - 7 = 3 + 54 ÷ 3 - 7 Multiplication Step 3: 3 + 54 ÷ 3 - 7 = 3 + 18 - 7 Division Step 4: 3 + 18 - 7 = 21 - 7 Addition Step 5: 21 - 7 = 14 Subtraction

PEMDAS! P = Parentheses first E = Exponents (Powers and Square Roots, etc. ) MD = Multiplication and Division (left-to-right) AS = Addition and Subtraction (left-to-right) BODMAS B Brackets first O Orders (Powers and Square Roots, etc. ) DM Division and Multiplication (left-to-right) AS Addition and Subtraction (left-to-right)

Note: in the UK they say BODMAS (Brackets, Orders, Divide, Multiply, Add, Subtract) and in Canada they say BEDMAS (Brackets, Exponents, Divide, Multiply, Add, Subtract). It all means the same thing! It doesn't matter how you remember it, just so long as you get it right. You can remember by saying Please Excuse My Dear Aunt Sally Pudgy Elves May Demand A Snack Popcorn Every Monday Donuts Always Sunday Please Eat Mom's Delicious Apple Strudels People Everywhere Made Decisions about Sums

5. Intro to Decimals Vocabulary Decimal Number Decimal point Place Value Position, place เลขทศนย ม จดทศน ยม คาประจำ หลก ตำแหน ง Decimal digits Tenths Hundredths Thousandths หลกทศน ยม หลกสวน สบ หลกสวน รอย หลกสวน พน

Here is the number "forty-five and six-tenths" written as a decimal number: The decimal point goes between Ones and Tenths. 45. 6 has 4 Tens, 5 Ones and 6 Tenths, like this:

Place Value It is all about Place Value ! When we write numbers, the position (or "place") of each digit is important. In the number 327: the "7" is in the Ones position, meaning 7 ones (which is 7), the "2" is in the Tens position meaning 2 tens (which is twenty), and the "3" is in the Hundreds position, meaning 3 hundreds. "Three Hundred Twenty Seven"

And that is a Decimal Number! We can continue with smaller and smaller values, from tenths, to hundredths, and so on, like in this example:

6. Rounding Vocabulary Rounding up Rounding down Nearest Increase การปด เศษข น การปดเศษล ง ใกลท สด เพมข น

How to Round Numbers • Decide which is the last digit to keep • Leave it the same if the next digit is less than 5 (this is called rounding down) • But increase it by 1 if the next digit is 5 or more (this is called rounding up) Example: Round 74 to the nearest 10 • We want to keep the "7" (it is in the 10 s position) • The next digit is "4" which is less than 5, so no change is needed to "7" Answer: 70 (74 gets "rounded down")

Example: Round 86 to the nearest 10 • We want to keep the "8" • The next digit is "6" which is 5 or more, so increase the "8" by 1 to "9" Answer: 90 (86 gets "rounded up")

7. Intro to Fractions Vocabulary Numerator ตวเศษ Simplification of ทำใหเปนเศ ษสวนอยางต a fraction Denominator ตวสวน Improper Fraction Quotient ผลหาร Common Fraction เศษสวนสาม ญ ำ ตวเศษเก น เศษสวน Equivalent fractions ทเทา Elements of a fraction กน องคประกอบของเศษสวน

Example one-half one-third

8. Conversation : Fractions and Decimals Vocabulary Denominator (ตวหาร ( Convent (การแปลงผน ( Division (การหาร(

9. Fraction Properties Vocabulary Commutative Property for Fraction Addition and Multiplication Associative Property for Fraction Addition and Multiplication

Identity Property for Fraction Addition and Multiplication Inverse Property for Fraction Multiplication Distributive Property of Multiplication over Addition for Fraction or Subtraction

Closure Property for Fraction Addition Closure Property for Fraction Multiplication Additive Property of Equality Multiplicative Property of Equality

10. Comparing Fractions Cross Multiplying Negative Fraction Vocabulary Same denominator least Common Multiple(LCM) multiply top and bottom Positive Fraction

When two fractions have the same denominator they are easy to compare:

But when the denominators are not the same we need to make them the same (using Equivalent Fractions).

11. Operations with Fractions Vocabulary Reciprocal Multiplying a fraction Subtracting and Adding Fractions Common Denominator

To add (or subtract) two fractions: 1) Find the least common denominator. 2) Write both original fractions as equivalent fractions with the least common denominator. 3) Add (or subtract) the numerators. 4) Write the result with the denominator.

12. Mixed Numerals and Improper Fractions Vocabulary Rational Number Proper Fraction Mixed numerals Improper Fractions Convert

Mixed numerals are numbers which have both a whole number part and a fractional part. Improper fractions have numerators (the top number) as large as, or larger than, their denominators (the bottom numbers).

Mixed numerals to improper fractions Improper fractions can be created from mixed numerals.

13. Operations with Properties Vocabulary Proportion Equations Equality Ratio