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6th Grade Math Chapter 1 Decimals Lesson 1-1 Understanding Whole Numbers Definition Facts/Characteristics A number written in digits and place value The place of the digit 5 in 254 is tens. The value of 5 is 50 Vocabulary Word Standard form 524 is standard form 1,286 is standard form Examples It is not the only way to write a number Non-Examples Definition Facts/Characteristics A sum that shows the place and value of each digit of a number The expanded form shows the value of each digit Vocabulary Word Expanded form 1,000 + 200 + 80 + 6 is the expanded form of 1286 Examples “1 thousand 2 hundred 86” is the short word form Non-Examples Definition Facts/Characteristics A number in standard form is separated into groups of three digits using commas. Each of these groups is called a period. Each period in a number written in standard form has between 1 and 3 digits Vocabulary Word Period A period in math is A Examples not a dot at the end of a sentence. Non-Examples Lesson 1-2 Reading and Writing Decimals Decimal Place Value Decimals in Expanded Form Recall the definition of expanded form Example: write 1.893 in expanded form 1 + 0.8 + 0.09 + 0.003 Decimals in Word Form Write 23.876 in word form 23.876 And eight hundred seventy six thousandths Twenty-three Lesson 1-3 Comparing and Ordering Decimals Ordering Decimals on a Number Line Compare and order 0.47, 0.34, 0.21, 0.58 Compare Decimals Using Place Value Use <,>, or = to compare 4.28 and 4.8 These digits are the same 4.28 4.80 write a zero at the end of the number so each number has the same number of decimal places Tenths digit is different, 2 < 8. 4.28 < 4.8 Compare digits starting with the highest place value Lesson 1-4 Estimating With Decimals Definition Facts/Characteristics Numbers that are easy to compute mentally Also called “friendly numbers” as mental calculations are easy Vocabulary Word 3.67 x 42.5 4 x 40 = 160 3.67 x 42.5 ≈ 160 Examples Compatible Numbers 10.93 + 3.25 11 + 3 10.93 + 3.25 ≈ 14 Non-Examples Definition Facts/Characteristics Add the “front-end Gives a higher estimate digits,” estimate the as involves the cents, less sum of the remaining likely to be short of money Vocabulary Word Front-End Estimation $3.98 6.49 then look 9.08 at the cents +3.47 adjust the estimate 21 21 + about $2 = $23 Examples $3.98 + $6.49 4 + 7 = 11 $3.98 + $6.49 ≈ $11.00 Non-Examples Lesson 1-5 Adding and Subtracting Decimals Commutative Property of Addition Changing the order of the addends does not change the sum. 5.78 + 9.3 = 9.3 + 5.78 Associative Property of Addition Changing the grouping of the addends does not change the sum (3.2 + 8) + 4 = 3.2 +( 8 + 4) Identity Property of Addition The sum of 0 and any number is that number 4.5 + 0 = 0 + 4.5 = 4.5 Finding Decimal Sums Line up the decimal points!!! Add: 3.842 2.450 write zeros so that all +1.300 decimals have the same 7.592 number of digits to the right of the decimal point Finding Decimal Differences Line up the decimal points!! 7 10 Subtract: 68.0 - 51.8 16.2 rename as 7 and 10 tenths Estimate answers first then check for reasonableness! Whole Numbers - Decimals Subtract: 60-23.68 Estimate an answer 59.109 10 Solve: 60.00 - 23.68 n 36.32 write a decimal point and two zeros rename as 59 and 10 tenths, then rename as 9 and10 hundredths Lesson 1-7 Multiplying Decimals Commutative Property of Multiplication Changing the order of the factors does not change the product. 5.78 x 9.3 = 9.3 x 5.78 Associative Property of Multiplication Changing the grouping of the factors does not change the product (3.2 x 8) x 4 = 3.2 x ( 8 x 4) Identity Property of Multiplication The product of 1 and any number is that number 4.5 x 1 = 1 x 4.5 = 4.5 Whole Number X Decimal 0.25 x 5 1.25 two decimal places 0 decimal places Add the number of decimal places in the factors to find the number of decimal places in the product. Decimal X Decimal 0.25 x .015 125 +025 .00375 two decimal places three decimal places move the decimal point five places to ………………………………………………..the left Add the number of decimal places in the factors to find the number of decimal places in the product. Lesson 1-8 Multiplying and Dividing Decimals by 10, 100, and 1,000 Multiplying by 10, 100 and 1,000 Move decimal point to the right as many places as there are zeros 3.5 x 10 = 35 3.5 x 100 = 350 3.5 x 1,000 = 3500 0.67 x 10 = 6.7 0.67 x 100 = 67 0.67 x 1,000=670 Pattern: think about direction decimal point moves and the number of spaces Dividing by 10, 100 and 1,000 Move decimal point to the left as many places as there are zeros 3500 ÷ 10 = 350 3500 ÷ 100 = 35 3500 ÷ 1,000 = 3.5 0.67 ÷ 10 = .067 0.67 ÷ 100 =.0067 0.67 ÷ 1,000=.000670 Pattern: think about direction decimal point moves and the number of spaces Lesson 1-9 Dividing Decimals Definition Facts/Characteristics A decimal that stops All terminating decimals or terminates, as in a can be written as a remainder of 0 fraction Vocabulary Word Terminating Decimals Examples Non-Examples Dividing by a Whole Number Divide as with whole numbers. Place the decimal point in the quotient above the decimal point in the dividend. Definition Repeats the same digit or group of digits Facts/Characteristics A bar, or line, is drawn over the digits that repeat Vocabulary Word Repeating Decimals Examples Non-Examples Dividing by a Whole Number Decimal ÷ Decimal Multiply both the dividend and the divisor by the same number, (multiple of 10), so the divisor becomes a whole number. Lesson 1-10 Order of Operations Using Order of Operations Please Excuse My Dear Aunt Sally Do all operations within parentheses first Multiply and divide in order from left to right Add and subtract in order from left to right