Review: Number Systems

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Malcolm Todd
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1 Review: Number Systems Divisibility Prime/Composite Properties Factors/Multiples Prime Factorization GCF/LCM Decimals Coordinate Graphing Fractions Integers

2 A number is divisible by If the last digit is even (ends in a 0,,,6, or ) EX),97 If the sum of the digits is divisible by EX) If the last two digits form a number divisible by EX), If the last digit is a 0 or. EX) 0 6 If the number is divisible by and. (the sum of the digits is divisible by and it is even) EX) 9 If the sum of the digits is divisible by 9. EX) 7 0 If the last digit is 0. EX),900 Using the divisibility rules, determine whether the number is divisible by,,,, 6,, 9 or 0. Check each box that the given ),96 ),9 ) 7,,7,60 ),60 What is a COMPOSITE NUMBER??? A number divisible by more than two numbers. (more than factors!!!) EX) is composite because you can multiple x and x to equal. What is a PRIME NUMBER??? A number divisible by ONLY the number and itself (only factors!!) EX) is prime because the only thing you can multiply to equal is x Practice: Tell whether each number is prime or composite: ) 9 ) 6) 9) 7 7) 9 0) Page

3 Associative Property- Grouping changing the grouping of numbers does not change the sum/product. Commutative Property- Order- changing the order does not change the sum/product. Additive Identity Property- the identity element of addition is ZERO because any number ADDED to zero will always be itself. Multiplicative Identity Property- the identity element of multiplication is ONE because any number MULTIPLIED by one will always be itself. Additive Inverse Property- A number added to its inverse to ALWAYS equal zero. Multiplicative Inverse Property- A number multiplied by its inverse to ALWAYS equal ONE. Distributive Property - The distributive property is when you multiply a number times a sum Identify the property shown: ) B (C D) = (B C) D ) = 7. ) 6( + ) = 6() + 6() ) = ) + - = 0 6) x+y+z = z+x+y Match the examples on the left with the correct property on the right. a. () = (). Associative Property of Multiplication b. a (b c) = (a b) c. Commutative Property of Multiplication c. + ( + 6) = ( + ) + 6. Associative Property of Addition d = Commutative Property of Addition Simplify: A) ( + x) B) (x + y) + 7(x + y) C) (x + ) + (x + ) Exponents: The exponent tells us how many times we have to multiply the base by itself. For Example: means: x x x = Write each expression in exponential form g g g Find each value z 0 9. Page

Example: x x x or x Write the prime factorization of each number in exponential notation. Use the L Method.. 6. 7. 0.

4 Prime Factorization: Rewriting a number to show the product of all of its prime factors. L Method Example: 6 Don t Forget: When you have all of the prime numbers to rewrite the problem 9 Remember to put them in order from least to greatest. Example: x x x or x Write the prime factorization of each number in exponential notation. Use the L Method Factors and Multiples List all of the factors of each number.. : 6. 7: List the first multiples of each number. 7. :. : GCF Greatest Common Factor LCM Least Common Multiple Just the Left Make an L Example: Example: = = GCF = 60 = LCM Find the GCF AND LCM of each set of numbers-show YOUR WORK!! Use the L Method.. and 6.,, and 6. 6 and 0., 6, and Page

5 GCF/LCM WORD PROBLEMS. Shanika and Jarvis are making bead bracelets to sell in a booth at the fair. They have yellow beads, 0 blue beads, and 0 red beads. How many bracelets will they make if they want each bracelet to have the same number of beads? 6. Jason is filling grab bags for the school festival. Two hundred bags are lined up on a long table. He has already placed crackers and other food items in each bag and now has a limited amount of prizes to add to some of the bags. If he places prize A in every th bag, prize B in every th bag, and prize C in every th bag, which bag will have all three prizes? Name the quadrant that contains the point:. (, 7). (, ). (, 0). (7, ). The point where the x-axis and y-axis intersect is called the. Reflection: The flip of a figure over the x-axis or y-axis When reflecting across X-axis, X values stay same and Y values change signs When reflecting across Y-axis, Y values stay same and X values change signs. REMEMBER: What I say, stays the same. 6. Draw the image formed by reflecting WAG across the y-axis. Be sure to label the new image y W G A x W A G 7. Give the coordinates of point A, (-, ), after it is reflected over the y-axis. o A =. Give the coordinates of point X, (, ), after it is reflected over the x-axis. o X =

6 *Rounding Use the digit to the RIGHT If the digit is 0 to to the floor If the digit is or above give it a SHOVE Drop all of the digits after *To compare or order Line up decimals Write vertically Use phantom zeros Think Money$$$ Compare using <, >, = Example: Round 0.76 to the nearest hundredths =. Practice: Round. to the nearest tenths = Round.06 to the nearest hundredths = Round 7.09 to the nearest tenths = Round.7 to the nearest hundredths = Example: Order from least to greatest: 0., 0., greatest to least:.606,.06, *When adding and subtracting decimals: Write the problem vertically lining up the decimals Fill in with phantom zeros to hold place values Add or subtract normally Bring the decimal straight down in your answer EXAMPLE: Practice #: Practice #: Practice #: Practice #:.7-.6 =.6.7 = = 9.7 =. +.7 = Page

7 *When multiplying decimals: Write the problem vertically do NOT line up decimals After you multiply normally, start at the far right of your answer and count the total number of decimal places in each factor. The total number of decimal places is the number you move the decimal in the answer. EXAMPLE:.6 X. Practice #:. x. Practice #: 7 x.7.6 place x. places places *When dividing decimals by whole numbers: Place the decimal point straight up in your answer Divide normally Add zeros after the decimal point in the dividend and continue dividing EXAMPLE 0.6 Practice #.6 Practice # Check 0.0 x 0.6 *When dividing decimals by decimals: Remember whatever you do the outside you must do to the inside. Ex. If your divisor has two decimals, you must move the decimal two places to the right in the divisor and in the dividend. Place the decimal point straight up in your answer Divide normally Add zeros after the decimal point in the dividend and continue dividing 6. Check: x 9. move decimal one place value right. Practice #:.6. Practice #:.0. = Practice #: =

8 Simplify: to reduce a fraction, divide both the numerator and denominator by their GCF..).) 9 9.).).) 0 60 Equivalent: two fractions that represent the same amount. (multiply or divide BOTH numerator and denominator by the same number)??? 0.) =.) =.) =.) =.) = 0 9?? Compare/Order: )convert to decimals ) find LCM and rename fractions using LCM ) cross multiply.) 9.) 9.).) Put the following in order from least to greatest. (USE ORIGINAL FRACTIONS IN ANSWERS)..) 7,,, 6 0.) 6,,, 0 0 Put the following in order from greatest to least. (USE ORIGINAL FRACTIONS IN ANSWERS)..), 0 0, 0,.) 7, 6, 6, 9 Page 7

9 Writing Mixed Numbers as Improper Fractions ) Multiply the denominator of the fraction by the whole number. ) Then add the numerator to that product. ) The result of the sum is the numerator of the improper fraction. ) The denominator remains the same. 7.).).).) 7 Writing Improper Fractions as Mixed Numbers ) Divide the numerator by the denominator. ) The quotient becomes the whole number. ) The remainder is the numerator ) The denominator remains the same..).).).) 9 6 The reciprocal is used when dividing fractions. To find the reciprocal of a number, simply FLIP or SWITCH the numerator and the denominator. To write the reciprocal of a mixed number, you must first turn the mixed number into an improper fraction. EX: The reciprocal of Find the reciprocal: ) is ) 9 ) ) 7 ) 0

10 Example:. Find the LCM of the denominators. Write an equivalent fraction for each. Add or subtract the fractions. Add or subtract the whole numbers. Simplify your answer * Remember you may have to borrow from the whole number when subtracting fractions ½ Step : LCM of and is! + ¾ Step : = Step : + = 7 Step : 7 = Example: 6-9 Step : LCM of 6 and 9 is! Step : = 6 Step : 9 - Step : ) 0 - =.) 6 + =.) - = To multiply fractions: To divide fractions: (stay, switch, flip). Cross reduce if possible. Keep the first fraction. Multiply numerators. the second fraction (the reciprocal). Multiply denominators. Change to. Simplify. Multiply numerators, multiply denominators. Simplify Example: = Step : Change to Step : Example: = Step and : 9 9 Step : x 9 Step : = 0 Step : = Step : 0 = 6 Step : x Step : = x = x =.) 9 6 =.) 0 7 =.) 9 Page 9

11 Integers: All positive AND negative WHOLE numbers including zeros. Numbers greater than zero are positive numbers. Numbers less than zero are negative numbers. On a number line o the farther a number is to the right, the greater that number is o the farther the number is to the left, the smaller the number is. Examples: - < 7 - < - 0 > -6 Positive: Negative: Zero: Gain, above sea level, up, rise, increase, deposit, Loss, below sea level, down, decrease, withdrawal, Sea level, origin Absolute Value: the distance a number is from zero on a number line - = Opposites: two numbers that are the same distance from 0, but are in opposite directions -9 and 9 Write as an integer: ) Loss of 7 yards ) deposit 9 dollars ) ft below sea level Write the opposite: ) -70 ) 0 6) 0 Find the absolute value: 7) - ) 6 9) - 0 Is it an integer?: 0) ) / ) -6. Write in descending order: ) -, -0, 0,,, -, - Write in ascending order: ) -0., -0.7, -0., 0., -0. Word Problem: ) Friends decided to go golfing. Kevin had a score of -. Logan had a score of +. Alex had a score of -. Which golfer had the best score? Worst score?

12 . Simplify the expression: 6 A)6 B) C)6 D)6 7. What is the prime factorization of 0? A) B) C) D). What is another way of expressing? A) B) C)6 D)6. Which of these is a prime number? A)69 B) C)7 D)7. Sal handed out flyers that gave students the time and place of tryouts for the school soccer team. What is written in exponential notation? A) B) C) D). Karen has a softball game every days and a soccer game every days. If she has both a softball and soccer game on the same day, how many days will it be before she plays in both games again? A)0 B)7 C) D) 9. Tim works in a shipping department of a toy store. Every 6 weeks he receives a shipment of games. Every 9 weeks he receives a shipment of bicycles. If time received both a shipment of both the games and bicycles today, when is the next time both will arrive on the same day? A) weeks B) weeks C) weeks D)7 weeks 0. Find the GCF of and? A) B) C) D). Find the LCM of, 6 and? A)0 B) C) D)60 6. A nursery in Raleigh has beech trees, pine trees, and 0 maple trees. The manager of the nursery wants each group of trees to have the same number of trees in each row. What is the greatest number of trees that each group can have in a row? A)6 B) C)9 D). What is the prime factorization of? A) x 6 x 7 B) x x 7 C) x x 7 D) x x 7. Which pair of numbers are both factors of? A) and 7 B) and C) and D) 6 and

13 . Karen, Diane and Marilyn were having lunch together. They all ordered the same sandwich. Karen ate ½ of hers, Diane ate / of hers, and Marilyn ate / of hers. Who ate the most of their sandwich? A)Karen C)Marilyn B)Diane D)Susan. Adam weighs 96 pounds. His father weighs times as he does. How much does Adam s father weigh? A) lbs. B)6 lbs. C)77 lbs. D) lbs.. What is the least common denominator for the following fractions? / and 7/ A)6 B) C) D) 6. Suzanne needs material for a school project. She buys. yards at $.7 a yard. What is the total cost of material? A)$. C)$. 7. Find A)7. C).7 B)$.7 D)$. B)7.6 D)6.. Franklin bought pencils for $0.79 each, notebooks for $.9 each, and comic book for $.9. How much change will he receive from $0? A)$.6 C)$.97 B)$6.0 D)$ A) B)60 C)0.6 D)0 0. One of the performers at the circus is Zack, the human cannonball. On Saturday he does three shows. His distances measure 9. meters,. meters, and 6. meters. What is the total distance Zack flies that day? A)0.6 m B). m C)0.9 m D). m. Steak costs $.90 a pound at the market. Mary buys. pounds. Find the cost. A)$7.0 B)$6. C)$. D)$.7. Graham has $6.69 in his checking account. He takes out $.. How much money does he have left? A)$. B)$. C)$7.0 D)$9.07. An English teacher bought copies of the same book for her students. She spent $99.6. How much did each book cost? A)$6. B) $6. C) $.9 D) $.97. Round 0.7 to the nearest tenth? A) 0.7 B) 0.7 C) 0.79 D) 0.. Evaluate A) 0.0 B). C). D) 0.

14 6. Charles ordered pizzas for a party. At the end of the party, / of one pizza was left over, and /6 of the other pizza was left over. How much pizza was eaten at the party? A) B) An average sized person can burn about calories a minute while jogging. Which of the following is equivalent to that amount? 9 A) calories B) calories 6 C) D) C) calories D) calories 7. Christina is cutting wood in order to build the roof of a new house. The piece of wood she is cutting is ¼ feet long. If Christina cuts / feet from it, how long is the remaining piece of wood? A) ft B) ft 7 C) 0 ft D) 0 ft 0. Each week Kelly spends / of her allowance on CD s, /6 of her allowance on clothes, and saves / of her allowance. What does Kelly do with the smallest part of her allowance? A)buys CD s B)buys clothes C)saves D)goes to the movies. In a track-and-field meet, a triple jumper is given attempts to jump as far as possible. Willie s attempts are listed in the table. Attempt # Which statement is true? Length (yd) A) His st attempt was his longest jump B) His rd attempt was his shortest jump C) His jump length increased with each attempt D) His jump length decreased each attempt. Which statement is true? A) B) C) D). What fraction of the triangles is shaded? A)9/ B)/ C)9/0 D)/0. What is ¾ of ¾? A) B)/ C)9/6 D) Page

HOW TO DIVIDE: MCC6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE

HOW TO DIVIDE: MCC6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE MCC6.NS. Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE Dividend A number that is divided by another number. Divisor A number by which another number