Squares and Square roots
|
|
- Todd Taylor
- 6 years ago
- Views:
Transcription
1 Squares and Square roots Introduction of Squares and Square Roots: LECTURE - 1 If a number is multiplied by itsely, then the product is said to be the square of that number. i.e., If m and n are two natural numbers such that n m, then n is said to be the square of m. The square root of a number is that number which when multiplied to itsely gives the original number as the product. Let the square root of b is denoted by i.e., b a and b a Square Numbers: b A natural number is called a square or a square number if it is the square of any number. i.e., for a rational number m, if n m, then n is a square or square number e.g. 4, 16, 5, 81 etc. are square numbers. when a number is expressed as the product of its prime factors, then the expressed number is a square if its prime factors contain even powers only Note: No prime number can be a square number. Ex is a square number since its prime factors contain even powers only. it means 144 is a square of 1. Ex: 3 5 odd power even power is not a square number since one of its prime factor i.e. has odd power. Ex. 1: Determine whether 736 is a square number or not. Sol. Let us express 736 as a product of prime factors even powers Hence 736 is a square number. Properties of a square number: (i) Every square number ends with either, 1, 4, 5, 6, or 9. (ii) The number of zeroes at the end of a square of a number ending with zero, is always even Note: 49 is the only square number in which both the digits are square numbers. (iii) A square number can never end with the digits, 3, 7, or 8 ex not a square not a square
2 (iv) The square of an even number is even and that of an odd number is odd. Ex (v) The square of a proper fraction is smaller than the fraction Ex and < 3 (vi) For every natural number n, the sum of the first n odd natural numbers is n. Ex (6) sum of the first 6 odd numbers. (vii) Pythagorean Triplet: There positive numbers, m, n and p are siad to form a Pythagorean triplet, if m + n p, where p is the largest number. Ex. (3, 4, 5) is a Pythagorean triplet Since (5) Note: For every natural number p > 1, we have (p) + (p 1) (p + 1) So (p, p 1, p + 1) forms a Pythagorean triplet. (viii)square of a number can never be negative i.e., it is always positive or zero. In other words, square of a negative as well as a positive number is always a positive number. Ex. ( 4) 16 (4) 16 (ix) If a number has 1, 5, 6 and in its unit place, then its square would also have 1, 5, 6 and in its unit place. Ex (x) There are n non-square numbers between the squares of the numbers n and (n + 1) Ex Here n 3, n + 1 4m b 6 between 9 and 16, we have 6 non square numbers (xi) The sum of square of first n natural numbers is 1 6 n(n + 1) (n + 1). Note: The square of any integer other than 1, and 1 is either a multiple of 4 or exceeds a multiple of 4 by 1. Squaring a number of the form 45 (where x is tens digit and 5 is units digit). (x5) (1x + 5) (1x + 5) (1x + 5) 1 x + 5x + 5x + 5 1x + 1x + 5 x(x + 1) Ex. (45) 4 (4 + 1)
3 Square of a 3 digit number of the form 5 ab. If a number is of the form 5ab, where 5 is hundreds digit and a and b are its tens and units digit respectively, then (5 ab) (5 + ab) 1 + (ab) Ex. (51) (5 + 1) 1 + (1) Square a number of the form 5a (where a is unit and 5 is tens digit). (5a) (5 + a) 1 + a Ex. (57) (5 + 7) 1 + (7)
4 Squares and Square roots LECTURE - Square Roots: The square root of a number a is that number which when multiplied by itsely gives a as the result. i.e. a a a Note: The numbers whose square roots are whole numbers are called perfect squares. ex. 4, 9, 5, 81 etc. Square of a prime number is never a prime Square root of a negative number is not defined in the set of a real number. Methods of determining square roots: (i) By Repeated subtraction: Every square number can be expressed as the sum of successive odd numbers starting from 1. If a number is a perfect square and we subtract successive odd numbers from it, until we get zero as the final result. The number of stepin which we get zero is the square root of the number. Ex 1: Determine the square root of 169 by the method of repeated subtraction. Sol we get in 13 th step so (ii) By prime factorization: (a) Express the given number as a product of prime factors. (b) Make pairs of similar factors (c) The product of prime factors, after taking one factor out of every pair will give the square root of the number. Ex. Determine square root of 964. Sol
5 (iii) By long division: (a) Group the digits in pairs, starting with the digit in unit place. Each pair or remaining digit is called a period. (b) Take the largest number whose square is equal to or just less than the first period. Take this number as the divisor and also as the quotient. (c) Subtract the product of the divisor and quotient from the first period and bring down the next period to the right of the remainder. This becomes new dividend. (d) The new divisor is obtained by taking two times the quotient and enter it with a suitable digit which is also taken as the next digit of the quotient, taken in such a way that the product of the new divisor and this digit is just less than or equal to the new dividend. (e) Repeat these steps till all the periods have been taken up. Ex. Find square root of Sol Find square roots of (i) 169, (ii) 196, (iii) 964 Square roots of dicimal number: (a) Group the digit in pairs/periods from right to left in integral part and from left to right in the decimal part. (b) Put the decimal point in quotient when integral part is over and first group of the decimal is brought down. Ex. Find square root of Sol. Square root of fraction: If a and b are positive numbers, then square root of ab ab a b a square root of b a a b b Ex. Ecaluate Sol
6 Squares and Square roots LECTURE - 3 Estimating a Square Root: In estimating a square root, we determine the two squares between which the given number lies. Ex. Estimate the square root of 15 Sol. Let us check squares of some numbers (1) 1, () 4, (3) 9 (4) lies between 9 and 16 (35) 15 So, 15 lies between (35) and (4) (36) 196 (37) 1369 (38) 1444 (39) lies between these two numbers i.e < 15 < 151 (38) < 15 < (39) 15 is nearest to (Approx.) Some problems based on finding the perfect squares (1) To find the smallest number by which given number is to be multiplied to make it a perfect square. (a) Factories the given number and form pairs of like prime factors. (b) Prime factors that are left unpaired are to be multiplied to given number to make it perfect square. Ex. Find the smallest number by which 7 must be multiplied to make it a perfect square. Sol () (3) (5) odd power to make it a perfect square, make all powers of prime factors as even Hence, 7 must be multiplied by 3 5 i.e., 3 to make it a perfect square. () To find the smallest number by which given number is to be divide to make it a perfect square. Ex. Find the smallest number by which 648 must be divided to make it a perfect square. Sol odd power even power
7 Hence 648 must be divided by () 1 i.e. to make it a perfect square. (3) To find smallest number to be added to the given number to make it a perfect square. (i) Find square of the given number by long division method. (ii) Square the successor of the quotient obtained. (iii) Subtract the given number from the obtained square. The result obtained after subtraction is the required number. Ex. Find the smallest number that should be added to 4571 to make it a perfect square. Sol. (i) By long division method: Square of successor of quotient () 484 Required number (ii) By estimation method: Given number is a 5 digit number, it could be square of 3-digit number. () 4, (3) 9 (1) 441, () 484 Q 4571 lies between 441 and 484. Hence required number (4) To find the smallest number to be subtracted from the given number to make it a perfect square. Ex. Find the smallest number to be subtracted from 5798 to make it a perfect square. Sol. (i) BY long division: Hence Remainder i.e. 38 should be subtracted from 5798 to make it a perfect square. required number (4) (ii) By Estimation method: Pick up the perfect square which is less than the given number Subtract the choosen perfect square from given number The difference obtained is the required number. (5) To find the the smallest number added/subtracted to make it a perfect square: Use the methods discussed above to solve such kind of problems. Ex. Find the smallest number to be added/subtracted from 6591 to make it a perfect square.
Class 8: Square Roots & Cube Roots (Lecture Notes)
Class 8: Square Roots & Cube Roots (Lecture Notes) SQUARE OF A NUMBER: The Square of a number is that number raised to the power. Examples: Square of 9 = 9 = 9 x 9 = 8 Square of 0. = (0.) = (0.) x (0.)
More informationSquare & Square Roots
Square & Square Roots 1. If a natural number m can be expressed as n², where n is also a natural number, then m is a square number. 2. All square numbers end with, 1, 4, 5, 6 or 9 at unit s place. All
More informationQuantitative Aptitude Preparation Numbers. Prepared by: MS. RUPAL PATEL Assistant Professor CMPICA, CHARUSAT
Quantitative Aptitude Preparation Numbers Prepared by: MS. RUPAL PATEL Assistant Professor CMPICA, CHARUSAT Numbers Numbers In Hindu Arabic system, we have total 10 digits. Namely, 0, 1, 2, 3, 4, 5, 6,
More informationQuestion: 1 - What will be the unit digit of the squares of the following numbers?
Square And Square Roots Question: 1 - What will be the unit digit of the squares of the following numbers? (i) 81 Answer: 1 Explanation: Since, 1 2 ends up having 1 as the digit at unit s place so 81 2
More informationQ.1 Is 225 a perfect square? If so, find the number whose square is 225.
Chapter 6 Q.1 Is 225 a perfect square? If so, find the number whose square is 225. Q2.Show that 63504 is a perfect square. Also, find the number whose square is 63504. Q3.Show that 17640 is not a perfect
More informationFree GK Alerts- JOIN OnlineGK to NUMBERS IMPORTANT FACTS AND FORMULA
Free GK Alerts- JOIN OnlineGK to 9870807070 1. NUMBERS IMPORTANT FACTS AND FORMULA I..Numeral : In Hindu Arabic system, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 called digits to represent any number.
More informationObjectives: Students will learn to divide decimals with both paper and pencil as well as with the use of a calculator.
Unit 3.5: Fractions, Decimals and Percent Lesson: Dividing Decimals Objectives: Students will learn to divide decimals with both paper and pencil as well as with the use of a calculator. Procedure: Dividing
More informationA natural number is called a perfect cube if it is the cube of some. some natural number.
A natural number is called a perfect square if it is the square of some natural number. i.e., if m = n 2, then m is a perfect square where m and n are natural numbers. A natural number is called a perfect
More informationPlace Value (Multiply) March 21, Simplify each expression then write in standard numerical form. 400 thousands thousands = thousands =
Do Now Simplify each expression then write in standard numerical form. 5 tens + 3 tens = tens = 400 thousands + 600 thousands = thousands = Add When adding different units: Example 1: Simplify 4 thousands
More informationClass 8: Factors and Multiples (Lecture Notes)
Class 8: Factors and Multiples (Lecture Notes) If a number a divides another number b exactly, then we say that a is a factor of b and b is a multiple of a. Factor: A factor of a number is an exact divisor
More informationMultiples and Divisibility
Multiples and Divisibility A multiple of a number is a product of that number and an integer. Divisibility: A number b is said to be divisible by another number a if b is a multiple of a. 45 is divisible
More informationALGEBRA: Chapter I: QUESTION BANK
1 ALGEBRA: Chapter I: QUESTION BANK Elements of Number Theory Congruence One mark questions: 1 Define divisibility 2 If a b then prove that a kb k Z 3 If a b b c then PT a/c 4 If a b are two non zero integers
More information5. Find the least number which when multiplied with will make it a perfect square. A. 19 B. 22 C. 36 D. 42
1. Find the square root of 484 by prime factorization method. A. 11 B. 22 C. 33 D. 44 2. Find the cube root of 19683. A. 25 B. 26 C. 27 D. 28 3. A certain number of people agree to subscribe as many rupees
More informationNumber Sense and Decimal Unit Notes
Number Sense and Decimal Unit Notes Table of Contents: Topic Page Place Value 2 Rounding Numbers 2 Face Value, Place Value, Total Value 3 Standard and Expanded Form 3 Factors 4 Prime and Composite Numbers
More informationExtra Practice 1. Name Date. Lesson 1: Numbers in the Media. 1. Rewrite each number in standard form. a) 3.6 million b) 6 billion c)
Master 4.27 Extra Practice 1 Lesson 1: Numbers in the Media 1. Rewrite each number in standard form. 3 a) 3.6 million b) 6 billion c) 1 million 4 2 1 d) 2 billion e) 4.25 million f) 1.4 billion 10 2. Use
More informationDeveloping Conceptual Understanding of Number. Set D: Number Theory
Developing Conceptual Understanding of Number Set D: Number Theory Carole Bilyk cbilyk@gov.mb.ca Wayne Watt wwatt@mts.net Vocabulary digit hundred s place whole numbers even Notes Number Theory 1 odd multiple
More informationExtra Practice 1. Name Date. Lesson 1: Numbers in the Media. 1. Rewrite each number in standard form. a) 3.6 million
Master 4.27 Extra Practice 1 Lesson 1: Numbers in the Media 1. Rewrite each number in standard form. a) 3.6 million 3 b) 6 billion 4 c) 1 million 2 1 d) 2 billion 10 e) 4.25 million f) 1.4 billion 2. Use
More informationAdding Fractions with Different Denominators. Subtracting Fractions with Different Denominators
Adding Fractions with Different Denominators How to Add Fractions with different denominators: Find the Least Common Denominator (LCD) of the fractions Rename the fractions to have the LCD Add the numerators
More informationClass 6 Natural and Whole Numbers
ID : in-6-natural-and-whole-numbers [1] Class 6 Natural and Whole Numbers For more such worksheets visit www.edugain.com Answer the questions (1) Find the largest 3-digit number which is exactly divisible
More informationMATH LEVEL 2 LESSON PLAN 3 FACTORING Copyright Vinay Agarwala, Checked: 1/19/18
MATH LEVEL 2 LESSON PLAN 3 FACTORING 2018 Copyright Vinay Agarwala, Checked: 1/19/18 Section 1: Exact Division & Factors 1. In exact division there is no remainder. Both Divisor and quotient are factors
More information16.1 Introduction Numbers in General Form
16.1 Introduction You have studied various types of numbers such as natural numbers, whole numbers, integers and rational numbers. You have also studied a number of interesting properties about them. In
More informationLong Division. Trial Divisor. ~The Cover-up Method~
Long Division by Trial Divisor ~The Cover-up Method~ Many students have experienced initial difficulty when first learning to divide by a multi-digit divisor. Most of the emphasis is placed on the procedure,
More informationClass 8 Cubes and Cube Root
ID : in-8-cubes-and-cube-root [1] Class 8 Cubes and Cube Root For more such worksheets visit www.edugain.com Answer the questions (1) Find the value of A if (2) If you subtract a number x from 15 times
More informationAn ordered collection of counters in rows or columns, showing multiplication facts.
Addend A number which is added to another number. Addition When a set of numbers are added together. E.g. 5 + 3 or 6 + 2 + 4 The answer is called the sum or the total and is shown by the equals sign (=)
More informationClass 8: Square Roots & Cube Roots - Exercise 7A
Class 8: Square Roots & Cube Roots - Exercise 7A 1. Find the square of each of the following numbers i. Square of 1 = 1 1 = 196 ii. Square of 137 = 137 137 = 18769 iii. Square of 17 = 16 289 iv. Square
More informationPre-Algebra Unit 1: Number Sense Unit 1 Review Packet
Pre-Algebra Unit 1: Number Sense Unit 1 Review Packet Target 1: Writing Repeating Decimals in Rational Form Remember the goal is to get rid of the repeating decimal so we can write the number in rational
More informationSaxon Math K, Math 1, Math 2, and Math 3 Scope and Sequence
,,, and Scope and Sequence Numbers and Operations Number Sense and Numeration Counts by 1 s, 5 s, and 10 s Counts by 2 s, 25 s Counts by 100 s Counts by 3 s, 4 s Counts by 6 s, 7 s, 8 s, 9 s, and 12 s
More informationI can use the four operations (+, -, x, ) to help me understand math.
I Can Common Core! 4 th Grade Math I can use the four operations (+, -, x, ) to help me understand math. Page 1 I can understand that multiplication fact problems can be seen as comparisons of groups (e.g.,
More informationCourse Syllabus - Online Prealgebra
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 1.1 Whole Numbers, Place Value Practice Problems for section 1.1 HW 1A 1.2 Adding Whole Numbers Practice Problems for section 1.2 HW 1B 1.3 Subtracting Whole Numbers
More informationMental Calculation Policy 2014
Mental Calculation Policy 2014 RECEPTION Children count reliably with numbers from one to 20 and place them in order. Children can say which number is one more or one less than a given number up to 20
More information1. 1 Square Numbers and Area Models (pp. 6-10)
Math 8 Unit 1 Notes Name: 1. 1 Square Numbers and Area Models (pp. 6-10) square number: the product of a number multiplied by itself; for example, 25 is the square of 5 perfect square: a number that is
More informationWhat I can do for this unit:
Unit 1: Real Numbers Student Tracking Sheet Math 10 Common Name: Block: What I can do for this unit: After Practice After Review How I Did 1-1 I can sort a set of numbers into irrationals and rationals,
More information1999 Mathcounts National Sprint Round Solutions
999 Mathcounts National Sprint Round Solutions. Solution: 5. A -digit number is divisible by if the sum of its digits is divisible by. The first digit cannot be 0, so we have the following four groups
More information4 digit number. 7. In a school there are 5985 students. On a rainy day 1009 students were absent. How many were present on that day? I 8. The sum of two numbers is 7854. If one of the numbers is 2435,
More informationModular Arithmetic and Doomsday
Modular Arithmetic and Doomsday Blake Thornton Much of this is due directly to Joshua Zucker and Paul Zeitz. 1. Subtraction Magic Trick. While blindfolded, a magician asks a member from the audience to
More informationIntroduction to Fractions
Introduction to Fractions A fraction is a quantity defined by a numerator and a denominator. For example, in the fraction ½, the numerator is 1 and the denominator is 2. The denominator designates how
More informationG E N E R A L A P T I T U D E
G E N E R A L A P T I T U D E Aptitude for GATE The GATE syllabus for General Aptitude is as follows: Verbal Ability: English grammar, sentence completion, verbal analogies, word groups, instructions,
More informationTable of Contents. Table of Contents 1
Table of Contents 1) The Factor Game a) Investigation b) Rules c) Game Boards d) Game Table- Possible First Moves 2) Toying with Tiles a) Introduction b) Tiles 1-10 c) Tiles 11-16 d) Tiles 17-20 e) Tiles
More informationNumber Sense Unit 1 Math 10F Mrs. Kornelsen R.D. Parker Collegiate
Unit 1 Math 10F Mrs. Kornelsen R.D. Parker Collegiate Lesson One: Rational Numbers New Definitions: Rational Number Is every number a rational number? What about the following? Why or why not? a) b) c)
More informationTravelling Integers. Materials
Travelling Integers Number of players 2 (or more) Adding and subtracting integers Deck of cards with face cards removed Number line (from -25 to 25) Chips/pennies to mark players places on the number line
More informationPublished in India by. MRP: Rs Copyright: Takshzila Education Services
NUMBER SYSTEMS Published in India by www.takshzila.com MRP: Rs. 350 Copyright: Takshzila Education Services All rights reserved. No part of this publication may be reproduced, stored in a retrieval system,
More information4. Subtracting an even number from another even number gives an odd number. 5. Subtracting an odd number from another odd number gives an even number
Level A 1. What is 78 32? A) 48 B) 110 C) 46 D) 34 2. What is 57 19? A) 37 B) 38 C) 42 D) 32 3. What is 66 8? A) 58 B) 57 C) 52 D) 42 4. Subtracting an even number from another even number gives an odd
More informationPlace the First Digit
Lesson 2. Place the First Digit When you divide, you can use estimation or place value to place the first digit of the quotient. Divide. 6q w,266 Estimate.,200 4 6 5 200, so the first digit of the quotient
More informationSchool of Business. Blank Page
Logarithm The purpose of this unit is to equip the learners with the concept of logarithm. Under the logarithm, the topics covered are nature of logarithm, laws of logarithm, change the base of logarithm,
More informationAddition quiz. Level A. 1. What is ? A) 100 B) 110 C) 80 D) What is ? A) 76 B) 77 C) 66 D) What is ?
Level A 1. What is 78 + 32? A) 100 B) 110 C) 80 D) 40 2. What is 57 + 19? A) 76 B) 77 C) 66 D) 87 3. What is 66 + 9? A) 76 B) 79 C) 74 D) 75 4. Adding two even numbers gives an even number. 5. Adding two
More informationStudy Material. For. Shortcut Maths
N ew Shortcut Maths Edition 2015 Study Material For Shortcut Maths Regd. Office :- A-202, Shanti Enclave, Opp.Railway Station, Mira Road(E), Mumbai. bankpo@laqshya.in (Not For Sale) (For Private Circulation
More informationDescription Reflect and Review Teasers Answers
1 Revision Recall basics of fractions A fraction is a part of a whole like one half (1/ one third (1/3) two thirds (2/3) one quarter (1/4) etc Write the fraction represented by the shaded part in the following
More information+ 4 ~ You divided 24 by 6 which equals x = 41. 5th Grade Math Notes. **Hint: Zero can NEVER be a denominator.**
Basic Fraction numerator - (the # of pieces shaded or unshaded) denominator - (the total number of pieces) 5th Grade Math Notes Mixed Numbers and Improper Fractions When converting a mixed number into
More information100 IDEAS FOR USING A HUNDRED SQUARE
100 IDEAS FOR USING A HUNDRED SQUARE These ideas are in no particular order and can be adapted to any age range or ability. The objectives are for children to learn to recognise numbers, understand numbers
More informationA C E. Answers Investigation 3. Applications = 0.42 = = = = ,440 = = 42
Answers Investigation Applications 1. a. 0. 1.4 b. 1.2.54 1.04 0.6 14 42 0.42 0 12 54 4248 4.248 0 1,000 4 6 624 0.624 0 1,000 22 45,440 d. 2.2 0.45 0 1,000.440.44 e. 0.54 1.2 54 12 648 0.648 0 1,000 2,52
More informationQUESTION BANK SUB : MATHS CLASS : III
QUESTION BANK SUB : MATHS CLASS : III Ch-1 Marks- 1 A) Choose the right answer:- 1.The smallest 4-digit number is: a.9999 b.1000 c.9000 2.The largest 4-digit number formed by 8,0,1,9 is? a. 8910 b. 9810
More informationCALCULATING SQUARE ROOTS BY HAND By James D. Nickel
By James D. Nickel Before the invention of electronic calculators, students followed two algorithms to approximate the square root of any given number. First, we are going to investigate the ancient Babylonian
More informationName: Class: Date: Class Notes - Division Lesson Six. 1) Bring the decimal point straight up to the roof of the division symbol.
Name: Class: Date: Goals:11 1) Divide a Decimal by a Whole Number 2) Multiply and Divide by Powers of Ten 3) Divide by Decimals To divide a decimal by a whole number: Class Notes - Division Lesson Six
More informationMeet #3 January Intermediate Mathematics League of Eastern Massachusetts
Meet #3 January 2009 Intermediate Mathematics League of Eastern Massachusetts Meet #3 January 2009 Category 1 Mystery 1. How many two-digit multiples of four are there such that the number is still a
More information2008 Cedar Ridge Test Solutions
2008 Cedar Ridge Test Solutions 1) The value of 1.4 + 0.03 + 0.009 + 7 is Step 1: Line up all of the decimals in the equation: 1.4 0.03 0.009 + 7 8.439 2) Solve: 4 + 2 x 3 4 2 + 3 = Answer: 8.439 Order
More information2. Nine points are distributed around a circle in such a way that when all ( )
1. How many circles in the plane contain at least three of the points (0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)? Solution: There are ( ) 9 3 = 8 three element subsets, all
More informationMultiplying Whole Numbers. Dividing Whole Numbers. ex: 3, ex: 6,
Multiplying Whole Numbers. Write the problem vertically. Multiply the ones digit of the bottom number by each of the digits in the top number, right to left 3. Bring down a zero and then multiply the tens
More informationGrade 8 Square and Square Roots
ID : ae-8-square-and-square-roots [1] Grade 8 Square and Square Roots For more such worksheets visit www.edugain.com Answer t he quest ions (1) The total population of a village is a perf ect square. The
More information2014 Edmonton Junior High Math Contest ANSWER KEY
Print ID # School Name Student Name (Print First, Last) 100 2014 Edmonton Junior High Math Contest ANSWER KEY Part A: Multiple Choice Part B (short answer) Part C(short answer) 1. C 6. 10 15. 9079 2. B
More informationThe Real Number System and Pythagorean Theorem Unit 9 Part B
The Real Number System and Pythagorean Theorem Unit 9 Part B Standards: 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion;
More informationGAP CLOSING. Powers and Roots. Intermediate / Senior Student Book GAP CLOSING. Powers and Roots. Intermediate / Senior Student Book
GAP CLOSING Powers and Roots GAP CLOSING Powers and Roots Intermediate / Senior Student Book Intermediate / Senior Student Book Powers and Roots Diagnostic...3 Perfect Squares and Square Roots...6 Powers...
More informationCHAPTER 3 DECIMALS. EXERCISE 8 Page Convert 0.65 to a proper fraction may be written as: 100. i.e = =
CHAPTER 3 DECIMALS EXERCISE 8 Page 21 1. Convert 0.65 to a proper fraction. 0.65 may be written as: 0.65 100 100 i.e. 0.65 65 100 Dividing both numerator and denominator by 5 gives: 65 13 100 20 Hence,
More informationNu1nber Theory Park Forest Math Team. Meet #1. Self-study Packet. Problem Categories for this Meet:
Park Forest Math Team 2017-18 Meet #1 Nu1nber Theory Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. Geometry: Angle measures in plane figures including supplements and
More informationEstimating with Square Roots
ACTIVITY 3.2 Estimating with Square Roots The square root of most numbers is not an integer. You can estimate the square root of a number that is not a perfect square. Begin by determining the two perfect
More informationDownloaded from DELHI PUBLIC SCHOOL
Worksheet- 21 Put the correct sign:- 1. 3000 + 300 + 3 3330 2. 20 tens + 6 ones 204 3. Two thousand nine 2009 4. 4880 4080 5. Greatest four digit number smallest five digit number. 6. Predecessor of 200
More informationIntermediate A. Help Pages & Who Knows
& Who Knows 83 Vocabulary Arithmetic Operations Difference the result or answer to a subtraction problem. Example: The difference of 5 and is 4. Product the result or answer to a multiplication problem.
More informationTo divide a number by a power of 10, you can use the exponent to determine how the position of the decimal point changes in the quotient.
Lesson 5.1 Algebra Division Patterns with Decimals To divide a number by 1, 1, or 1,, use the number of zeros in the divisor to determine how the position of the decimal point changes in the quotient.
More informationFSA Math Review. **Rounding / Estimating** **Addition and Subtraction** Rounding a number: Key vocabulary: round, estimate, about
FSA Math Review **Rounding / Estimating** Rounding a number: Key vocabulary: round, estimate, about 5 or more add one more-----round UP 0-4 just ignore-----stay SAME Find the number in the place value
More informationThe Sixth Annual West Windsor-Plainsboro Mathematics Tournament
The Sixth Annual West Windsor-Plainsboro Mathematics Tournament Saturday October 27th, 2018 Grade 7 Test RULES The test consists of 25 multiple choice problems and 5 short answer problems to be done in
More informationEstimate Quotients Using Multiples
Lesson 4.1 Estimate Quotients Using Multiples Find two numbers the quotient of 142 4 5 is. Then estimate the quotient. You can use multiples to estimate. A multiple of a number is the product of a number
More informationWhatcom County Math Championship 2016 Individual 4 th Grade
Whatcom County Math Championship 201 Individual 4 th Grade 1. If 2 3 is written as a mixed fraction, what is the difference between the numerator and the denominator? 2. Write 0.92 as a reduced fraction.
More information4 What are and 31,100-19,876? (Two-part answer)
1 What is 14+22? 2 What is 68-37? 3 What is 14+27+62+108? 4 What are 911-289 and 31,100-19,876? (Two-part answer) 5 What are 4 6, 7 8, and 12 5? (Three-part answer) 6 How many inches are in 4 feet? 7 How
More informationUse each digit card once to make the decimal number nearest to 20
NUMBER Level 4 questions 1. Here is a number chart. Circle the smallest number on the chart that is a multiple of both 2 and 7 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
More informationReal Numbers and the Number Line. Unit 1 Lesson 3
Real Numbers and the Number Line Unit 1 Lesson 3 Students will be able to: graph and compare real numbers using the number line. Key Vocabulary: Real Number Rational Number Irrational number Non-Integers
More informationQUANT TECHNIQUES STRAIGHT FROM SERIAL CAT TOPPER BYJU
QUANT TECHNIQUES STRAIGHT FROM SERIAL CAT TOPPER BYJU INDEX 1) POWER CYCLE 2) LAST 2 DIGITS TECHNIQUE 3) MINIMUM OF ALL REGIONS IN VENN DIAGRAMS 4) SIMILAR TO DIFFERENT GROUPING ( P&C) 5) APPLICATION OF
More informationLecture 8. Outline. 1. Modular Arithmetic. Clock Math!!! 2. Inverses for Modular Arithmetic: Greatest Common Divisor. 3. Euclid s GCD Algorithm
Lecture 8. Outline. 1. Modular Arithmetic. Clock Math!!! 2. Inverses for Modular Arithmetic: Greatest Common Divisor. 3. Euclid s GCD Algorithm Clock Math If it is 1:00 now. What time is it in 5 hours?
More informationMath Review Packet. Grades. for th. Multiplication, Division, Decimals, Fractions, Metric & Customary Measurements, & Volume Math in the Middle
Math Review Packet for th 5 th 6 Grades Multiplication, Division, Decimals, Fractions, Metric & Customary Measurements, & Volume 206 Math in the Middle Multiplying Whole Numbers. Write the problem vertically
More informationMAT 0002 Final Review A. Acosta. 1. Round to the nearest thousand. Select the correct answer: a b. 94,100 c. 95,000 d.
1. Round 94156 to the nearest thousand. 94000 94,100 95,000 d. 94,200 2. Round $67230 to the nearest $100. $68000 $67000 $67200 d. $67300 3. Subtract: 851 (476 61) 314 1,266 436 d. 446 PAGE 1 4. From the
More informationMAT 0002 Final Review A. Acosta
1. The page design for a magazine cover includes a blank strip at the top called a header, and a blank strip at the bottom called a footer. In the illustration below, how much page length is lost because
More informationSummer Math Completed 5 th grade Entering 6 th grade
Name Date Summer Math Completed 5 th grade Entering 6 th grade Instructions: Please complete the following problems showing all work. This packet is due on the first day of school and will count as your
More informationGeorgia Department of Education
Fourth Grade 4.NOP.1 Multiplication and division; Find the factor pairs for a given whole number less than or equal to 100; recognize prime numbers as numbers greater than 1 with exactly one factor pair.
More informationDIVISION REVIEW. Math Grade 6 Review Lesson 4 Information Organized by Beckey Townsend
DIVISION REVIEW Math Grade 6 Review Lesson 4 Information Organized by Beckey Townsend Divisibility Rules 2 A number is divisible by 2 if it ends in a zero or an even number. Example: The number 2,784 is
More informationGAP CLOSING. Powers and Roots. Intermediate / Senior Facilitator Guide
GAP CLOSING Powers and Roots Intermediate / Senior Facilitator Guide Powers and Roots Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions...5 Solutions...5
More informationTwenty Mathcounts Target Round Tests Test 1 MATHCOUNTS. Mock Competition One. Target Round. Name. State
MATHCOUNTS Mock Competition One Target Round Name State DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. This section of the competition consists of eight problems, which will be presented in pairs. Work
More informationBrilliant Public School, Sitamarhi. Class -V. Maths Worksheets. Session :
Brilliant Public School, Sitamarhi Class -V Maths Worksheets Session : 2012-13 Rajopatti,Dumra Road,Sitamarhi(Bihar),Pin-843301 Ph.06226-252314,Mobile:9431636758 Fill in the blanks : 1. A number is divisible
More informationThe Parkland Federation. February 2016
The Parkland Federation February 206 EYFS/KS Calculations: Recording Addition (page of ). Aggregation/combining 2. Augmentation/counting on 3. Counting Contexts: + + + + Pupils physically combining groups
More informationFor more information on the Common Core State Standards, visit Beast Academy Grade 4 Chapters 1-12:
Beast Academy Scope and Sequence for Grade 4 (books 4A through 4D). The content covered in Beast Academy Grade 4 is loosely based on the standards created by the Common Core State Standards Initiative.
More informationA C E. Answers Investigation 1. Applications. b. No; 6 18 = b. n = 12 c. n = 12 d. n = 20 e. n = 3
Answers Applications 1. a. Divide 24 by 12 to see if you get a whole number. Since 12 2 = 24 or 24 12 = 2, 12 is a factor b. Divide 291 by 7 to see if the answer is a whole number. Since 291 7 = 41.571429,
More informationLesson 0.1 The Same yet Smaller
Lesson 0.1 The Same yet Smaller 1. Write an expression and find the total shaded area in each square. In each case, assume that the area of the largest square is 1. a. b. c. d. 2. Write an expression and
More informationMATH MILESTONE # A5 DIVISION
MATH MILESTONE # A5 DIVISION The word, milestone, means a point at which a significant change occurs. A Math Milestone refers to a significant point in the understanding of mathematics. To reach this milestone
More informationMath 10/11 Honors Section 3.6 Basic Trigonometric Identities
Math 0/ Honors Section 3.6 Basic Trigonometric Identities 0-0 - SECTION 3.6 BASIC TRIGONOMETRIC IDENTITIES Copright all rights reserved to Homework Depot: www.bcmath.ca I) WHAT IS A TRIGONOMETRIC IDENTITY?
More informationUNIT 1. numbers. multiples and factors NUMBERS, POSITIONS AND COLUMNS DIGITS
numbers. multiples and factors UNIT 1 NUMBERS, POSITIONS AND COLUMNS Our number system is called the decimal system.it is based on tens. This is probably because we have ten fingers and thumbs. A digit
More informationWORKING WITH NUMBERS GRADE 7
WORKING WITH NUMBERS GRADE 7 NAME: CLASS 3 17 2 11 8 22 36 15 3 ( ) 3 2 Left to Right Left to Right + Left to Right Back 2 Basics Welcome back! Your brain has been on holiday for a whilelet s see if we
More informationNumber Theory. Konkreetne Matemaatika
ITT9131 Number Theory Konkreetne Matemaatika Chapter Four Divisibility Primes Prime examples Factorial Factors Relative primality `MOD': the Congruence Relation Independent Residues Additional Applications
More informationMathematics Enhancement Programme TEACHING SUPPORT: Year 3
Mathematics Enhancement Programme TEACHING UPPORT: Year 3 1. Question and olution Write the operations without brackets if possible so that the result is the same. Do the calculations as a check. The first
More informationYou found trigonometric values using the unit circle. (Lesson 4-3)
You found trigonometric values using the unit circle. (Lesson 4-3) LEQ: How do we identify and use basic trigonometric identities to find trigonometric values & use basic trigonometric identities to simplify
More information4th Grade Mathematics Mathematics CC
Course Description In Grade 4, instructional time should focus on five critical areas: (1) attaining fluency with multi-digit multiplication, and developing understanding of dividing to find quotients
More informationSimple Solutions Mathematics Level 3. Level 3. Help Pages & Who Knows Drill
Level 3 & Who Knows Drill 283 Vocabulary Arithmetic Operations Difference the result or answer to a subtraction problem. Example: The difference of 5 and 1 is 4. Product the result or answer to a multiplication
More informationXSEED Summative Assessment Test 2. Maths, Test 2. XSEED Education Maths Grade 4 1
Maths, Test 2 4 PART I Short Answer Questions. Assign mark for the correct answer. 600 30 Marks = 2. Assign 2 marks for correctly solving the problem. 2 = 2 2 0 6 4 8 2 4 8 0 2 0 2 4 2 4 0 0 3. Assign
More informationFirst Step Program (Std V) Preparatory Program- Ganit Pravinya Test Paper Year 2013
First Step Program (Std V) Preparatory Program- Ganit Pravinya Test Paper Year 2013 Solve the following problems with Proper Procedure and Explanation. 1. Solve : 1 1 5 (7 3) 4 20 3 4 4 4 4 2. Find Value
More information