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14.6: Exercise - Mathematics


Skills

Counting Board And Quipu

1) In the following Peruvian counting board, determine how many of each item is represented. Please show all of your calculations along with some kind of explanation of how you got your answer. Note the key at the bottom of the drawing.

2) Draw a quipu with a main cord that has branches (H cords) that show each of the following numbers on them. (You should produce one drawing for this problem with the cord for part a on the left and moving to the right for parts b through d.)

a. 232b. 5065
c. 23451d. 3002

Basic Base Conversions

3) 423 in base 5 to base 104) 3044 in base 5 to base 10
5) 387 in base 10 to base 56) 2546 in base 10 to base 5
7) 110101 in base 2 to base 108) 11010001 in base 2 to base 10
9) 100 in base 10 to base 210) 2933 in base 10 to base 2
11) Convert 653 in base 7 to base 1012) Convert 653 in base 10 to base 7
13) 3412 in base 5 to base 214) 10011011 in base 2 to base 5

(Hint: convert first to base 10 then to the final desired base)

The Caidoz System

Suppose you were to discover an ancient base-12 system made up twelve symbols. Let’s call this base system the Caidoz system. Here are the symbols for each of the numbers 0 through 12:

Convert each of the following numbers in Caidoz to base 10

Convert the following base 10 numbers to Caidoz, using the symbols shown above.

19) 17520) 3030
21) 1000022) 5507

Mayan Conversions

Convert the following numbers to Mayan notation. Show your calculations used to get your answers.

23) 13524) 234
25) 36026) 1215
27) 1050028) 1100000

Convert the following Mayan numbers to decimal (base-10) numbers. Show all calculations.

James Bidwell has suggested that Mayan addition was done by “simply combining bars and dots and carrying to the next higher place.” He goes on to say, “After the combining of dots and bars, the second step is to exchange every five dots for one bar in the same position.” After converting the following base 10 numbers into vertical Maya notation (in base 20, of course), perform the indicated addition:

33) 32 + 1134) 82 + 15
35) 35 + 14836) 2412 + 5000
37) 450 + 84438) 10000 + 20000
39) 4500 + 350040) 130000 + 30000

41) Use the fact that the Mayans had a base-20 number system to complete the following multiplication table. The table entries should be in Mayan notation. Remember: Their zero looked like this…. Xerox and then cut out the table below, fill it in, and paste it onto your homework assignment if you do not want to duplicate the table with a ruler.

(To think about but not write up: Bidwell claims that only these entries are needed for “Mayan multiplication.” What does he mean?)

Binary and Hexadecimal Conversions

Modern computers operate in a world of “on” and “off” electronic switches, so use a binary counting system – base 2, consisting of only two digits: 0 and 1.

Convert the following binary numbers to decimal (base-10) numbers.

42) 100143) 1101
44) 11001045) 101110

Convert the following base-10 numbers to binary

46) 747) 12
48) 3649) 27

Four binary digits together can represent any base-10 number from 0 to 15. To create a more human-readable representation of binary-coded numbers, hexadecimal numbers, base 16, are commonly used. Instead of using the 8,13,1216 notation used earlier, the letter A is used to represent the digit 10, B for 11, up to F for 15, so 8,13,1216 would be written as 8DC.

Convert the following hexadecimal numbers to decimal (base-10) numbers.

50) C351) 4D
52) 3A653) BC2

Convert the following base-10 numbers to hexadecimal

54) 15255) 176
56) 203457) 8263

Exploration

58) What are the advantages and disadvantages of bases other than ten.

59) Supposed you are charged with creating a base-15 number system. What symbols would you use for your system and why? Explain with at least two specific examples how you would convert between your base-15 system and the decimal system.

60) Describe an interesting aspect of Mayan civilization that we did not discuss in class. Your findings must come from some source such as an encyclopedia article, or internet site and you must provide reference(s) of the materials you used (either the publishing information or Internet address).

61) For a Papuan tribe in southeast New Guinea, it was necessary to translate the bible passage John 5:5 “And a certain man was there, which had an infirmity 30 and 8 years” into “A man lay ill one man, both hands, five and three years.” Based on your own understanding of bases systems (and some common sense), furnish an explanation of the translation. Please use complete sentences to do so. (Hint: To do this problem, I am asking you to think about how base systems work, where they come from, and how they are used. You won’t necessarily find an “answer” in readings or such…you’ll have to think it through and come up with a reasonable response. Just make sure that you clearly explain why the passage was translated the way that it was.)

62) The Mayan calendar was largely discussed leading up to December 2012. Research how the Mayan calendar works, and how the counts are related to the number based they use.


14.6: Exercise - Mathematics

In single variable calculus we saw that the second derivative is often useful: in appropriate circumstances it measures acceleration it can be used to identify maximum and minimum points it tells us something about how sharply curved a graph is. Not surprisingly, second derivatives are also useful in the multi-variable case, but again not surprisingly, things are a bit more complicated.

It's easy to see where some complication is going to come from: with two variables there are four possible second derivatives. To take a "derivative,'' we must take a partial derivative with respect to $x$ or $y$, and there are four ways to do it: $x$ then $x$, $x$ then $y$, $y$ then $x$, $y$ then $y$.

Example 14.6.1 Compute all four second derivatives of $f(x,y)=x^2y^2$.

Using an obvious notation, we get: $f_=2y^2qquad f_=4xyqquad f_=4xyqquad f_=2x^2.$

You will have noticed that two of these are the same, the "mixed partials'' computed by taking partial derivatives with respect to both variables in the two possible orders. This is not an accident&mdashas long as the function is reasonably nice, this will always be true.

Theorem 14.6.2 (Clairaut's Theorem) If the mixed partial derivatives are continuous, they are equal.

Example 14.6.3 Compute the mixed partials of $ds f=xy/(x^2+y^2)$. $ f_x=qquad f_=- $ We leave $f_$ as an exercise.


Mathematics : Word Problems – Exercise and Solutions

Word problems are seen in our everyday lives. This involves sum, difference, positive difference and product of numbers. The most important thing you need to remember in solving word problems is the INTERPRETATION OF THE QUESTION . If you’re able to correctly interpret the question, the solution becomes easy.

Sum – the result of addition

Difference – the result of subtraction

Positive difference – larger number minus smaller number

Product – the result of multiplication

The sum of a set of numbers is the result when the numbers are added together.

The sum of four consecutive numbers is 78.

Let the numbers be a, a+1, a+2, a+3.

Subtract 6 from both sides

The numbers 18, a+1 = 19, a+2 = 20, a+3 = 21

The difference between two numbers is the result of Subtracting one from the other. It is usual to subtract the smaller number from the larger one. This gives a positive difference.

The difference between 7 and another number is 12. Find two possible values for the number.

Thus the number could be 19 or -5.

The product of two numbers is the result when the numbers are multiplied together

Find the product of -6, 0.7 and 6 2/3.

Convert 0.7 to a proper fraction = 7/10, 6 2/3 = 20/3

The product of two numbers is 8 4/9 . If one of the numbers is 1/4, find the other number.

Combining products with Sum and Differences

Find the positive difference between 45 and the product of 4 and 15

Difference between 45 and 60 = 60 – 45 = 15.

Find the product of 8 and the positive difference between 3 and 9.

Positive difference = 9 – 3 = 6

Find the sum of 2.5 and the product of 3 and 2.5

Sum and Product = 2.5 + <3 x 2.5>
= 2.5 + <7.5>
= 10.0

Problems Involving Equations

The product of a certain number and 8 is equal to twice the number subtracted from 24. Find the number

The product of x and 8 = 8x

twice x (2x) subtracted from 24 = 24 – 2x

The sum of 42and a certain number is divided by 4. The result is equal to double the number. Find the number

the sum of 42 and the number = 42 + d

the sum divided by 4 = 42 + d
4

result is double the number 2d = 42+ d = 2d
4

multiply both sides by 4 = 42 + d = 2d x 4

subtract d from both sides

The sum of two numbers is 22. The sum of 3/4 of one of the numbers and 1/5 of the other number is 11. Find the two numbers.

Let the numbers be a and b = a + b = 22

The sum of 3/4 of one number (3/4 a) and 1/5 of the other number (1/5 b) is 11 = 3/4 a + 1/5 b = 11

a + b = 22, therefore b = 22 – a

Substitute b into second equation

Classwork Exercises

  1. The sum of 8 and a certain number is equal to the product of the number and 3. Find the number
  2. Four times a certain number is equal to the number subtracted from 40. Find the number
  3. I subtract 14 from a certain number, I multiply the result by 3. The final answer is 3. Find the number
  4. The sum of two numbers is 21. Five times the first number added to 2 times the second number is 66. Find the two numbers.
  5. 2 is added to twice a certain number and the sum is doubled. The result is 10 less than 5 times the original number. Find the original number.
  6. The sum of two numbers is 38. When 8 is added to twice one of the numbers, the result is 5 times the other number.
  7. 5/12 of a number is subtracted from 3/4 of the number. Their positive difference is 7 less than 5/6 of the number. Find the number.
  8. Find the number such that when 3/4 of it is added to 3 1/2, the sum is the same as when 2/3 of it is subtracted from 6 1/2.
  9. The sum of two numbers is 21. 3/4 of one of the numbers added to 2/3 of the other gives a sum of 15. Find the two numbers.
  10. 1/3 of a number is added to 5. The result is one and half times the original number. Find the number.

  1. The sum of 8 and a certain number is equal to the product of the number and 3. Find the number
    Let the number be x.
    The sum of 8 and x = 8 + x
    The product of the number and 3 = 3x
    Sum of 8 and x (8 + x) is equal to the product of the number and 3 (3x) = 8 + x = 3x
    Subtract x from both sides of the equation = 8 + x – x = 3x -x
    = 8 = 2x
    Divide both sides by 2 = x = 4.
  2. Four times a certain number is equal to the number subtracted from 40. Find the number
    Let the number be a
    Four times the number = 4 x a = 4a
    four times the number (4a) is equal to the number subtracted from 40 (40 – a): 4a = 40 – a
    Add a to both sides = 4a + a = 40 – a + a
    = 5a = 40
    Divide both sides by 5 = 5a/5 = 40/5
    Therefore, a = 8
  3. I subtract 14 from a certain number, I multiply the result by 3. The final answer is 3. Find the number
    Let the number be c
    Subtract 14 from the number = c – 14
    Let the result be d, so c – 14 = d
    Multiply the result by 3 = 3 x d = 3d
    Final result is 3, hence 3d =3
    Divide both sides by 3, d = 1
    Remember c – 14 = d (1)
    c – 14 = 1
    c = 1 + 14 = 15
  4. The sum of two numbers is 21. Five times the first number added to 2 times the second number is 66. Find the two numbers.
    Let the 2 numbers be x and y
    Sum of the 2 numbers = x + y = 21
    Five times the first number (5x) is added to 2 times the second number (2y) to give 66= 5x + 2y = 66
    There are 2 equations – x + y = 21 ……….. eqn 1
    – 5x + 2y = 66 ……… eqn 2
    Eliminate one variable by multiplying equation 1 with 2 and equation 2 with 1
    – x + y = 21 x 2 = 2x + 2y = 42 …….. eqn 1
    – 5x + 2y = 66 x 1 = 5x + 2y = 66 ……eqn 2
    Subtract equation 1 from 2 = 5x + 2y = 66 – 2x + 2y = 42
    New equation = 3x = 24
    Divide through by 3, x = 8
    To find y = Pick any of the equations (8) + y = 21, y = 21 – 8 = 13
    Or 5(8) + 2y = 66, 2y = 66 – 40 = 26, 2y = 26, y = 13.
    The two numbers are 8 and 13.
  5. 2 is added to twice a certain number and the sum is doubled. The result is 10 less than 5 times the original number. Find the original number .
    Let the number be z
    2 is added to twice the number = (2 + 2z)
    The sum is doubled = (2 + 2z) + (2 +2z)
    Result is 10 less than the original number = 5z – 10
    Complete equation is = (2 + 2z) + (2 +2z) = 5z – 10
    = 2 + 2z + 2 + 2z = 4 + 4z
    4 + 4z = 5z – 10
    Collect like terms to either sides of the equation
    4z – 5z = -10 – 4
    -z = -14
    Divide through by -, z = 14
    6. The sum of two numbers is 38. When 8 is added to twice one of the numbers, the result is 5 times the other number.
    Let the two numbers be x and y
    Sum of x and y = x + y = 38
    8 is added to twice a number = 8 + 2x , the result is 5 times the other number = 8 + 2x = 5y
    Two equations x + y = 38 and 8 + 2x = 5y
    Rearrange equation 2 = -2x + 5y = 8
    Solve simultaneously x + y = 38 …….. eqn 1
    -2x + 5y = 8 ……. eqn 2
    Multiply equation 1 by 2 and equation 2 by 1 – x + y = 38 x 2 = 2x + 2y = 76
    -2x + 5y = 8 x 1 = -2x + 5y = 8
    In order to eliminate one variable, add the two equations together = 2x + 2y = 76 …….. eqn 1
    + (- 2x) + 5y = 8 ……. eqn 2
    7y = 84, y = 12
    To solve for x, take any of the equations above = x + (12) = 38, x = 38 -12 = 26
    The two numbers are 26 and 12.


NCERT Solutions for Class 6 Maths Chapter 14

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Exercise 14.1, Exercise 14.2, Exercise 14.3, Exercise 14.4, Exercise 14.5 and Exercise 14.6 in English & Hindi Medium updated for 2021-2022.

Solutions for Prashnavali 14.1, Prashnavali 14.2, Prashnavali 14.3, Prashnavali 14.4, Prashnavali 14.5 and Prashnavali 14.6 in Hindi Medium PDF to free download. Download NCERT Solutions Offline Apps 2021-22 for Class 6 to use it without internet once downloaded. Videos of exercises are also given to for all answers based on CBSE Syllabus 2021-2022.

NCERT Solutions for Class 6 Maths Chapter 14

Class 6 Maths Chapter 14 all Exercises Solution

NCERT Solutions App for Class 6

Download Class 6 Maths Chapter 14 Solutions in PDF Format

Download NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry in PDF format. Solutions are easy and simplified. All the solutions are updated for new academic session 2021-22 based on updated NCERT Books 2021-22. For any query, Feel free to contact us.

Class 6 Maths Chapter 14 Solutions in English Medium

Class 6 Maths Chapter 14 Solutions in Hindi Medium

Class 6 Maths Exercise 14.1 & 14.2 Solutions in Video

Class 6 Maths Exercise 14.3 & 14.4 Solutions in Video

Class 6 Maths Exercise 14.5 & 14.6 Solutions in Video

About Class 6 Maths Chapter 14

In 6 Maths Chapter 14 Practical Geometry, we will learn to draw figures using compass, set-square, ruler and protector.

Construction of a circle when its radius is known:
Step 1: Open the compasses for the required radius.
Step 2: Mark a point with a sharp pencil where we want the centre of the circle to be and name it (say O).
Step 3: Place the pointer of the compasses at center O.
Step 4: Turn the compasses slowly to draw the circle.
Construction of a line segment of a given length:

Step 1: Draw a line l. Mark a point A on a line l.
Step 2: Place the compasses pointer on the zero mark of the ruler. Open it to place the pencil point upto the required length mark.
Step 3: Taking caution that the opening of the compasses has not changed, place the pointer on A and swing an arc to cut l at B.
Step 4: AB is the required line segment of required length.

Important Questions on Class 6 Maths Chapter 14

How to draw a circle of radius 3.2 cm?

Steps of construction: (a) Open the compass for the required radius of 3.2 cm. (b) Make a point with a sharp pencil where we want the centre of circle to be. (c) Name it O. (d) Place the pointer of compasses on O. (e) Turn the compasses slowly to draw the circle. Hence, it is the required circle.

What is a ruler?

A ruler ideally has no markings on it. However, the ruler in our instruments box is graduated into centimetres along one edge. It is use to draw line segments an to measure their lengths.

What is a Compass?

A pair – a pointer on one end and a pencil on the other. It is use to mark off equal lengths nut not to measure them. It is also use to draw arcs and circles.


Online Math Problem Solver

Solve your math problems online. The free version gives you just answers. If you would like to see complete solutions you have to sign up for a free trial account.

Basic Math Plan

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You can simplify and evaluate expressions, factor/multiply polynomials, combine expressions.

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You can solve all problems from the basic math section plus solving simple equations, inequalities and coordinate plane problems.
You can also evaluate expressions, factor polynomials, combine/multiply/divide expressions.

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Solve all type of trigonometric (sin, cos, tan, sec, scs, cot) expressions, equations, inequalities.
Graph trigonometric functions.
Trigonometry of a right triangle.

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Include everything above plus finding limits (lim), sums, matrices.

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Solve integral problems - definite, indefinite integrals.

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Solve your probability, combination, permutation problems. Statistics - find median, mean (arithmetic, geometric, quadratic), mode, dispersion, mormal distributions, t-Distribution.
The solver successfully do Statistical hypothesis testing


14.6: Exercise - Mathematics

Team/individual work 1: Properties of Riemann Integrals from Tao's book I, Chapter 11.
Theorem 11.4.1 (a,b,c) Linear Properties due to Matthew Straughn.
Theorem 11.4.3 Closed under min due to Peterson Moyo and Joshua Abrams.
Theorem 11.4.1 (g) Closed under extension due to Jorge Piovesan.
Theorem 11.4.1 (h) Closed under restriction due to Hyunjung Ra and Brian Nease.
Exercise 11.4.2 Solution due to Sara Pollock.
Exercises 11.5.1: Bounded piecewise continuous functions are integrable by Dave Flores and Amanda Towsend.
Exercises 11.6.3, 11.6.4 and 11.6.5: Integral test by Anatoly Kobozev.
Exercise 11.10.1: Integration by parts by Teresa Evans.

Homework 1 (due 2/15/07): Solutions compiled by Matthew Straughn.
--> Exercises from Tao's Book II:
(p.398-99) 12.1.3, 12.1.5, 12.1.6, 12.1.12, 12.1.15.

Homework 2 (due 2/22/07): Solutions compiled by Matthew Straughn.
--> Exercises from Tao's Book II:
(p. 405) 12.2.3, 12.2.4
(p. 408) 12.3.1
(p. 411) 12.4.7.

Homework 3 (due 3/1/07): Solutions compiled by Matthew Straughn.
--> Exercises from Tao's Book II:
(p. 417-19) 12.5.4, 12.5.5, 12.5.12, 12.5.13

Team/individual work 2:
Integration exercise in Analysis qualifying Jan 2007 Solution compiled by Matthew Straughn.
--> Topology Tao's book II, Chapter 12.
(p.412) 12.4.8 Completion of metric spaces by Josh Beach.
(p. 418) 12.5.10 Totally bounded (Josh Beach).

Homework 4 (due 3/9/07): Solutions --> Exercises from Tao's Book II:
(p. 417-19) Choose four out of:
(p. 422) 13.1.4
(p.425-426) 13.2.4, 13.2.6, 13.2.8, 13.2.9-13.2.11

Homework 5 (due 3/27/07): Solutions --> Exercises from Tao's Book II (choose 4 out of the following):
(p. 429) 13.3.5, 13.3.6
(p.432) 13.4.1, 13.4.2, 13.4.7*, 13.4.9
(p. 448-449) 14.2.1, 14.2.2

Homework 6 (due 4/3/07): Solutions --> Exercises from Tao's Book II (choose 4 out of the following):
(p. 452) 14.3.3, 14.3.4, 14.3.5, 14.3.8
(p.455) 14.4.3*
(p. 458) 14.5.3
(p. 460) 14.6.1
(p. 472) 14.7.2*

Homework 7 (due 4/17/07): --> Exercises from Tao's Book II (choose 4 out of the following):
(p. 540) 17.1.2, 17.1.4
(p. 552) 17.3.4
(p. 555) 17.4.3*, 17.4.4, 17.4.5
(p. 558) 17.5.1

Homework 8 (due 5/1/07): Exercises from Tao's Book II:
(p. 560-61) 17.6.1-17.6.4, 17.6.8
(p. 567) 17.7.1, 17.7.3


Free Printable Math Worksheets for Grade 4

This is a comprehensive collection of free printable math worksheets for grade 4, organized by topics such as addition, subtraction, mental math, place value, multiplication, division, long division, factors, measurement, fractions, and decimals. They are randomly generated, printable from your browser, and include the answer key. The worksheets support any fourth grade math program, but go especially well with IXL's 4th grade math curriculum, and their brand new lessons at the bottom of the page.

The worksheets are randomly generated each time you click on the links below. You can also get a new, different one just by refreshing the page in your browser (press F5).

You can print them directly from your browser window, but first check how it looks like in the "Print Preview". If the worksheet does not fit the page, adjust the margins, header, and footer in the Page Setup settings of your browser. Another option is to adjust the "scale" to 95% or 90% in the Print Preview. Some browsers and printers have "Print to fit" option, which will automatically scale the worksheet to fit the printable area.

All worksheets come with an answer key placed on the 2nd page of the file.

Mental addition

  • Complete the next whole hundred (missing addend)
  • Adding 1-and 2-digit numbers mentally (3 addends)
  • Adding whole tens (4 addends) (print in landscape)
  • Adding whole hundreds (2 addends) (print in landscape)
  • Adding whole hundreds (3 addends) (print in landscape)
  • Missing addend with whole hundreds (print in landscape)
  • Completing a whole thousand (missing addend) (print in landscape)
  • Missing addend problems 1: easy
  • Missing addend problems 2: a 3-digit number and a 1-digit number
  • Missing addend problems 3: involves one 3-digit number
  • Missing addend problems 4: 2-digit numbers

Mental subtraction

  • Subtract 2-digit numbers within 100
  • Subtract a 2-digit number from whole hundreds
  • Subtract whole tens within 1000 - easier
  • Subtract whole tens within 1000 - more difficult
  • Subtract whole hundreds 1
  • Subtract whole hundreds 2
  • Missing minuend / subtrahend with 2-digit numbers
  • Missing minuend / subtrahend with whole tens
  • Missing minuend / subtrahend - single-digit numbers, whole tens, or whole hundreds
  • Missing minuend / subtrahend&mdasha challenge
  • Subtract any number from 1000
  • Subtract any number from any whole thousand

Addition in columns

Subtraction in columns

Place value/Rounding

  • Build a four-digit number from the parts (print in landscape)
  • Find the missing place value from a 4-digit number (print in landscape)
  • Build a 5-digit number from parts (print in landscape)
  • Find the missing place value from a 5-digit number
  • Build a 6-digit number from parts
  • Find the missing place value from a 6-digit number
  • Mixed rounding problems 3 - as above but rounding to the underlined digit
  • Mixed rounding problems 4 - round to the nearest 10, 100, 1000, or 10,000 within 1,000,000
  • Mixed rounding problems 5 - round to any place value within 1,000,000

Roman numerals

These are completely optional, as Roman Numerals are not included in the Common Core standards.

Mental multiplication

  • Multiplication tables 2-10, random facts
  • Multiplication tables 2-12, random facts
  • Multiplication tables 2-10, missing factor
  • Multiplication tables 2-12, missing factor
  • Multiply a single-digit number by whole tens
  • Multiply a single-digit number by whole hundreds
  • Multiply a single-digit number by whole tens or whole hundreds
  • Multiply single-digit numbers, whole tens, or whole hundreds by the same
  • As above, but missing factor
  • The same as above, but also including whole thousands
  • As above, missing factor
  • Multiply in parts 1: single-digit number by a 2-digit number
  • Multiply in parts 2: single-digit number by a number near a whole hundred
  • Multiply in parts 3: single-digit number by a 3-digit number
    &mdash three operations
    &mdash four operations

Multiply in columns

Mental division

  • Division facts practice (tables 1-10)
  • Division facts practice (tables 1-12)
  • Missing dividend or divisor (basic facts)
  • Divide by 10 or 100
  • Divide by whole tens or hundreds
  • Divide whole tens and whole hundreds by 1-digit numbers mentally
  • Division with remainder within 1-100, based on basic facts
  • Division with remainder within 1-100
  • Division with remainder, divisor a whole ten
  • Division with remainder, divisor a whole hundred
  • Order of operations: add, subtract, multiply, divide, and parenthesis &mdash three operations
  • Order of operations: add, subtract, multiply, divide, and parenthesis &mdash four operations
  • Order of operations: add, subtract, multiply, divide, and parenthesis &mdash five operations

Long division

Factors

Measuring units

The following worksheets are slightly beyond Common Core Standards for 4th grade, and are optional.

    (for example, 34 mm = ___ cm ____ mm)
  • Convert between centimeters & meters (for example, 2 m 65 cm = _____ cm)
  • Mixed practice of the two above (millimeters, centimeters, and meters)
  • Convert between meters and kilometers (for example, 2,584 m = ____ km _____ m)
  • Mixed practice of the ones above (mm, cm, m, and km)
  • Convert between milliliters and liters (for example, 2,584 ml = ____ L _____ ml)
  • Convert between grams and kilograms (for example, 5 kg 600 g = ________ g)
  • Mixed practice of the two above: ml & l and g & kg
  • All metric units mentioned above - mixed practice
  • Convert between inches and feet (e.g. 35 in. = ___ ft ___ in.)
  • Convert whole miles & feet or yards
  • Convert between ounces & pounds (e.g. 62 oz = ___ lb ___ oz)
  • Convert between cups, pints, quarts, and gallons
  • All customary units mentioned above - mixed practice

Fractions

  • Subtract like fractions (denominators 2-12)
  • Subtract like fractions (denominators 2-25) (optional beyond the CCS)
  • Subtract a fraction from a whole number
  • Subtract a fraction from a mixed number
  • How much was subtracted from a whole number
  • Subtract mixed numbers (like denominators)
  • Subtract a fraction with tenths and another with hundredths (such as 2/10 + 6/100)

Fractions to mixed numbers or vv.

Decimals

  • Subtract mentally (1 decimal digit) &mdasheasy
  • Subtract mentally (1 decimal digit) &mdashmedium
  • Subtract mentally (1 decimal digit) —missing minuend/subtrahend
  • One number has 1 decimal digit, the other has 2
  • The numbers may have one or two decimal digits - challenge
    (subtract in columns)

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NCERT Class 6 Math Solution

NCERT Class 6 Mathematics Solution Easy Method NCERT Class 6 Mathematics Chapter 1 (Exercise 1.1, 1.2, 1,3) Chapter 2 (Exercise 2.1, 2.2, 2.3) Chapter 3 (Exercise 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7) chapter 4 (Exercise 4.1, 4.2, 4.3, 4.4, 4.4, 4.5,4.6) Chapter 5 (Exercise 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9) Chapter 6 (Exercise 6.1, 6.2, 6.3) Chapter 7 (7.1, 7.2, 7.3, 7.4, 7.5, 7.6) Chapter 8 (Exercise 8.1, 8.2, 8.3, 8.4, 8.5, 8.6) Chapter 9 (Exercise 9.1, 9.2, 9.3, 9.4) Chapter 10 (Exercise 10.1, 10.2, 10.3) Chapter 11 (Exercise 11.1, 11.2, 11.3, 11.4, 11.5) Chapter 12 (Exercise 12.1, 12.2, 12.3) chapter 13 (Exercise 13.1, 13.2, 13.3) Chapter 14 (Exercise 14.1, 14.2, 14.3, 14.4, 14.5, 14.6). NCERT Class 6 Math Homework NCERT Home task Class Six Easy Solution. Ncert board class 6 math.

Chapter 1 – Knowing Our Numbers

Chapter – 2 – Whole Numbers

Chapter – 3 – Playing With Numbers

Chapter – 4- basic Geometrical Ideas

Chapter – 5 – Understanding Elementary Shapes