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Class V - maths: Four Operations
One Word Answer Questions:
Q) Find the sum of the 432765 and 346056?
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Q) Find the difference of 98432 and 34567?
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Q) Fin dthe product of 39616 and 7?
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Q) Divide the following 81606 by 8?
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Q) In which property of addition when the order of the addends is changed, the sum remains the same?
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Q) Addition is finding the total or sum combining?
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Q) Finding the difference of two or more numbers is known as?
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Q) Multiplication can be defined as the?
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Q) Splitting into equal parts or groups is known as?
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Q) 436096 - 285766 =?
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Q) Find the product of the number 7777 * 19 = ?
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Q) The four basic mathematical operations are?
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Short Answer Questions:
Q) Write the Properties of Addition?
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Q) Write the properties of Subtraction?
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Q) Write the properties of Multiplication?
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Q) Write the properties of Division?
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Q) Explain about the Estimating Operations On Numbers?
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Q) What is Division?
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Q) What is Multiplication?
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Q) What is Subtraction?
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Q) What is Addition?
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Q) Add 34, 72, 514 and 26, 91, 015?
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Q) 12 + 9 - 14 * 6 / 3 = ?
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Q) Multiply 52917 by 4?
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Long Answer Questions:
Q) A factory produces 13,567 cars every month. How many cars are produced in 6 months?
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Q) 20 families went on a trip which cost them Rs 5, 34, 123. How much did each family pay?
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Q) What is the difference between the greatest 7-digit number and the smallest 8-digit number?
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Q) A carton can hold 16, 890 beads. If 9 such cartons are to be sent, what is the actual and approximate number of beads sent?
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Q) 1, 50, 345 bricks were used for Mr Sharms's house, and 2, 12, 345 bricks were used for Mr Verma's house. Whose house required more bricks and by how many?
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Q) Explain about the Estimating Operations On Numbers and give an example?
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Q) What is Addition an addition? Give an examples?
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Q) What is multiplication and division an addition? Give an examples?
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Q) Multiply 327 by 586?
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Introduction

There are four basic fundamental operations namely, addition, subtraction, multiplication and division.

Let us learn about these operations in detail.

The four basic mathematical operations are + , - , × , ÷.

The Four Fundamental Operations
Addition

"Addition is finding the total or sum combining two or more numbers"

Example:

The Four Fundamental Operations

Addition Of Larger Numbers

In order to find the sum of numbers, we have to add them.

Each number to be added in an addition is called an addend.

In an addition operation, we have two, three, four, or many addends.

The answer to an addition operation is called a sum

In order to find the sum of large numbers, the steps below are to be followed

  • Arrange the addends in the column form.
  • Start adding from the ones column, then move to the tens, and so on.
  • Regroup if required

Examples:

  1. Add 34, 72, 514 and 26, 91, 015.

Solution:

The Four Fundamental Operations

The process of above addition is the same as we add with the 6-digit numbers

We can add more than two addends and can also change the order of the addends. The sum will always be the same

  1. Add 62, 21, 238 ; 14, 653 and 3, 42, 36, 207 in two ways.

Solution:

The Four Fundamental Operations

Order is not changed             Order is changed

Properties of Additions

a)Order Property

When the order of the addends is changed, the sum remains the same.
1, 52, 286 + 34, 247 = 1, 86, 533 and
34, 247 + 1, 52, 286 = 1, 86, 533.

b)Zero Property

The sum of zero and the number is the number itself.
2, 34, 706 + 0 = 2, 34, 706
0 + 2, 34, 706 = 2, 34, 706

c)Grouping Property

The sum remains the same, even if the grouping of addends is changed.
(25000 + 4000) + 3000 = 32, 000
25000 + (4000 + 3000) = 32, 000
(25000 + 3000) + 4000 = 32, 000

Subtraction

"Finding the difference of two or more numbers is known as subtraction"

Example:

The Four Fundamental Operations

Subtraction Of Larger Numbers

In order to find the difference of two or more numbers, we have to subtract them.

The first number in subtraction is known as the minuend.
In the above example,(9 - 4 = 5), 9 is the minuend.

The number to be subtracted from the minuend is known as the subtrahend

In the above example, 4 is the subtrahend.

To subtract large numbers, we follow the steps given below:

  • Arrange the minuend and the subtrahend in column form.
  • Start subtraction from the ones column, regroup the digits if needed, then move to the tens column, and so on.
  • Arrange the numbers in columns by writing the greater number above the smaller number.

Example:

Subtract 8, 95, 56, 734 from 5, 72, 32, 610.

Solution:

The Four Fundamental Operations So, the answer is 3, 23, 24, 124.

Checking Subtraction

Addition is involved to check the accuracy of subtraction in such a way that:

  • Add the difference obtained and the subtrahend.
  • If the sum is equal to the minuend, the subtraction is correct.
  • Else there is a mistake in the calculation.

Example:

Subtract 3, 17, 25, 124 from 7, 24, 38, 297 and check the subtraction.

Solution:

First we will subtract both the numbers, and then add the difference to the subtrahend.

The Four Fundamental Operations
Properties of Subtractions
  • The order of the numbers involved in subtraction cannot be changed.
  • When a number is subtracted from itself, the difference is zero.
  • (Or)
  • When the minuend and the subtrahend are the same, the difference is zero.
  • Example:

  • 34, 46, 721-34, 46, 721 = 0.
  • Example:

  • When zero is subtracted from the number, the difference is the number itself.
  • 12, 98, 456-0 = 12, 98, 456.
Multiplication

"Multiplication can be defined as the process of repeated addition of a number".

Example:

The Four Fundamental Operations

Multiplying Larger Numbers

    In order to multiply larger numbers, we follow the steps below:

  • Start multiplying from the ones column.
  • Move to the tens column, add the carried over number if any, and so on.

Example:

Solution:

The Four Fundamental Operations

Multiplication Using The Expanded Form

Example:
Multiply 52917 by 4.

Solution:

This can be done by two methods

The Four Fundamental Operations

The table below shows multiplying of a number, by a 2- digit, 3 - digit and 4 - digit multiplier.

The Four Fundamental Operations
Properties of Multiplications
  • The product does not change even if the order is changed.
  • Example:

  • 234 × 192 = 44928 and 192 × 234 = 44928.
  • The product of any number and 1 is the number itself.
  • Example:

  • 365791 × 1 = 365791 and 1 × 365791 = 365791.
  • The product of a number and zero is zero.
  • Example:

  • 9723564 × 0 = 0 and 0 × 9723564 = 0.
  • Even if the grouping is changed, the product remains the same.
  • (43215 × 4) × 2 = 43215 × (4 × 2) = (43215 × 2) × 4 = 345720
Multiplication By Multipliers End with Zero

We know that,

  • A number when multiplied by 1 gives the number itself.
  • Example:

    5 × 1 = 5.
  • When a number is multiplied by 10, we put a zero to the right of the multiplicand to get the product.
  • Example:

    5 × 10 = 50.
  • In this way, when we multiply a number generally by 10, 100, 1000 etc., we put as many zeros to the right of the multiplicand as there are zeros in the multiplier.
  • Example:

    5 × 100 = 500 and 5 × 1000 = 1000.
  • This kind of multiplication where the number ends with zero can be done mentally with a little logic involved.

Example:

  • Multiply 50 by 40 mentally.
  • Solution:

    • Multiply the non-zero digits, 5 × 4 = 20.
    • Put as many zeros as there are in both the multiplicand and multiplier
    • The Four Fundamental Operations

      zero 1 zero 2 zeros

    2) Multiply 20 × 60 × 30.

    Solution:

    • Multiply the non-zero digits, 2 × 6 × 3 = 36.
    • Put as many zeros are there in all the three numbers.
    • So, the answer we get is 36000.

    3) Multiply 312 by 400 horizontally

    Solution:

    • Multiply the non-zero digits, i.e., 312 × 4 = 1248.
    • Put as many zeros as there are in the numbers.
    • Hence, 312 × 400 = 124800
    Lattice Multiplication

    Definition
    Lattice multiplication is a method of multiplying two numbers in a grid.
    The whole procedure is equivalent to regular long multiplication, but the advantage is that the lattice method breaks the process of multiplication into smaller steps.
    Let us learn the lattice multiplication of a 3 - digit multiplicand and a 3-digit multiplier.

    Example:

    Multiply 327 by 586.

    Solution:

    Since the multiplicand and the multiplier are 3- digit numbers, we draw a 3 × 3 square grid and divide each of the nine sub-squares with an oblique line.

    Steps to follow for lattice multiplication:

    • Write the digits of the multiplicand along the top horizontal side of the sub-squares.
    • Write the digits of the multiplier along the right vertical side of the sub-squares.
    • Multiply each digit of the multiplicand with one digit of the multiplier at a time.
    • Write the product by adding the sum (from the extreme right) of the numbers in each parallel.
    • The Four Fundamental Operations
    • So, the product of 327 × 586 = 191622
    Division

    "Splitting into equal parts or groups is known as division"

    Example:

    The Four Fundamental Operations

    Division Of Larger Numbers

    Let us see the division of numbers by 1- digit, 2- digit and 3 - digit divisors.
    The Four Fundamental Operations

    In all the three cases, the verifications are done by the following method:
    Dividend = Divisor × Quotient + Remainder

    1. 965 = 5 × 193 + 0.
    2. 965 = 965.
      Hence, verified.
    3. 5876 = 26 × 226 + 0
    4. 5876 = 5876.
      Hence verified.
    5. 27135 = 603 × 45 + 0
    6. 27135 = 27135.
      Hence, verified
    Division By 10,100 And 1000

    Example:

    There are 4560 books in 10 boxes. How many books are there in each box?

    Solution:

    456 ÷ 1 = 456
    So, 4560 ÷ 10 = 456

    The zero in the divisor divides the zero in the dividend.

    Example:

    Divide 25470 by 100.

    Solution:

    25470 ÷ 100.

    There are two zeros in the divisor. The digits in the dividend at the tens and ones place become the remainder and the rest of the digits will form the quotient.
    So, Quotient = 254 and Remainder = 70.

    Example:

    Divide 832567 by 1000.

    Solution:

    832567 ÷ 1000.

    There are 3 zeros in the divisor. The digits in the dividend at the hundreds, tens and ones place will form the remainder and the rest of the digits will form the quotient.
    Quotient = 832 and Remainder = 567.

    Properties of Division
    • If we divide a number by 1, the quotient is the number itself.
      367 ÷ 1 = 367.
    • If we divide a number by itself, the quotient is 1.
      367 ÷ 367 = 1.
    • If we divide 0 by a number, the quotient is 0.
    • Dividing a number by 0 does not make any sense

    Problem Solving Skills

    Before solving a problem, following points should be remembered

    1. Read the question carefully
    2. Understand the question thoroughly
    3. Find the facts given in the question
    4. Make a mental picture of the question
    5. Solve the question step by step
    6. Check the answer.
    Estimating Operations On Numbers

    Estimation gives us an approximation of required information which is close to the result
    Let us see the estimation of sum, difference, product and quotient of various Numbers.

    The Four Fundamental Operations
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