Learn Multiplication

Introduction for learn Multiplication:

In math, any two numbers can be manipulated by using operations. Basically, there are four different operators. Subtraction, addition, division and multiplication are the operations carried out. Here multiplication is an operator, which is denoted by (cross) × , (star) * . (dot) •. There are some basic rules for the multiplication of two numbers. In this article, we shall learn about multiplication operation. Also we shall learn to solve problems based on multiplication operation.

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Learn Multiplication Properties:

7 * 5 = 35

Here   7 is the multiplier

5 is the multiplicand

35 is the product.

For example:

3 * 5

Three times 5: 5 + 5 + 5 = 15.

Or five times 3: 3 + 3 + 3 + 3 +3 = 15

Properties of Multiplication:

There are several properties that are used while multiplying the given expressions.

1. Learn Distributive Property:

a * (b + c) = (a * b) + (a * c)

For example:

7 * (5 + 3) = (7 * 5) + (7 * 3)

Solution:

Left Handed Side  = 7 * (5 + 3)

= 7 * 8

= 56

Right Handed Side = (7 * 5) + (7 * 3)

= 35 + 21

= 56

Left Handed Side  = Right Handed Side

Hence the proof.

2. Learn Commutative Property:

a * b = b * a

For example:

7 * 5 = 5 * 7

Solution:

7 * 5 = 35

5 * 7 = 35

Both are same.

So 7 * 5 = 5 * 7

Hence the proof

3. Learn Associative Property:

a * (b * c) = (a * b) * c

For example:

7 * (5 * 3) = (7 * 5) * 3

Solution:

Left handed side:

7 * (5 * 3) = 7 * (15)

= 105

Right Handed side:

(7 * 5) * 3 = 35 * 3

= 105

Both are same.

So, 7 * (5 * 3) = (7 * 5) * 3.

Hence the proof

4. Learn Multiplicative Identity Property:

a * 1 = a

For example:

7 * 1 = 7

5 * 1 = 5

3 * 1 = 3

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Example Problems to learn Multiplication operations:


Example 1:

What is the Multiplication of 8 and 4.

Solution:

We can express the given problem as 8 * 4.

8 times 4 = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 32.

Or 4 times 8 = 8 + 8 + 8 + 8 = 32

Therefore the multiplication of 8 and 4 is 32.

Example 2:

What is the Multiplication of 9 and 3.

Solution:

We can express the given problem as 9 * 3.

9 times 3 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 27.

Or 3 times 9 = 9 + 9 + 9 = 27

Therefore the multiplication of 8 and 4 is 27.

Third Grade Math

Third Grade math:

The mathematics is the basic term. The grade 3 math are the included by arithmetic operations, and basic algebra. The grade 3mathematics contains multiplication, division, addition, subtraction, fractions and decimals, basic geometry, roman numbers. The following math based on the grade 3mathematics only.

Third Grade Time Facts:

1 day = 24 hr

1hr     = 60 min;

1 min  = 60 seconds,

1 hr    = 60 x 60 seconds = 3600 seconds

Third Grade multiplication:

The grade 3 multiplication is two parts these are the multiplicand, multiplier.

Third Grade Division:

The grade 3 division is three parts these are the dividend, quotient, divider, and reminder.

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Third Grade Math Examples:


Solve Third grade Math multiplication:

4487 x 4

Step 1:

Find the multiplier and multiplicand.

Multiplier = 4

Multiplicand = 4487

Step 2:

Start with left hand side to multiplicand to multiply by 4.

4487 x 4

1 7 9 4 8

Step 3:

Therefore the answer is 17948.

Third Grade Time Facts Example:

20 min =? Find how many seconds

Solution:

1 mins = 60 seconds

Therefore,

20 mins = 60 seconds x 20 = 1200 seconds

Answer:

20 min = 1200 seconds.

Example for expanding number:

Find the number 789 arrange the digits in a place value chart as shown below

Hundreds Tens Ones

7             8       9

Solution:

From the chart above, we see that:

The value of 7 is 7 x 100      = 700

The value of 8 is 8 x 10       = 80

The value of 9 is 9 x 1         = 9

Therefore, the expanded form of the number 789 is 700 + 80 + 9.

Third Grade Time Facts Example:

1 hr 20 min =? Find how many mins

Solution:

1 hr = 60 mins

Therefore,

1 hr 20 mins = 60 mins + 20 mins = 80 mins

Answer:

1 hr 20 min = 80 mins

Example for expanding number:

Find the number 1589 arrange the digits in a place value chart as shown below

Thousands Hundreds Tens Ones

1              5             8       9

Solution:

From the chart above, we see that:

The value of 1 is 1 x 1000   = 1000

The value of 5 is 5 x 100   = 500

The value of 8 is 8 x 10       = 80

The value of 9 is 9 x 1         = 9

Therefore, the expanded form of the number 1589 is 1000 + 500 + 80 + 9.

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Practice Problems for Third grade math:


Practice Problem 1:

Solve:

9854 x 4

Practice problem 2:

Expand the form 6795

Answer key:

39416
6000 + 700 + 90 + 5

Inequality in Math

Introduction to Inequality in math:
In math, inequality is a statement in relation to the relationship of a size or order of two items. In mathematical term, if the reason of the inequality is the equivalent for the all ideals of the variables for which are the members are distinct, and then the inequality is known as "unqualified" inequality. In this article we are going to see inequality examples.

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Example problems for Inequality:


Example 1:

Solve the inequality 2x+7 < 13.

Solution:

Given, inequality is 2x+7 < 13.

Subtract 7 with both sides, 2x+7-7 < 13-7

=>    2x  <  6

Divide 2 with both sides, `(2x)/(2)` < `(6)/(2)`

=> x < 3

The answer is, x < 3.

Example 2:

Solve the inequality 3x-2 > 16.

Solution:

Given, inequality is 3x-2 > 16.

Add 2 with both sides, 3x-2+2 > 16+2

=>    3x  >  18

Divide 3 with both sides, `(3x)/(3)` > `(18)/(3)`

=> x > 6

The answer is, x > 6

Example 3:

Solve the inequality x+3 `>=` 5.

Solution:

Given inequality is, x+3 `>=` 5.

Subtract the number 3 with both sides of inequality,

(x+3) - 3 `>=` 5 - 3

x  `>=` 2

The answer for this example is, x  `>=` 2.

Example 4:

Solve the inequality 7-x `>=` 8.

Solution:

Given inequality is, 7-x `>=` 8.

Subtract the number 7 with both sides of inequality,

(7-x) - 7 `>=` 8-7

-x `>=` 1

Multiply (-1) with both sides of an equation,

(-1) (-x)  `>=` 1 (-1)

When we doing this process, we need to change the symbol `>=`with `<=`.

Therefore, we get, x `<=`-1

The answer for this example is, x `<=`-1.

These are few examples in math inequality.

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Practice problems for Inequality:


Practice problem 1:

Solve the inequality x+3 < 2.

Answer: x < -1

Practice problem 2:

Solve the inequality 2-x > 0.

Answer: 2 > x

Practice problem 3:

Solve the inequality 3-x `>=` 5.

Answer: x `<=` -2

That's all about Inequality in math.

Math Assessments Geometry

Introduction to math assessments geometry:

Educational assessment is the process of documenting, usually in measurable terms, knowledge, skills, attitudes and beliefs. Assessments can focus on the individual learner, the learning community , the institution, or the educational system as a whole. (Source - Wikipedia)
In this article of math assessments geometry, math assessments questions and answers related to geometry are given. In addition, practice problems for math assessments are given.

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Math geometry assessments questions with answers:


1) Find the Circumference of a circle with radius 23 cm.

Solution:

Circumference of circle  = 2`pi`r

= 2 (3.14) 23

= 144.44 cm

2) Find the midpoint of the line joining ( 3, 7) and ( 6, 11 )

Solution: Given x1 = 3   x2 = 6

y1 = 7  y2 = 11

Midpoint =  ( `(x_1 + x_2)/2` , `(y_1 + y_2)/2` )

=  ( `(3 + 6)/2` , `(7+11)/2` )

=  ( `9/2` , `18/2` )

=  `( 4.5, 9 )`

3) Find the area of a square of side length 33.7 cm

Solution:

Area of a square  =  a^2

= 33.72

= 1135.69 cm2

4) Find the volume of cone given the radius is 11.4 cm and height is 12.7 cm.

Solution:

Volume of cone = 1/3 `pi` r2 h cubic units.

= 1/3  (3.14) * 11.42 * 12.7

=  0.33 * 3.14 * 129.96 * 12.7

=  1710.24 cm^3

5) Find the perimeter of the square with side length of 14.7 feet.

Solution:

Perimeter of square  = 4 * a

= 4 * 14.7

= 58.8 feet

6) The right triangle has the legs of  lengths 4 cm and 15 cm. what is the length of the hypotenuse?

Solution:       Given a = 4  and b = 15

By pythagorean theorem

c^2  =  a^2 + b^2

=  42 + 152

=  16 + 225

c^2   =  241

c = 15.52 cm

Length of the hypotenuse  =  15.52 cm

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Practice geometry assessments questions:


1) Find the Circumference of a circle with radius 13.5 cm.

2) Find the midpoint of the line joining ( 8, 14) and ( 12, 18 )

3) Find the area of a square of side length 20.5 cm

4) Find the volume of cone given the radius is 7 cm and height is 10 cm.

5) Find the perimeter of the square with side length of 22 feet.

6) The right triangle has the legs of  lengths 3 cm and 11 cm. what is the length of the hypotenuse?

Answers:

1) 84.78 cm   2) ( 10, 16 )    3) 420.25 cm^2   4) 507.74 cm^3   5) 88 ft   6) 11.4 cm

Geometry Math Activities

Introduction to Geometry Math Activities:

Geometry math deals problems with segments and construction terms.The term ‘Geometry’ meant for  a study of properties of figures such as shapes and  relationship for them. Geometry is the important branches of Mathematics. In real  life geometry plays very an important role from learning  that the concept of geometry have begun from ancient times. Geometry gives the ideas for many  geometrical shapes and figure construction.

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Geometry Math Activities Problems Square:


The area of a square A = side × side

Example 1:
The length of the side of a square table mat is 1 m 25 cm. Find the area for the mat.

Solution:
Length of the side of the square table mat=1m 25cm=125cm.
Hence, area of the mat = 125 × 125 sq cm
= 15625 sq cm

Example 2:
The length of square board side is 14 cm find its area

Solution:
Hence, area of the board = 14*14
=196 cm.
Example 3:
The floor of a room is in the form of a square of side 5 m. Find the perimeter.

Solution:
Side of the square=5m
The perimeter (P) of the floor is given by
P= 4×s
=4×5m = 20m
Thus, the perimeter of the floor of the room is 20 m.

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Geometry Math Activities Problems rectangle:


Area of Rectangle =length × Breadth
perimeter of a rectangle = 2 × length + 2 × breadth = 2 × (length + breadth)

Activities Problems Example 1:
The length of a rectangle board  12 cm and its breadth is 5 cm. Find  area for the rectangle.


Solution:
Length of the rectangle = 12 cm
Breadth of the rectangle = 5 cm
Hence, the area of the rectangle = 12×5sq cm=60 sq cm

Activities Problems Example 2 :
The length and breadth of a rectangular blackboard are 200 cm and 100 cm respectively. Find the perimeter.

Solution:
Length of the blackboard ( l) = 200 cm
Breadth of the blackboard (b) = 100 cm
Hence, perimeter (P) of the blackboard is given by
P = 2 × ( l+b)
= 2 × (200 cm + 100 cm)
= 2 × 300 cm = 600 cm
Thus, the perimeter of the blackboard is 600 cm.

Skills Tutor Math

Introduction to skills tutor math:

Let us study about the skills tutor math. The word tutor refers to a person who is teaching others about their doubts in various subjects through online which is a network connection that is made available all over the world.
The term skills tutor math is said to be as the method where we learn about various math problems with the clear explanations of their steps used to solve it.  Examples are discussed. Please express your views of this topic What is the Ratio by commenting on blog.

Example Problems - Skills tutor math:


Skills tutor math – Example 1:

Execute the division technique to calculate the ratio values for the number 13 by 52.


Solution:

Step 1: Given numbers: 13 and 52

Step 2: Follow the steps as given below to determine the ratio:

= `13/52`

= `1/4`

Step 3: Thus we have the calculate ratio of the given numbers 13 and 52 is 1:4.



Skills tutor math – Example 2:

To calculate the value of ‘g’ and to identify whether its value is positive or negative values carry out to calculate the equation which is given as 5g + 8 = -17.


Solution:

Step 1: Given equation: ‘5g + 8 = -17’.

Step 2: To calculate the value of ‘g’ follow the steps given below:

5g + 8 = -17

5g + 8 – 8 = -17 – 8 (‘1’ is subtracted on both sides)

5g = -17

`(5g)/5 = -25/5` (divide by ‘5’ on both sides)

g = -5

Step 3: By calculating the equation we obtained the value of ‘g’ as ‘-5’ – negative value.



Skills tutor math – Example 3:

Rajah is having 67 cakes with him and now he gave 41 cakes to his friends. Execute the steps that help to calculate the remaining number of cakes left with him?


Solution:

Steps 1: Given:

Rajah is having 67 cakes

Rajah gave 41 to his friends.

Step 2: To calculate the total number of cakes that Rajah have with him follow the steps as below:

= 67 – 41

= 26

Step 3: Thus the remaining number of cakes out of 67 that Rajesh have with him is calculated as ‘26’.

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Practice Problems - Skills tutor math:


Execute the division technique to calculate the ratio values for the number 24 by 30. (Answer: 4:5)
To calculate the value of ‘g’ and to identify whether its value is positive or negative values carry out to calculate the equation which is given as 8g + 1 = 17. (Answer: 2 – positive number)
Rajah is having 67 cakes with him and now he got 41 more cakes from his friends. Execute the steps that help to calculate the total numbers of cakes? (Answer: 108 cakes)

Math Number Model

Introduction to math number model:

Math number model is a math problem. Math number has real number, fractional number, natural number, integer, rational number, mixed number and decimal numbers. Number is basic for all the operation of math. Math number is satisfies or saying the real number construction. Let us see math model number in this article.


Math Number Model:


Math number model:

Math number model is a math problem like 8+2=_. Math number problem is helpful for understanding of math. The grade level kids learn the math number through the math number model.

Math number model is available for the following operations.

Addition
Subtraction
Multiplication
division

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Math Problem:

Math problem:

Math number model for addition:

Addition is one of the types of math number model. Here we use one dash. This dash is used to write the answer. Addition use two operands and one operator. We can put dash in operand place or the answer place. As like the following

Example:

2 + 1 = _
_ + 3 = 7
9 + _ = 15
Solution:

3
4
6
Math number model for subtraction:

Subtraction is one of the types of math number model. Subtraction use two operand and one operator. The following example explains the work of math number model in math problem.



Example:

5 – 2 = _
8 -_ = 4
_ - 6 = 4
Solution:

3
4
10


Math number model for multiplication:

Multiplication is one of the types of math number model. Multiplication use two operand and one operator. The following example explains the work of math number model in math problem.

Example:

6 * 4 =_
2 *_ = 16
_ * 7 = 21
Solution:

24
8
3
Math number model for division:

Division is one of the types of math number model. Division using two operand and one operator. The following example explains the work of math number model in math problem.

Example:

10 `-:` 2=_
25 `-:` _=5
_ `-:` 10=2
Solution:

5
5
20