Approaches to Problem Solving

Introduction to approaches to problem solving:-

In this article we are going to see the important approaches to problem solving. Algebra is a cluster of math, we use script like a, b, x and y to denote numbers. In Algebra we execute count, division, increase, allotment, extraction of roots and substituting. Variables and numbers used as real numbers, algebra is unique, importance and computational skills we obtain what are called algebraic expressions.

Simple approaches to solving- Example problems:-

Approaches to solving- Example problem1:-

Solve - 2 (x + 3) = - 10

Solution:-

Solving algebraic equation

- 2 (x + 3) = - 10

-2x – 6 = -10

-2x = - 10 + 6

-2x = - 4

x = 2.

Approaches to solving- Example problem2:-

5 ( x + 2 ) + 3 ( x – 2 ) = 10

Solution:-

Solving algebraic equations

5 ( x + 2 ) + 3 ( x – 2 ) = 10

5x + 10 + 3x – 6 = 10

5x – 3x + 10 - 6 = 10

2x + 4 = 10

2x = 10 – 4

2x = 6

x = 6/2

x = 3.

Approaches to solving- Example problem3:-

-2( x + 4 ) + 3 ( x + 2 ) = 4x + 20

Solution:-

Solving algebraic equation

-2( x + 4 ) + 3 ( x + 2 ) = 4x + 20

-2x – 8 + 3x + 6 = 4x + 20

-2x + 3x - 8 + 6 = 4x + 20

x - 2 = 4x + 20

x - 4x = 2 0+ 2

- 3x = 22

x = -22/3.

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Approaches to solving- practice problems:-

Problem 1:-

Solve 3x -2(2x - 5) = 2 (x + 3) - 8

Answer:-

x=4.

Problem 2:-

3 (x - 3) = 5(2x+1)

Answer:-2.

Problem 3:-

Solve 15 (m - 4) - 2 (m - 9) + 5 (m + 6) =0

Answer:-

2/3.

Math Children Computer

Introduction to math children computer:

Math children computer is the help through computer to the children in math. Chidren when they solve math homework problems they come across lot of difficulties as the online tutoring websites help children in solving their problems. Tuotr vista is one of the best online tutoring website that help in math shildren in online through computer. Here in this article let us see sample problems solved from tutorvista  for math children computer.

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Math children computer:


Basic algebra problems:

Example 1 :
What is the sum of 7 and 8? Express this statement by using place holder.
Solution :

We can write this statement, in short, as
7 + 8 = ?.

The answer for this problem would be 7 + 8 = 15.

Example 2 :
What number added to 10 will give 15?
Solution :
It is 10 + x = 15

Example 3 :
Rabi has 18 rupees. She buys vegetables for 8 rupees. Find the remaining amount she will have in her hands.
Solution :
We can write it as 18 – 8 = ?

The answer for this problem would be 18 - 8 = 10.

Example 4 :
Find the product of 5 and 12
Solution :
5 × 12 =?

The answer for this problem would be 5 × 12 = 60.

Example 5 :
When a number is multiplied by 4, the product is 116
Solution :
x × 4 = 116.

x = `116 / 4` = 29.

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Math children computer:


Example 6:
What is the sum of 9 and 10? Express this statement by using place holder.
Solution:

We can write this statement, in short, as
9 + 10 = ?.

The answer for this problem would be 9 + 10 = 19.

Example 7:
What number added to 12 will give 17?
Solution:
It is 12 + x = 17
The answer would be x = 17 - 12 = 5.

Example 8:
Rabi has 28 rupees. She buys vegetables for 12 rupees. Find the remaining amount she will have in her hands.
Solution:
We can write it as 28 – 12 = ?

The answer for this problem would be 28 - 12 = 16.

Example 9:
Find the product of 6 and 12
Solution:
6 × 12 =?

The answer for this problem would be 6 × 12 = 72.

Example 10:
When a number is multiplied by 4, the product is 84
Solution:
x × 4 = 84.

x = `84 / 4` = 21.

Basic Mathematics Solving Online

Introduction to learn for solving online basic mathematics

Mathematics is used in many fields like, engineering, science, and medicine. Through online we can easily solving the problems quickly. Through online student can get help and learn at any time. In basic math the students can receive first level of math education called primary education. Through online students can get more help and easily understand the problems. In this article we shall discuss to learn for solving basic mathematics example problems.

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Learn for solving online basic mathematics example problems


Example:

Solve the expression 6x + 12y - 4 + 3x + 5y + 10

Solution:

• +6x and +3x are like terms, and combined to get +9x,

• +12y and +5y combine the like terms to get +17y, and

• -4 and +10 combine the like term and get +6

So after simplify, the expression:

9x + 17y + 6

Example:

The cost of 8 fruits is `$` 120; find the cost of 15 fruits.

Solution:

Step 1:

Consider the given problem as if the 8 fruits cost is `$` 120. Find the cost of 15 fruits?

Step 2:

8 fruits cost =120

15 fruits cost = 15/8 x120

=225

Answer:

Therefore the cost of 15 fruits is `$` 225

Example:

Solve the equations 6x-12=3x+6

Solution:

Step 1:

Given equation

6x-12=3x+6

Step 2:

Add 12 on both side of the equation

6x-12+12=3x+6+12

6x=3x+18

Step 3:

Subtract 3x on both side of the equation

6x-3x=3x-3x+18

Step 4:

Simplify the x value

3x=18

x=`18/3`

Answer:

Therefore x=6

Example:

The length of the rectangle is 140 cm and breadth is 60cm find the area of the rectangle.

Solution:

Rectangle length, l         = 140 cm

Rectangle breadth, b     = 60 cm

Area of the rectangle = l x b

Therefore 140 x 60 = 8400 sq.cm

The area of the rectangle is 8400 sq.cm

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Learn for solving online basic mathematics practice problems


Problem:

Solving the expression 6x + 12y - 4 + 2x + 3y + 8

Answer:

8x + 15y + 4

Problem:

Solving the equation 10x – 36 = 6x + 4

Answer:

x =10

Problem:

The cost of 6 fruits is `$` 120; find the cost of 20 fruits.

Answer:

Cost of 20 fruits is `$` 400

Word Problems in Math

Introduction to word problems:

Word Problems are the main chapter in 2nd grade math. These 2nd grades math involves basic arithmetic word problems. The basic arithmetic operations are add, subtract, multiply and divide. In this topic we have to seen about the addition and subtraction and multiplication and division word problems. Usually word problems are difficult here these 2nd grade math problems are very simple to study.

Example Word Problems in 2nd grade math

Example 1:

If the cost of 2 cakes is Rs.6 and the cost of one milk shake is Rs.20. Calculate the total price of cake and milk shake.

Solution:

The cost of 2 cakes = Rs.6

The cost of one milk shake = Rs.20

The total price of cake and milk shake = 6 +20.

Here + is the addition operation that is used for adding purpose.

Total price = Rs.26.

Example 2:

Ram has 5 pieces of pizza. He shares to 2 pieces of pizza to his sister. Calculate the remaining number of pizza.

Solution:

Total number of pieces = 5

Left out pieces = 2

Remaining number of pieces = 5 – 2

That is 3.

Here - is the subtraction operation that is used for subtracting purpose.

Example 3:

If the price of one ball is 20 dimes. Find the price of 5 balls.

Solution:

The price of one ball = 20 dimes

Therefore the price of 5 balls = 5 x 20

That is 100 dimes.

Here X is the Multiplication operation that is used for multiplication purpose.

Example 4:

If the rate of 10 bobby dolls is 100. Calculate the rate of 1 bobby doll.

Solution:

The rate of 10 bobby dolls = 100

We have to calculate the rate of 10 bobby dolls. For this we can do the division.

Therefore, the rate of one bobby doll = 100 / 10

Here / is the division operation that is used for dividing purpose.

These are the main types of word problems in 2nd grade math.

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Practice Problems


1. There are 5 apples and 15 jack fruits.  Find the total number of fruits.

Answer: 20 fruits

2. One bun costs 7 dimes Find the rate of 15 buns.

Answer : 105 dimes

3. The cost of 1 kg of carrots be dollar 12 find the cost of half kg of carrots.

Answer : 6 dollars

Equivalent Definition Math

Introduction to equivalent definition math:

The equivalent is the term in the mathematics. It defines the equivalent definition fractions math and the equivalent ratio for the numbers. The fraction of the two numbers has the equivalent fraction for the fraction of other two numbers. Here we are going to see about the equivalent fraction for the two numbers.The equivalent fraction may be find by the common multiplication or the division of the common number in both numerator and also the denominator. I like to share this Derivatives Table with you all through my article.


Example problems for equivalent definition math:


Example 1 for equivalent definition math:

Find the equivalent fraction for `2/5` .

Solution:

The given fraction is `2/5` .

We have to find the equivalent triangle, for that we multiply or divide the numerator or the denominator by the common number to get the equivalent fraction.

Multiply the above fraction by 5 on the denominator and also numerator

`2/5`  `xx` `5/5` = `10/ 25`

Multiply the given fraction by 3 also we get the equivalent fractions.

`2/5`  `xx` `3/3` =` 6/ 15`

Divide the given fraction by 4 to get the equivalent fractions.

`2/4``-:` `5/4`= (`2/4` )/ (`5/4` )

`2/4``-:` `5/4`   = `2/5`  `xx` `4/4`

`2/4``-:` `5/4`   = `8/20`

Divide the given fraction by 8 to get the equivalent fraction.

`2/8``-:` `5/8`  = (`2/8` ) / (`5/8` )

`2/8``-:` `5/8` =` 16/40`

The equivalent fractions of `2/5 ` are `10/ 25` ,` 6/ 15` , `8/20` and `16/40` .


Example 2 for equivalent definition math:

Find the equivalent fraction for `4/7` .

Solution:

The given fraction is `4/7` .

We have to find the equivalent triangle, for that we multiply or divide the numerator or the denominator by the common number to get the equivalent fraction.

Multiply the above fraction by 2 on the denominator and also numerator.

`4/7` `xx`` 2/2` =` 8/ 14`

Multiply the given fraction by 5 also we get the equivalent fractions.

`4/7` `xx`` 5/5` = `20/ 35`

Divide the given fraction by 3 to get the equivalent fractions.

`4/3``-:` `7/3` = (`4/3` )/ (`7/3` )

`4/3``-:` `7/3` = `4/7`  `xx` `3/3`

`4/3``-:` `7/3` = `12/21`

Divide the given fraction by 9 to get the equivalent fraction.

`4/9``-:` `7/9`  = (`4/9` ) / (`7/9` )

`4/9``-:` `7/9` = `36/63`

The equivalent fractions of `4/7 ` are `8/ 14` , `20/ 35` , `12/21` and `36/63` .

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Practice problem for equivalent definition math:


Find the equivalent fraction for `1/7` .
Answer: `2/14` , `4/28` , `5/ 35` .

Basic Subtraction Fraction

Introduction-basic subtraction fraction:

Study fraction math (from the Latin fractus, broken) is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (`1/2`, `5/8`, `3/4`, etc.) and which consist of a numerator and a denominator in study fraction math.

Source: Wikipedia

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Definition-basic subtraction fraction:


Fractions are frequently used in mathematics, science and the world impressive like us. They have been used by human sovereign whereas the time of the new Egyptians and are still used by public to solve problems in their day-by-day lives.

Fraction math came into regular use in the 16th century. Look at this study fraction math:

`25/50`

Solve subtraction of fraction with same denominators:

Just as we subtract fractions, we can take off numbers with same denominator.

Example:

`5/2`-`3/2`=?

Solution:

= `5/2`-`3/2`

=`(5-3)/(2)`

=`2/2`

=1

Solve subtraction of fraction with different denominators:

Just as we subtract fractions, numbers also can be taking from with unlike denominators. The common denominator is realized by finding out the LCM.

Example:

`4/2`-`5/3`=?

Solution:

=`4/2`-`5/3`                                              (we need to take LCM of 2 and 3)

=`(12-10)/(6)`                                         (we need to perform subtraction operation)

=`2/6`                                                 (divided by 2, both the numerator and denominator)

=`1/3`                                                 (then, we get result)

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Example- basic subtraction fraction:


Example 1:

If Sam get `$15` in a day and pay out `$10` , what part of his weekly pay did he keep?

Solution:

Step 1: Numerator: amount saved=15-10=5

Step 2: Denominator: salary = $15

Step 3: Part or fraction

=`(15-10)/(15)`                                             (we need to perform subtraction operation)

= `(5)/(15)`                                                  (divided by 5, both the numerator and denominator)

=`1/3`                                                     (then, we get result)

Answer is `1/3`

Example 2:

`12/4`-`2/3`=?

Solution:

=`12/4`-`2/3`

=`6/2`-`2/3`                                                    (we need to take LCM between 2 and 3)

=`(18-4)/(6)`                                                  (we need to perform subtraction operation)

=`(14)/(6)`                                                       (numerator and denominator are divided by 5)

=`7/3`                                                         (then, we get result)

Answer is `7/3`

Inequality Math

Introduction to inequality in math:

In mathematics, an inequality is a statement about the relative size or order of two objects or about whether they are the same or not. (Source : Wikipedia).In inequality we are using many number of mathematical symbol and each one represent the particular operation. I like to share this Compound Inequality Solver with you all through my article.

>  greater than symbol

<  less than symbol

>=  greater than or equal to

<= less than or equal to

=  equal to

!= not equal to

Here we are going to study about how solve the inequality problems and its example


Math example problems:


Example: 1

Solve the following inequality equation.

4x+3+2x +5 < 2x+4

Solution:

In the left hand side combine the like term first

4x+3+3x +5 < 2x+4

7x + 8 < 2x + 4

Add both sides -4 we get

7x + 8 - 4 < 2x + 4 - 4

In right hand side 4 - 4 will be cancelling

7x+ 4 < 2x

Add both sides -2x

7x -2x + 4 < 2x -2x

5x + 4 < 0

Add both sides -4 we get

5x + 4 -4 < -4

5x < -4

Divide both sides 5 we get

(5x / 5) < - `(4/5)`

x < - `(4/5)`

Therefore the x value less than - `(4/5)`

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math example : 2


Solve the following inequality 2x - 23 > x - 4

Solution:

First we have to solve the x value

Add both sides +4 we get

2x - 23 +4 > x + 4 – 4

In right hand side 4 - 4 will be canceling

2x - 19 > x

Add both sides 19 we get

2x + 19 -19 > x + 19

2x > x+19

Add both sides –x we get

2x – x > x-x +19

x > +19

Here the greater than symbol represent the x value greater than 19 that is 20, 21, 22 ……