# Problem Solving Skills

Introduction :

In this lesson we can understand how to solve problems and devolving math problem solving skills. It is helping you to improve problem solving skills. In mathematical terms we can see different types of problem solving skills. Following statements are describing about the problem solving skills. Let us see few of the basic operation problem solving skills.
Solving Skills:

Fraction:  A fraction describes a group of numbers. It numbers between 0 and 1 or 1 and 2 etc. Fraction retrieve from a division of a whole number like 2/ 3   Let us see some fraction problem and how to solving method.

Problem solving skills1:

Solve: `(5)/(6)`  + `(5)/(3)`

Solution:

Above problem is showing fraction addition. So we should solve this problem in fraction addition operation.

Step 1: `(5)/(6)`  +  `(5)/(3)`

Here numerator values are same, but denominators are different. So we should take LCM then only we can add both values. (We can take LCM if denominators are different).

Step 2:  `(5)/(6)`  + `(5)/(3)`

Take LCM to 6, 3 (therefore LCM is 6)

we have to change denominators values like 6.

Step 3: `(5*1)/(6*1)` = `(5)/(6)`  ,  `(5*2)/(3*2)` = `(10)/(6)`

= `(5)/(6)` + `(10)/(6)`

Now denominators are same so add both values

Step 4: `(5)/(6)`  +  `(10)/(6)`

=`(15)/(6)`

Therefore  `(5)/(6)` +  `(5)/(3)` = `(15)/(6)`

Algebra: Algebra is defined as the part of mathematics which includes the study of laws of the operations that includes the equations and various structures including polynomials. Let us see some algebra problem and how to solving method.

Problem solving skills2:

Find b value: 5(b + 6) + 12 = 3b + 2

Solution: In the above problem we have to find b value

Step1:  5(b + 6) + 12 = 3b + 2

Multiply 5(b+6)

Therefore 5b +30 + 12 = 3b + 2

Step 3: simplify 5b +30 + 12 = 3b + 2

5b + 42 = 3b + 2 (add – 42 by both sides)

5b +42 – 42 = 3b +2 – 42 (remove combine terms Like -42 + 42 = 0)

5b = 3b -40

Step 3: Add -3b by both sides

5b -3b = + 3b - 3b - 40 (remove combine terms Like (+3b -3b= 0)

2b = -40

b= -40 / 2

b = -20

Step 4: Therefore b values is -20.
Pythagoras' Theorem:

Hypotenuse is longest sides of triangle. The square of the hypotenuse is equal to the sum of the square of the other two sides. Therefore a2 + b2= c2

Problem solving skills 3:

Solve this angle

Solution:

Step 1: here we can find c value using Pythagoras formula.

a^2 + b^2= c^2

Step 2:  We know a and b values substitute the given values:

3^2 + 4^2 = c^2      (32 = 9   || 42 = 16)

9 + 16 = c^2

25 = c^2         (take root)

5 = c

Step3: Therefore c values is   c = 5
Practice Problem:

1)      2(6n + 4 ) + 2 = 10 n + 8   Answer: n = - 1

2)      Solve: 256/12 + 569 / 12   Answer:  825

3)      Solve : 6/16+4/12             Answer: 15/24