Math Problem Solving

Introduction to math problem solving:

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. (Source: From Wikipedia). Now, we are going to see some of the solving problems in math.

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Solving math problems:


Example problem 1:

Solve the equation for x: 5x + 20 = 8x + 50

Solution:

5x + 20 = 8x + 50

Subtract 20 on both sides of the equation

5x + 20 - 20 = 8x + 50 – 20

5x = 8x + 30

Subtract 8x on both sides of the equation

5x – 8x = 8x + 30 – 8x

-3x = 30

Divide by -3 on both sides of the equation

-3x / -3 = 30 / -3

x = -10

So, the answer is x = -10.

Example problem 2:

Simplify the expression: 12x – 12 + 22x - x + 22

Solution:

Add the like terms in the given expression

12x – 12 + 22x - x + 22 = 12x + 22x - x – 12 + 22

= (12 + 22 -1) x + (-12 + 22)

= 33 x + 10

So, the answer is 33x + 10.

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Few more solving math problems:


Example problem 3:

Length and breadth of a rectangle are 20 cm and 13 cm respectively.

(i) Find its area.

(ii) Find its perimeter.

Solution:

(i)    Area of the rectangle = Length × Breadth

= l × b

= 20 * 13

= 260 Sq. cm.

(ii)Perimeter of rectangle = 2 (l + B)

= 2 (l + b)

= 2 (20 + 13)

= 2 * 33 = 66 cm.

So, the answer is

(i) Area = 260 sq. cm.

(ii) Perimeter = 66 cm.

Example problem 4:

Two angles of a triangle are of measures 80 and 42. Find the measure of the third angle.

Solution:

Let us take the third angle be x.

Sum of three interior angles of the triangle is 180 degrees.

80 + 42 +x = 180 degree

By solving this, we get

122 + x = 180 degree

Subtract 122 on both sides, we get

122 + x - 122 = 180 – 122

x = 58 degrees.

Practice math problems with answers:

1)  Two angles of a triangle are of measures 70 and 42. Find the measure of the third angle.(answer: 68 degrees)

2)  Solve the equation for x: 10x + 20 = 8x + 50 (Answer: x=15)