Doing Math Online

Introduction to doing math online:

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 math problems online.

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Online math problems:


Example problem 1:

Simplify the expression: 20x + 6y - 14x - 10y - 2x - 2z

Solution:

20x + 6y - 14x - 10y - 2x - 2z

Add the like terms in the given expression

(20 - 14 - 2) x + (6 + (-10)) y - 2z

Simplify the expression

4 x - 4y - 2z

So, the answer is 4 x - 4y - 2z.

Example problem 2:

Evaluate the expression (-8 + y) × 5 + 40 ÷ 8 - y when y = 8.

Solution: Here, we substitute the value of 8 in the place of y,

(-8 + y) × 5 + 40 ÷ 8 - y becomes

(-8 + 8) × 5 + 40 ÷ 8 - 8 = 0 × 5 + 40 ÷ 8 – 8

= 0 + 5 - 8

= -3.

So, the answer is -3.


Few more online math problems:


Example problem 3:

Simplify the equation: 6x + 8 = 9x – 31

Solution:

6x + 8 = 9x – 31

Subtract 8 on both sides of the equation

6x + 8 - 8 = 9x – 31 – 8

6x = 9x – 39

Subtract 9x on both sides of the equation

6x – 9x = 9x – 39 – 9x

-3x = -39

Divide by -3 on both sides of the equation

`(-3x) / -3 = -39 / -3`

x = 13

So, the simplified answer is 13.

Example problem 4:

Find the distance between the two points (5, 10), (15, 17)?

Solution: Let d be the distance between A and B.

Then d (A, B) = `sqrt((x2 - x1)^2 + (y2 - y1)^2)`

= `sqrt((15 - 5)^2 + (17 - 10)^2)`

= `sqrt(10^2 + 7^2)`

= `sqrt(100+49)`

= `sqrt(149)`

= 12.2 units.

So, the distance between the given points is 12.2 units.

I have recently faced lot of problem while learning algebraic expression word problems, But thank to online resources of math which helped me to learn myself easily on net.

Online practice math problems:


1)      Simplify the expression:  1x - 11y + 9x - 6y. (Answer: 10 x - 17y)

2)      Solve for the variable x:  2(x + 1) = 32 + x (Answer: x = 30).

3)      Solve for the variable x:  2x + 12 = 12 (Answer: x = 0).