Easy Solving Math Problems

Introduction to easy solving math problems:

Mathematics is the vast area, which involves both simple problems and complex problems. Solving simple problems is very easy, because simple problems involves simple basic concepts and formulas. Once we understand the basic concepts and formulas, the simple problems are easy to solve.
In this article of easy solving math problems, some easy math problems are solved and in addition, easy practice problems are given.

Easy solving math problems:


Example 1:

Multiply:  ( x + 1 ) ( x + 4 )

Solution:

( x + 1 ) ( x + 5 )  =  x ( x + 5 ) + 1 ( x + 5 )

=  x2 + 5x + 1x + 5

=  x2 + 6x + 5

Example 2:

Calculate the perimeter of rectangle with the length and width are 12 cm and 14 cm.

Solution:

Perimeter   =  2( l+ w )

=  2( 12 + 14 )

=  2 (26)

=  52 cm

Example 3:

Find the area of a triangle with base of 10 m and a height of 4 m.

Solution:

Area of  triangle  = ½ b h

= ½ (11) (4)

= 22 m2

Example 4:

Find the volume of cube with the side length of 13 m.

Solution:

Volume of cube  =  a3

= 133

= 2197 m3

Example 5:

Simplify: 6x + 2(x – 4)

Solution:

6x + 2(x – 4)  =  6x + 2x - 8

=  8x - 8

=  8( x - 1 )

Example 6:

Find the range for the given set of numbers:

{ 7 , 12 , 14 , 17 , 20 }

Solution:

Range   =  Maximum value - Minimum value

=  27 - 10

=  17

Example 7:

Find the Mean of the given data set: { 4, 10, 12, 18 }

Solution:

Mean   =  ( 4 + 10 + 12 + 18 ) / 4

=  44 / 4

= 11

Example 8:

Find the Circumference of a circle with radius 22 cm. Use 3.14 as pie value.

Solution:

Circumference of circle  = 2`pi`r

= 2 (3.14) 22

= 138.16 cm

Example 9:

Michael bought a doll for `$` 13 and he sold it for `$` 17. What is his gain?

Solution:

Cost price of doll   =  $ 13

Selling price of Clock  =  $ 17

Profit  or  Gain   =  Selling price - Cost Price

=  17 - 13

=  $ 4


Easy solving practice problems:


1) Multiply:  ( x + 2 ) ( x + 3 )

Answer: x2 + 5x + 6

2) Simplify: 2x + 3(x – 2)

Answer: 5x - 6

3) Find the volume of cube with the side length of 5 m.

Answer: 125 m3

4) Find the Mean of the data set: { 1, 3, 6, 10 }

Answer: 5

5) Find the Circumference of a circle with radius 11 cm. Use 3.14 as pie value.

Answer: 69.08 cm

1st Grade Math Fractions

Introduction of 1st grade math fractions:

The 1st grade math fractions are nothing but the fractions that is made to have the meaning of the numerator and the denominator. The numerator and the denominator play the important role in the fractions which gives the reducing of the fractions. Let us see the fraction that involves in the first grade. The 1st grade math fraction gives the simple fraction which gives the basic ideas of the fraction.

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1st grade math fractions:


This gives the each area mentioned in the red color which is the equal fractions or the equal amount. Therefore we have an idea ½ is made equal to the 2/4 and ½ is made equal to 4/8. For our reference when an apple is made to cut exactly down the middle, into two equally pieces, the first piece is identical to the one half of the apple. When the another apple is made into 4 equal pieces, then the two pieces of that apple shows the identical part of the apple that shows ½ , Hence we can say that ½ is made equal to 2/4. The fractions that are made to have the part whole number relationship.

The part whole number of a fraction of the number like 1/5 can be done through the whole number that requires the five equal parts and the one of these parts that is being considered. Let us have the briefing of the quotient or the ratio. The quotient is nothing but the term that has the 2/3 in which the 2 is the numerator and the 3 is the denominator. The method can be mentioned as 2/3. The ratio is made to have the briefing that gives the situation on it. Hence there are two boys or the every three girls in the team hence in this case two-thirds of the teams are boys.

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Examples for 1st grade math fractions:


Example 1: Sum up the two fractions (1/2 + ½)

Solution: ½ + ½ = 2/2.

Answer = 1.

Example 2: Sum up the two fractions (3/2 + ½)

Solution: 3/2 + ½ = 4/2.

Answer = 2.

Help Solve Math Problems

Help in solving math problems:

In this article we help how to solve the math problem in step by step. In math problems solving is the processes of simplification. We can say that, mathematics is mostly involved and experienced the process called solving. The math problem involves some operation known as monomial, polynomial degree equations solve method. Now we help you to solve some monomial, polynomial as a linear equation and the solving them and explained step by step for clear understanding.

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Help in solving monomial math problems:


Math help to solve the monomial problems

Solve: 12x + 9

Step 1: First write the equation, in this equation we have to find the variable of x

12x + 9

Step 2: Put 12x + 9 = 0

12x + 9 = 0

Step 3: subtract 9 on both side

12x + 9 – 9 = 0 -9

12x = -9

Step 4: divide 12 on both side

`(12x)/(12)` = `(-9)/(12)`

x = ` -3/4`

Let us we help you in another similar math problems.

Solve: 12x - 9

Step 1: First write the equation, in this equation we have to find the variable of x

12x - 9

Step 2: Put 12x - 9 = 0

12x - 9 = 0

Step 3: Add 9 on both side

12x - 9 + 9 = 0 + 9

12x = 9

Step 4: divide 12 on both side

`(12x)/(12)` = `(9)/(12)`

x = `3/4`

Therefore value of x = `3/4`

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Help in solving polynomial math problems:


Math help for the polynomial math problem:

Example: solve by factoring x^2 - 20x + 100 = 0

Solution:

Step 1: First write the equation, in this equation we have to find the variable of x

x^2 - 20x + 100 = 0

Step 2: Split the middle value -20 into -10 and -10 when we add both, we get -20, If we multiply -10 with -10 we get 100, therefore the factor is

x^2 -10x -10x + 100 = 0

Step 4: now take the common values out.

x(x- 10) -10(x -10) = 0

(x -10) (x – 10) = 0

Step 5: now separate the values and it is equal to zero

x – 10 = 0 →(1) ;  x -10 = 0 → (2)

Step 6: Add 10 on both side of the equation (1) and (2)

For equation (1)

x -10 + 10 = 0 + 10

x = 10

For equation (2) the same

x = 10

The answer for the math problem is x =10


Practice problems:


1) Solve: 3x + 9 = 0

2) Factor x^2 + 3x + 2 = 0

Answer:

1) x = -3

2) x = -1, -2

Learn Acceleration

Introduction to learn acceleration:-

Learn acceleration is the rate of alteration of velocity with respect to time. In math word acceleration can be define the rate at which a point speeds up or speeds down. The unit of measurement used for acceleration as per SI units is m/s^2. In math, the word acceleration is used to represent an increase in speed and a decrease in speed is known as deceleration. Galileo was the first to discover that objects falling to earth have a constant acceleration which is known as acceleration due to gravity, denoted by ‘g’ and has a value of 9.79 m/s^2.

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Types of learn Acceleration:-


There are two types of learn acceleration:-

• Instantaneous acceleration

• Average acceleration.

The ratio of the change in velocity and time interval is known as Average acceleration and instantaneous acceleration is the change in velocity at one time.

Acceleration can also be determined using the formula F= m A.

Where F = force,

m is the mass of the object.

A is the acceleration.

This is according to the Newton’s second law of motion, which states that a body experiences a force ‘F’ while experiencing an Acceleration ‘A’, given by the equation F= mA where m is the mass of the body.

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Example problems for learn acceleration:-


Learn Acceleration is calculated using the formula A= Change in velocity/ Time

Learn acceleration problem1:-

A car accelerates from 15 m/s to 20 m/s in 5 seconds. What is the car’s acceleration?

Solution:-

Acceleration = Change in velocity/Time

A = 20 – 15/ 5

= 5/5

= 1

And on simplifying, we get

= 1 m / s^2

Learn acceleration problem2:-

A car accelerates from 30 m/s to 50 m/s in 10 seconds. What is the car’s acceleration?

Solution:-

Acceleration = Change in velocity/Time

A = 50 – 30/ 10

= 20/10

= 2

And on simplifying, we get

= 2 m / s^2.

Learn Numbers for Kids

Learn numbers for kids –Introduction:

A number is a mathematical object used in counting and measuring. A notational symbol which represents a number is called a numeral, but in common usage the word number is used for both the abstract object and the symbol, as well as for the word for the number. In addition to their use in counting and measuring, numerals are often used for labels. (Source Wiki)



Learn numbers for kids – Types:


Natural numbers

Integers

Rational numbers

Real numbers

Complex numbers

Computable numbers

Natural Numbers:

The natural Numbers are the numbers. This is the most common numbers are the natural numbers.

That is: one, two, three, four, …..n this is the natural numbers

Integers:

The integers are if less than 0 and same as the positive side.

That is: -n . . . . . . -4, -3, -2, -1, 0, 1, 2, 3, 4 . . . , +n

Rational Numbers:

A rational number is a digit that can be in the form y/z where y and z are digits and z is not equal to zero.

A rational number is:

X/Y

Where y is not zero

Real Numbers:

The real numbers are including all of the calculating numbers. Real numbers are usually write using decimal numbers, in which a decimal point is located to the right of the number with place value one.

That is: 123.5567

Complex numbers

Complex numbers of the form i{y}, where y is a non–zero real number are called imaginary numbers.

a+ bi, bi = imaginary number

Computable numbers

The computable numbers are the set of all real numbers.


Learn numbers for kids – Examples


Learn numbers for kids – Example 1:

Adding the two real number 325.87 + 687.45

325.87
+687.45
1013.32
Answer:

1013.32

Learn numbers for kids – Example 2:

Multiplying natural numbers and the complex numbers 3 (4 + 8i)

Solution:

3 x (4 + 8i)

= 12 + 24i

Answer:

12 + 24i

Learn numbers for kids – Practice Problems:

Multiply the two integer numbers: -8 x 64

Answer:

-512

Integer Length in Math

Introduction:

Definition integer:

Integers are the numbers with either positive or negative sign. Integer includes natural numbers and whole numbers also. Fractions are numbers that does not include in integer. Integer can be represented from negative numbers to positive numbers.

Example   …….-3, -2, -1, 0, 1, 2, 3, ………………

Integer Length in math:

Integer length is the number of digits of an integer. For example consider the number 54876. In this example the length of the given number is 5 since it consists of 5 digits. Integer length is nothing but the number of bits. Integer length is the number of place digits in a given number.

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Example of Integer Length


Find the integer length of the number given below.

542316

Solution

Here the number of bits of numbers given is 6. So the integer length of the number 542316 is 6.

There is also the possibility of increase in integer length in math.

In the case of performing arithmetic operations like addition and multiplication the integer length will increase.

Example 1. Find the sum of 548 + 736 and find the integer length of the answer obtained.

Solution

5 4 8
7 3 6 +
----------
1 2 8 4
-------------

Here the length of the integer is 4.

Example 2. Find the product of 578 * 21

Solution:

5 7 8

2 1 *
------------------
5 7 8
1 1 5 6
--------------------
1 2 1 3 8
--------------------

Here the integer length is 5

Example 3. Find the difference 9875 – 2456

Solution:

9 8 7 5

2 4 5 6 -

----------------
7 4 1 9
------------------

Here the integer length is 4


PROBLEMS ON INTEGER LENGTH


Find the integer length of the following problem after performing the given arithmetic operation.

Add a) 5894 + 654
b) 124356+54120

2.  Subtract a)6548-3546

b)7812 - 120

3.  Multiply a) 456*23

b) 1596*324

4.  Divide   a) 625/5

b)1100/11

Answers:

1. a) 4     b)6

2. a) 4     b)4

3. a)5      b)6

4. a)2      b)3

Grade 9 Math

Introduction of grade nine fraction math:

The grade nine fraction maths is nothing but the fraction that involves the division, multiplication and subtraction. The grade nine fraction maths gives the most basic ideas of the fractions. Thus the fraction of the math gives the various topics and understandings of the math. The grade nine fraction math gives you various formation of the reduction of the fraction.

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Grade nine fraction math:


Grade nine fraction math are the one which makes the form that gives the changes that shows the form in the fraction method. When the method gives the comparing of the two terms. The comparisons of the terms are the one which gives the changes that makes the form of the terms in the comparison of the two fractions. Hence we can find the largest and the smallest terms when compared between the two terms.


Examples for grade nine fraction math:


Example 1: Compare the two fractions 3/4 and 1/6?

Solution: When comparing the two fractions we found that 3/4 is greater than the 1/6.

Example 2: Compare the two fractions 4/5 and 2/2?

Solution: When comparing the two fractions we found that 4/5 is lesser than the 2/2.

Example 3: Compute the fractions with regrouping in the fractions like “1/80 + 4/80 + 9/80 + 6/80” is made to regrouping as “1/80+9/80 +6/80+4/80” the second terms are considered as simpler one these terms leads to the sum of ten [(1+9)/80, (6+4)/80] this made easier to keep the track off.

Example4: Compute the fractions with regrouping like “3x/80 + 2y/80 + 4x/80 + y/80 = 7” hence the regrouping of the x and y terms which can be made simpler.

This can be regrouped as 7x/80 + 3y/80 = 7.

Example 5: The 2 39 reduced to a fraction is obtained as the terms, 2/39 this terms can be prepared through the terms 2/39 = 2/39.

1) The given fraction 2/39 is not made to reduce to the lowest terms. Hence the fractions cannot reduce to the lowest terms.

2) The above terms cannot be reduced with the common terms.

Example 6: The 45 reduced to a fraction is obtained as the terms, 45/100 this terms can be prepared through the terms 45/100 = 9/20.

1) The given fraction 45/100 is not made to reduce to the lowest terms. Hence the fractions are reduced to the lowest terms.

2) The above terms can be reduced with the common terms like 5.

3) The value 5 is the greatest common divisor or the greatest common factor of the both numbers 45 and 100.

4) Hence the 45/100 can be reduced through the value five which results to the 9/20.