Problem Solving Loop

Introduction to problem solving loop:

Problem solving loop is the situation where there is a struck in betweeen the problem and thinking how to solve the loop that is that situation of difficulty to continue with the problem. Method for problem solving loop is to learn the  basic formulas and method of solving that math problems, then see the solved problems of that similar type. Now we get an idea of how to solve that problem then try to solve that problem step by step. Let us see problems that you feel loop may occur for problem solving loop. I like to share this Binomial Probability Problems with you all through my article.

Problem Solving Loop:

Example 1:

If four times of a number is equal to 48. Then find what exactly the number is?

Solution:

let us assume the unknown number as " X "

Given   4 * X = 48.

Move leftside term to right

Then          X = `48/4`

The unknown number x is

X = 12

Example 2:

Find the Coefficients combined in the given equation:

24x^2 + 7y + 5xy + 12

Solution:

Here Coefficient of x^2 is 24

Coefficient of y is 7

Coefficient of xy is 5

Example 3:

Evaluate 22 - (-3) × 4   + (-6) / 3

Solution :

= 22 - (-3) × 4 + (-6) / 3

= 22 - (-12) + (-2)

= 22 + 12 - 2

= 22 + 10

= 32

Example 4:

Find the value of the expression 4x + 7 , if x = 7

Solution:

use x = 7 in the given expression 4x + 7

4x+ 7 = 4(7) + 7

= 28 + 7

X  = 35

Here the value of the expression is 35. Understanding completing the square problems is always challenging for me but thanks to all math help websites to help me out.

Problem Solving Loop:

Example 5:

Find the value of the expression 25x+8 , if x= 3

Solution:

Substitute x = 3 in the given expression 25x+8

25+8 = 25(3)+8

= 75 + 8

X  = 83

Here the value of the expression is 83.

Example 6:

Solve: 8x - 2 = 118

Solution:

Given, 8x - 2 = 118

8x = 118 + 2

8x = 120

x = `120/8`

or    x = 15

Example 7:

Solve the following system:

x + y = 14 - (1)

4x - y = 11 - (2)

Solution:

Solve the (1) equation

y =14 -x

substitute in (2)equation

4x - (14 - x)=11

4x - 14 + x=11

5x=25

x=5

substitute value of x in (1)equation

5 + y=14

y=9

The solution is, (5, 9).

Balance Interest

Introduction to balance interest

Interest is money paid for the use of borrowed assets also called as “rent of money”. The interest is calculated upon the value of the money borrowed and years and then rate of interest. There are two interest can be calculated they are simple interest and compound interest. Simple interest consist only the interest amount but the balance amount we get, by subtracting the principle amount form the compound interest is the interest of that amount Having problem with Simple Interest Rate Formula keep reading my upcoming posts, i will try to help you.

Simple Interest

Formula to find the simple interest

`S.I=(P*N*R)/100`

Where,

S.I is the simple interest
P is the principle amount or amount borrowed or deposited money in bank
N is the number of years
R is the rate of interest
When money is deposited in bank, then interest is called as "rent of money". Since interest is paid to the depositer

When money is borrowed interest is paid to the lender.

Example:

To buy a computer, David borrowed $3000 at 9% simple interest calculated yearly. If he will be making monthly payments for four years,

Calculate:

(a) the amount of interest to be paid,

(b) the total amount to be paid back,

(c) the monthly payment amount.

Formula:

`S.I=(P*N*R)/100`

Where,

S.I is the simple interest
P is the principle amount or amount borrowed or deposited money in bank
R is the rate of interest
`S.I=(3000*4*9)/100`

S.I=$1080

The amount of interest to be paid back is $1080

To find the total amount, the balance amount he going to pay is interest, so add the interest amount to the principle.

The total amount to be paid back after four years is $3000 + $1080 = $4080

The monthly payment amount   = `4080 /(12*4)`

=`4080/48`

= $85


Compound Interest

Formula to find the compound interest

`C.I=P(1+R/100)^n `

Where,

C.I is the compound interest

P is the principle

R is the rate of interest

n is the number of years

Let take example

P=$1000 R=10% n=2

`C.I=P(1+R/100)^n `

`C.I=1000(1+10/100)^2`

Amount=$1210

The balance amount from the amount = 1210-1000

= $210

The balance amount is the interest paid for the amount. The interest can also be calculated for the amount along with the balance amount for the upcoming days.

Solving Set Complement

Introduction to solving set complement

Let `xi` be the universal set. Let A be a set in `xi` . Then the complement of the set A is the set of all elements in U that doesnot belong to A. The complement of the set A is denoted by A’ or A c.

For example: Let `xi` = {1, 2, 3, 4, 5} and A = {1, 2}

Then A’ = {3, 4, 5}. Here we have taken the values of `xi` that doesn’t belong to A.

Using the complement concept, the important law known as De Morgan’s laws is given by:

1. (AUB)’ = A’∩ B’

2. (A ∩ B)’ = A’UB’

Now let us see few problems on this topic solving set complement. I like to share this Complement of a Set with you all through my article.

Example Problems on Solving Set Complement.

Ex 1: Let `xi` = {0, 1, 2, 3, 4, 5, 6}. Let A = {0, 1, 2, 3} and B = {3, 4, 5, 6}. Find A’UB’

Soln: Given: A = {0, 1, 2, 4,5, 6} `=>` A’ = {4, 5, 6}

B = {3, 4,5, 6} `=>` B’ = {0, 1, 2}

Therefore A’UB’ = {0, 1, 2, 4, 5, 6}

Ex 2: Let `xi` = {a, b, c, d, e, f} Let A = {a, b, d}

Let B = {b, c, d, e, f}. Find A’∩ B’.

Soln: Given: A = {a, b, d} `=>` A’ = {c, e, f}

B = {b, c, d, e, f} `=>` B’ = {a}

Therefore A’∩ B’ = { } [Empty set]

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More Example Problems on Solving Set Complement.

Ex 3: Let `xi` = {p, q, r, s, t, u, v}. Let A = {p, r, t, v} and B = {p, q, r, s}. Find (A’∩ B’)’

Soln: Given: A = { p, r, t, v} `=>` A’ = {q, s, u}

B = { p, q, r, s} `=>` B’ = {t, u, v}

A’ U B’ = {q, s, t, u, v}

Therefore (A’ U B’)’ = {p, r} [Here only p and r are not an element of A’UB’]

Ex 4: Let`xi` = {1, 2, 3, 4, 5, 6, 7}.Let = {1, 3, 5, 7}

and Y= {2, 4, 6, 7}. Find (‘X’∩ Y’)’

Soln: Given: X = {1, 3, 5, 7} `=>` X’ = {2, 4, 6}

Y = {2, 4, 6, 7} `=>` Y’ = { 1, 3, 5}

Therefore X’∩ Y’ = { } [Empty set]

Therefore (X’∩ Y’)’ = {1, 2, 3, 4, 5, 6, 7} [Empty set (`O/` )complement is the universal set (`xi` )and vice versa]

Negative Plus a Negative Equals a Positive

Introduction to Negative plus a negative equals a positive:

Negative plus negative equals to negative only. The given rule is wrong. This rule is only possible for multiplication. When we can add two negative numbers we have to get a negative number only. This is the important addition rule.  In this article we are going to study about the addition rule negative plus negative equal to negative through example problems. Having problem with Positive Integers keep reading my upcoming posts, i will try to help you.

Brief Summary about the Rule Negative Plus a Negative Equals a Negative

Addition Rules:

There are 3 important addition rules.  They are listed as in the following manner,

Positive number+ Positive number = Positive number
Negative number+ Negative number = negative number
When we can add both positive and negative we have to subtract the larger number from the smaller number and then the largest number sign is the resultant sign.

The rule negative plus negative is equals to positive is only possible when we can do the multiplication.  This rule is not applicable for addition. I have recently faced lot of problem while learning how to add integers, But thank to online resources of math which helped me to learn myself easily on net.

Example Problems the Rule Negative Plus a Negative Equals a Negative

Example 1:

Simplify the following values -21 + 8 – 7

Solution:

The given values are -21 + 8 – 7

First we have to simplify the first two values then we have to get

-13 – 7

Now we have to simplify the two negative values using the following addition rule

Negative number+ Negative number = negative number

That is -13 -7 = -20

This is the solution for the given values -21 + 8 – 7.

Example 2:

Subtract the following expressions -5x and -10x

Solution:

The given expression is -5x and -10x

Here the variable x is common for both terms, So we have to take out that term as common,

That is x (-5 -10)

Now we have to simplify the values in side the parentheses for using the following rule,

Negative number+ Negative number = negative number

That is x (-15)

The solution is -15x.

Kinds of Trigonometry

Introduction to the trigonometry:

Trigonometry is the division of mathematics that compact with triangles, circles, oscillations. The trigonometry is completely crucial to much of geometry. The trigonometry is particularly right triangle. Trigonometry deals with relations among the sides and the angles of triangles. In the trigonometry, the trigonon means triangle and metron means measurements. Let we see detailed about the trigonometry. Having problem with What is Trigonometry keep reading my upcoming posts, i will try to help you.

Kinds of Trigonometry:

There are main kinds of the trigonometry. These trigonometry kinds are following:

Plain trigonometry
Spherical trigonometry

Plain Trigonometry:

Plain trigonometry is the specific kinds of the trigonometry types. The Plain trigonometry is the right angle of the similar plans. The plain trigonometry is the also kind of the plain triangle. Rotating ray is generating using the plain trigonometry. The plain trigonometry is the fundamental concept of trigonometry.

In the above diagram OA is the starting side and OB is the rotation of the final states. The final state is also called as the terminal sides. The angle and its measurement is positive the counter clock wise direction is generated.

An angle with the vertex is the middle of the circle and is defined the angle unit of the measurement.I have recently faced lot of problem while learning Trigonometric Form of a Complex Number, But thank to online resources of math which helped me to learn myself easily on net.

Spherical Trigonometry:

The spherical trigonometry is other kinds of the trigonometry.The division of the spherical geometry are the spherical trigonometry. It is concerned with the sphere of the polygon. The spherical trigonometry is relation between the angles and the sides. This spherical trigonometry is most import for calculations in astronomy and orbital.The common form for the spherical trigonometry is following:

`(sin alpha)/(sin a)=(sin beta)/(sin b)=(sin gamma)/(sin c)`

Where a, b, c are represent as the angles.

The identities of the spherical trigonometry:

The identity of the Spherical trigonometry is the spherical law of the cosines.

Cos c = cos a cos b + sina sinb cosc

The identity of the Spherical trigonometry is the spherical law of the sine.

`(sin x)/(sin X)=(sin y)/(sin Y)=(sin z)/(sin Z)`

Operations with Radicals Help

Introduction to operations with radicals help:

In mathematics the advanced math radicals with a square root of a number x is a number r such that r2 = x, Let we assume the square roots value  √ 3025 and the square roots value can be written as 55.Here we see about the problems in operations with radicals help. Understanding Adding Radicals is always challenging for me but thanks to all math help websites to help me out.

(Source – Wikipedia).

Operations with Radicals Help Problems

An expression that has a square root, cube root, etc.

Radicals:
The most simple form of radical symbol is √

The usage of the radical in the math is 3`sqrt(x - 6)`

Where 3 is an index and √ referred as radical symbol x – 6 referred as radicand symbol.

Square root
The given number is multiplied with the same number to form a definite value are referred as square root

The simple form of radical symbol is √

Is this topic math problems 7th grade hard for you? Watch out for my coming posts.

Problems in Operations with Radicals Help

Problems 1 in operations with radicals help

Determine the operations with radicals help roots `sqrt(5476)`
Step1: First we have to determine the minimum factors of 5476 , we get….

`sqrt(5476)`  =  `sqrt(74 xx 74)`

Step2: `sqrt(5476)`  = `sqrt(74)` 2

We know `root(n)(x)` n = x

Step3: Hence the given square roots value for that the given radical with root is 5476 = 74.

Problems 2 in operations with radicals help

Determine the operations with radicals help roots `sqrt(5329)` ÷ `sqrt(5776)`
Step 1: Factors of 5329 = 73 × 73

`sqrt(5329)` = `sqrt(73 xx 73)`

= `sqrt(74)`2

Step 2: Square roots of 732 = 79;                                we know `root(n)(x)` n = x   , here n = 2

Step 3: Factors of 5776 = 76 × 76

`sqrt(5776)` = `sqrt(76 xx 76)`

Step 4:  `sqrt(76)`2 = 76      ;                                                  we know `root(n)(x)` n = x   , here n = 2

Step 5: so, `sqrt(5329)` ÷ `sqrt(5776)`   = 73 ÷ 76

Answer of the given radical is 73 ÷ 76 =0.96

Problems 3 in operations with radicals help 65

Determine the operations with radicals help roots 3136`sqrt(3136)`  ÷ `sqrt(4225)`
Step 1: Factors of 3136 = 56 × 56

3136 = `sqrt(56 xx 56)`

= `sqrt(56^2)`

Step 2: Square roots of 732 = 79;                                we know `root(n)(x)` n = x   , here n = 2

Step 3: Factors of `sqrt(4225)` = 65 × 65

`sqrt(4225)` = `sqrt(65 xx 65)`

Step 4: `sqrt(65^2)` = 65      ;                                                  we know `root(n)(x)` n = x   , here n = 2

Step 5: so, `sqrt(3136)`  ÷ `sqrt(4225)`     = 56 ÷ 65

Answer of the given radical is 56 ÷ 65 = 0.86

Six Grade Math Proportional

Introduction to six grade math proportional:
Proportion is the relation between elements and a whole. Proportion is a correspondence among the measures of the members of an entire work, and of the whole to a certain part selected as standard. From this result the principles of symmetry. In this article we shall discuss six grade math proportion example problems. (Source: wikipedia)

Six Grade Math Proportional Example Problem

Here we are going to solve grade six math proportional problems with detailed solution.

Example:

A bike travels 350 miles in 6 hours to reach a particular city. In 7 hours how many miles the bike travels?

Solution:

Step 1:

Consider the problem as If the bike takes 6 hour then the he travel 350. If bike takes 7 hours how many miles bike travels?

Step 2:

The proportional relationship directly:

6=>350

7=>`7/6` x350

=>800

Answer:

Therefore the bike traveled 7 hours in 480.3 miles

Example:

A person travels from Chennai to Delhi in 9 hours at the speed rate of 50 km/ hours. What is the time taken to reach Chennai to Delhi at the speed rate of 75 km/hours?

Solution:

Step 1:

Speed (km)                              Time (hours)

50                                                  9

75                                                  x

We know that as the speed is increase the time is decrease.

Therefore two quantities are in inverse variation

Step 2:

That is 50: 75 = x: 9

75 × x = 9 x 50

x = 9 x `50/75 ` = 6

Therefore time to taken Chennai to Delhi at the speed rate of 75km /hr = 6 hours

Example:

A person travels from one place to another place in 10 hours at the speed rate of 40 km/ hours. What is the time taken to reach one place to another at the speed rate of 60 km/hours?

Solution:

Step 1:

Speed (km)                              Time (hours)

40                                                  10

60                                                  x

We know that as the speed is increase the time is decrease.

Therefore two quantities are in inverse variation

Step 2:

That is 40: 60 = x: 10

60 × x = 40 x 10

x = 40 x `10/60 ` = 6

Therefore time to taken one place to another place at the speed rate of 60km /hr = 6.6 hours

Six Grade Math Proportional Practice Problem

Problem:

A bike travels 500 miles in 5 hours to reach a particular city. In 8 hours how many miles the bike travels?

Answer:

The bike traveled 8 hours in 800miles

Problem:

Eight employees can do a particular work in 14 days. In how many days 7 employees will do the same job?

Answer:

8 employees can do the same work in 16 days.

Stories about Math

Introduction for Stories about Math:
This article help your students because it is motivated and successful problem solvers. The math problems are in the form of stories. Each story focuses on a combination of math concepts including: Multiplication, division, decimals, patterns, fractions, percentages, probability and ratios. To make selecting appropriate stories a simple task, the contents lists the primary concepts covered in each. In this article we shall discuss about math stories. The following examples are involved in stories about math.

Read the Math Stories and Answer the Questions Math Stories are Given Below:

It’s an exciting day for Tom! He is fifteen years old today and he’s having a birthday party in the park this evening. Tom and his friends, Peter and Janice, are getting things ready.

It takes 187 minutes for Tom and Peter to set up the tables and chairs so that everyone will have a place to sit and eat. They set up 147 tables and each table has two chairs. The others will sit on benches and blankets. The colorful red tabletops and balloons they tied to the chairs make things look very festive.

They all had a needle and thread and made the strings to hang from the trees. It takes 154 minutes to make the popcorn strings. Tom‘s string has 245 pieces of popcorn. Peter’s string has 366 and Janice’s string has 282.

Just before the party starts, they start cooking the hotdogs. That takes 139 minutes. Tom knows he has invited 134 girls and 166 boys in all. He bought enough hot dogs for each person to have three.

It is hard to clean up the mess, but, sure enough, the birds eat all of the popcorn, so that makes it easier.

Questions for Stories about Math:

1. What was the sum of the minutes it took Tom and his friends to prepare for the party?

2. How many hot dogs did Tom have for his friends at the party?

3. How many pieces of popcorn did the birds eat from the strings in the trees altogether?

4. How many chairs were there for people to sit on?

5. What was the total number of guests Tom invited to the party?

Answers for Stories about Math:

1. 187+ 154+139 = 480

2. (134+186)*3 = 960

3. 245+366+282 = 893

4. 147*2 = 294

5. 134 + 186 = 320