Simple Interest - Basics For Finance Math

By Manjit Singh Atwal
Simple Interest

In this presentation, I am going to explore the concept of the simple interest. Students in finance courses need good understanding about the interest. So, let's explore interest.

What is interest?

In simplest language, interest is the time value of money. For example, if I borrow $10 from my friend today and I spend this $10 bill to buy a fruit cake. If I return the same $10 to my friend after 5 years, would my friend be able to buy the same fruit cake with $10 after five years? Probably, not.

Things get expensive and money loses value over time. The fruit cake I bought for $10 today would probably cost $12 or more after five years.

Therefore, is this reasonable to return the same amount of money we borrowed couple years ago?

No, we have to add some extra money with the original amount; we borrowed, to match the value of money with the inflation (inflation is the degree by which the things we use get expensive). The extra money we add with the original amount (Principle) is called the interest.

Formula to calculate simple interest:

If the original money borrowed is "P" and "R" is the rate of interest and the money is borrowed for "T" years then the interest "I" can be calculated as follows:

I = PRT

Some students don't understand the rate of interest. The rate of interest is just how much money will be added to $100 if it is borrowed for one year. For example, if the rate of interest is 8%, it means if I borrow $100 today then I have to payback $108 after one complete year. Hence, I added $8 for using $100 for a full year and which is interest.

For $200 the interest for the whole year at same rate is $16.

When the money borrowed is not $100 or it's multiple and some other weird number such as $733.58 then we have math formula to deal with this. To find interest in this case the interest rate is converted into decimal and then multiplied with this weird amount and with number of years too.

Consider a person borrowed $733.58 at a rate of 12%. Calculate the simple interest for 2 years.

In the given problem, Money borrowed P = $733.58

Rate of interest R = 12% = 0.12

Divide the %age rate by 100 to convert it into a decimal.

Number of years T = 2 years

Simple interest "I = PRT".

Substitute the values for "P", "R" and "T" in the above formula to calculate the simple interest "I" as shown below:

I = 733.58 * 0.12 * 2

I = 176.06

Hence the simple interest is $176.06 (rounded to nearest cent)

If you or your kids or students need help with fractions, get the book "Ultimate Fractions Workbook" which teaches Simplifying Fractions and explains every single problem about fractions using very effective but easiest way. Kids read the book themselves and solve the problems in the book without any help from teachers or tutors. Give it a try with 60 day money back guarantee.blogspot.com,blogspot,blogger

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Quadratic Equations - Factoring Method To Solve!

By Manjit Singh Atwal
Solving Quadratic Equations Using Factors

Quadratic equations are degree two equations and there are many ways to solve them. Quadratic equations are similar to quadratic trinomials (most often when written in the standard form); they can be solved by using the factor method for trinomials.

If students know how to factor a quadratic trinomial, then it is very easy for these students to solve many quadratic equations using this method.

For example; consider there is the given equation "x² + 6x + 8 = 0" and we are asked to solve this. If we analyze this equation, the left side is a standard quadratic trinomial and it can be factored easily.

We start to solve the equation as given below:

x² + 6x + 8 = 0

Find two factors of "8" which add upto "6". By brain storming for factors of number "8", we find that numbers "4" and "2" are the required factors of "8" which add up to "6".

Hence, we can factor the given polynomial "x² + 6x + 8" to, "(x + 2) (x + 4)" and we can rewrite our quadratic equation using the above factors as shown below:

(x + 2) (x + 4) = 0

Now the given factors multiply with each other to give zero (on right hand side of the equation). As you know, if two numbers multiply to give zero, then either of them is equal to zero or both of them equal to zero. Therefore, we can separate both the factors by writing them equal to zero individually as shown below:

x + 2 = 0 Or x + 4 = 0

Now, if we solve the above linear equations, we get two values of "x" as shown in the next step:

x = - 2 Or x = - 4

Hence the solution of the given equation have been found and which can be written as shown below:

x = -2, - 4

The students can show the whole work all together as shown below:

x² + 6x + 8 = 0

(x + 2) (x + 4) = 0

x + 2 = 0 Or x + 4 = 0

x = - 2 Or x = - 4

x = -2, - 4 is the answer.

Therefore many quadratic equations can be solved by using the factor method but students should know how to factor quadratic polynomials. You can read my articles on factoring quadratic trinomials for more help.

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Greatest Common Fractor (gcf) And Least Common Multiple (lcm)

By Manjit Singh Atwal
LCM and GCF

There are many reasons which make math a hard and most hated subject among the average students. One of the most important reasons is the insufficient knowledge of basic math concepts such as least common multiple (lcm) and greatest common factor (gcf). Many students don't care about these basic concepts when there is a right time to learn these basic math skills.

After reading this article students who lack the knowledge of least common multiple and greatest common factor, can better understand these skills and they can apply this knowledge in higher math concepts, such as solving fractions or algebraic expressions.

Least Common Multiple (LCM):

If students know the times tables, then they can find multiples of a number quite easily as multiples are the "times" of the given number. To find least common multiple of two numbers students have to find multiples of both numbers and pick a common multiple which is the smallest of all. That smallest common multiple of both numbers is called the least common multiple.

For example; consider we want to find "lcm" of numbers "6" and "8". To find "lcm" of these number write the first 5 multiples of both the numbers as shown below:

6 = 6, 12, 18, 24, 30

8 = 8, 16, 24, 32, 40

Now by looking at first five multiples of both the numbers, we can locate the common multiple for both, which is "24". There is no other multiple smaller than 24, which is common for both the given numbers.

Hence, "24" is the "lcm" of "6" and "8".

Some times there is no common multiple in first five multiples of both the numbers, in this case write the next five multiples to locate the least common multiple.

Greatest Common Factor (gcf):

Similar to the "lcm", greatest common factor is another key skill students need to understand from the core. To find the greatest common factor of two numbers students need to find all the factors of both the numbers and then the biggest common factor is called the greatest common factor or gcf.

For example; consider we want to find the gcf of numbers "12" and "32". To find the gcf of the given numbers write all the factors of given numbers as shown below:

12 = 1, 2, 3, 4, 6, 12

32 = 1, 2, 4, 8, 16, 32

By looking at all the factors of both the numbers, it is clear that number "4" is the greatest common factor for the given numbers "12" and "32".

Students can practice more similar problems on lcm and gcf to get more confident in both of these key skills.

Its the responsibility of students to learn right math concepts at right time and the responsibility of educators and parents is to make sure the kids have learned the basic math concepts before upgrade them to learn higher math.

If you or your kids or students need help with fractions, get the book "Ultimate Fractions Workbook" which teaches Simplifying Fractions and explains every single problem about fractions using very effective but easiest way. Kids read the book themselves and solve the problems in the book without any help from teachers or tutors. Give it a try with 60 day money back guarantee.

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Many Ways To Use Hundreds Chart

By Manjit Singh Atwal
Grade one students need to be very good in counting from one to one hundred. To teach kids count to one hundred, teachers and parents can use a hundred chart.

But teacher and parents should not stop only at teaching from one to hundred using a hundred chart, but this chart can be used to explore many other basic math skills. Hundred chart can be used to teach even and odd numbers, skip counting by 5's and 10's and later in grade two or three, this chart can be used to introduce kids with prime and composite numbers.

Once kids are very familiar with counting from one to twenty, they should be introduced with hundred chart. In this chart, first thing to do is ask kids to say all the numbers from one to hundred. Once kids can say all the numbers from one to one hundred by looking at the chart, then parents or teachers should ask the kids to say all the numbers from their memory without using the chart.

When students have memorized the numbers from one to one hundred, then they should use a blank hundred chart to write numbers from 1 to 100. Once a student can fill whole chart using right numbers, then teacher or parents can use this chart, filled by student with numbers from 1 to 100, to introduce this student with even and odd numbers. Ask the student to color all the even numbers in red and color all odd numbers in blue. While coloring these numbers even and odd numbers will get fed into the little one's memory.

Next, ask the students to look at the column with 5 at one's place, and ask them to color these boxes with yellow color. As all these numbers are odd numbers and already been colored in blue, when students use yellow color on blue these boxes turns into green and create interest in kids to color them all. Now all the green boxes in the chart are counting by fives, which is a very strong basic skill to learn five times table and other times tables.

Once kids got familiar with skip counting by fives, the next step is to ask them to color the boxes with zero at one's place in yellow. As these boxes with even numbers, already colored in red, the new color becomes orange when kids color yellow on red. Now all the orange boxes contain all the numbers need to learn counting by tens.

Hence, hundred chart can be used many ways to teach kids numbers from 1 to 100, even and odd numbers and skip counting skills.blogspot.com,blogspot,blogger

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Divisibility Tests Or Divisibility Rules

By Manjit Singh Atwal
Divisibility Tests For Math Kids

Kids in grade six or higher grades should be able to tell quickly if a number is divisible by small prime numbers, such as 2, 3 or 5. Divisibility test or rules are very helpful to predict the divisibility of large numbers. I have explained the basic tests one by one in this presentation.

1. Divisibility test for 2:

All the numbers having one of the digits from 0, 2, 4, 6, 8 at their ones place are divisible by 2. For example; numbers 338, 5334, 924, 10002 and 23440 have the ones digit as 8, 4, 4, 2 and 0 respectively, hence are divisible by 2. On the other hand, 23669 has 9 at ones place, hence not divisible by 2.

2. Test for 3:

To test the divisibility for three, add all the digits of the number and if the sum is divisible by three then the given number is also divisible by three. If the sum is not divisible by three then the given number is not divisible by 3 as well. For example; given number is 61224, and we want to check if this number is divisible by 3. To test add all the digits of the number (6 + 1+ 2 + 2 + 4 =15), the sum of digits is 15 and which is divisible by 3, hence 61224 is divisible by 3. In other words it can be said that 3 is a factor of 61224.

3. Test for 4:

If the number formed using the tens and ones digits of the given number is divisible by 4 then the given number is divisible by 4. For example; consider the given number is 916 and the tens and ones digits make 16 which can be divided by 4, hence 916 is divisible by 4.

4. Test for 5:

If the ones digit is "0" or "5" then the number can be divided by 5. For example; consider the given number is 30085, as the ones digit is 5, hence the given number 30085, can be divided by 5.

5. Test for 6:

If a given number is divisible by 2 and 3 both then it can be divided by 6 too. For example; consider the given number is 774. This number is divisible by 2, as the ones digit is four. Now add the digits (7 + 7 + 4 = 15) to get 15 and which is divisible by 3, hence 774 is divisible by 3 too. Now because 774 is divisible by 2 and 3 both therefore it is divisible by 6 as well.

6. Test for 9:

Test for 9 is similar to test for 3. Add all the digits of the number and if the sum can be divided by 9 then the number itself can be divided by 9.

7. Test for 10:

If the ones digit of a number is zero then this number can be divided by 10. For example; 230 has "0" at ones place, hence it is divisible by 10.

Keep in mind that if a given number is divisible by 2 then 2 is called the factor of the given number.

If you or your kids or students need help with fractions, get the book "Ultimate Fractions Workbook" which teaches Simplifying Fractions and explains every single problem about fractions using very effective but easiest way. Kids read the book themselves and solve the problems in the book without any help from teachers or tutors. Give it a try with 60 day money back guarantee.blogspot.com,blogspot,blogger

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What Are Rational And Irrational Numbers?

By Manjit Singh Atwal
Rational and irrational numbers are taught in grade nine math. Students are learning rational numbers already since grade six, but irrational numbers are introduced in grade nine (in most schools). When I start teaching grade nine students, they look very confused about these two kinds of numbers. Let's take on these both types one by one.

Rational numbers:

In the real number system, rational numbers are the fractions (mainly). Any number that can be written in the form "p/q", where "p" and "q" are both integers and "q" is not equal to zero, is called the rational number. There is a letter symbol of "Q" to denote these.

For example; 2/3 and -2/3 are both the examples of rational number.

But they are not limited to fractions only. All the terminating (ending) decimals and repeating decimals are the in the this category. For example; 2.5, - 2.5, 5.009 and repeating decimals like 0.3333... and 2.666.... fall under the symbol Q.

Also, all the integers can be changed to fractions by making one as their denominator; hence all the integers such as - 5, - 4, - 3, 0, 1, 2, 3 and so on fall in this category.

Therefore rational numbers contain a variety of numbers in them. Below there are more example of rational numbers.

0, 1, -1, 2, -2, 0.56, 3.125, 3/6,-5/2, 3.22222...., 0.99999....

Irrational Numbers:

These are defined as the non-repeating and non-terminating decimals. In other words, if a decimal is not ending and numbers after decimals are not in a pattern that number is a rational number. These kinds of numbers are obtained when square root of a number (which is not a perfect square) is calculated.

For example; 3.013004751224... is an irrational number. Look at the pattern after the decimal are not in a pattern and no body can predict what is coming after last digit "4" and also this is a non-terminating decimal.

If we find the square root of number "2" using the calculator, we find a decimal which is an irrational number. Similarly the square root of number "3" falls in the same category. But be careful in case of perfect squares such as "4", as the square root of four is "2" which is a natural number and hence a rational number but not an irrational number because four is a perfect square. Similarly all other perfect squares like, 16, 25, 36, 49, 64, 81, 100, 121, 144 and so on should be cared about their category.

Similarly the square root of next perfect square "9" is "3" which is not an irrational.

I always ask my students to remember the irrational number as they are non-ending and non-repeating decimals and everything else is rational numbers.

If you or your kids or students need help with fractions, get the book "Ultimate Fractions Workbook" which teaches Simplifying Fractions and explains every single problem about fractions very effective but easiest way. Kids read the book themselves and solve the problems in the book without any help from teachers or tutors. Give it a try with 60 day money back guarantee.

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Teens - Where or Where Has Your Persistence Gone?

By Shirley Slick
A characteristic that very young children seem to have in abundance but seems to completely disappear by the time students reach 1st year Algebra is persistence. What happens to it? Can it be found again?

One need only watch a baby learning to crawl or pull themselves up to standing or begin walking to see extreme persistence at work. Babies never give up, even when they hurt themselves. Once they have mastered walking, the focus gets switched to language development. They show the same persistence with learning to speak and beginning to learn language. Children are reinforced by entire family units as they learn language related skills. Children enter school excited to learn--to begin to read and write. And they never doubt that they have the ability to learn because we as a society have taught them to believe that they can learn to read and write.

Something strange apparently happens between those preschool years and the high school years because Algebra students are quite literally lacking any persistence. It is not at all uncommon for high school students try a math problem once and if unsuccessful to simply give up. And this happens over and over and with student after student.

But this just didn't make sense that a quality that existed in such abundance should disappear. So what is at work here? I believe that the key to what is happening can be identified in the 2nd paragraph. Notice that after walking is mastered, the efforts switch to language skills. There is no mention of or attention given to mathematics.

In reality, because of misinformation from Piaget, it has been thought that abstract thinking needed for mathematics should wait until age 11. Consequently, parents have never been encouraged to work with their pre-school children with math. This means the persistence which became a natural part of language skills was never instilled into mathematics. We have only recently learned that children are actually capable of learning basic math skills and logic during ages 1 to 4. This information, however, is very new and is just beginning to be given to parents of preschoolers.

So, for all teenagers who seem to lack persistence with Algebra, you can take some solace in the fact that your preschool years didn't have you as prepared for math as for language. However, that is no excuse to fail. You can develop persistence now. Persistence is the ability to maintain action regardless of your feeling. You press on even when you feel like quitting. You are persistent is other areas--maybe learning to skateboard, or play an instrument. You just need to apply persistence to Algebra as well. You can be successful!

Shirley Slick, "The Slick Tips Lady," is a retired high school math teacher and tutor with degrees in Mathematics and Psychology and additional training in brain-based learning/teaching. Her goals: (1) to help parents help their children with math, (2) to help eliminate the horrendous Algebra failure rate, and (3) to inform the general public about problematic issues related to the field of education. For your free copy of "10 Slick Tips for

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