Math is EDUCATIONAL!!

Multiplying two fractions is easier than adding, taking and dividing fractions. To multiply two fractions together all you need to do be able to do is times the numerators together, and times the denominators together. The numerator is the top part of the fraction, and the denominator is the bottom part of the fraction.

Example 1

Work out 2/7 × 3/5

= 6/35 (Since 2×3=6 and 7×5=35).

Let’s take a look at another example when you have to times another fraction by a whole number.

Example 2

Work out 5 × 3/8.

First write 5 as 5/1.

So we have 5/1 × 3/8.

= 15/8 (since 5×3=15 and 8×1=8)

Let’s take another example of timesing 3 fractions together.

Example 3

Work out 1/3 × 1/2 × 2/9.

To do this all you do is times all the numerators, and times all the denominators.

= 2/54 (since 1×1×2=2, and 3×2×9 is 54)

= 1/27  (simplify the fraction by dividing by 2)

Our last example looks at multiplying two mixed fractions together. When you multiply two mixed fractions together, the easiest way to do this will be to convert the mixed fractions to improper fractions.

Example 4

Work out 2 1/3 × 1 1/5.

First of all you will need to write the two mixed fractions to improper fractions.

Therefore our question can be written as:

7/3 × 6/5.

Now it’s the same as before. Times the numerators, and times the denominators!

42/15 (since 7 × 6 =42, and 3 × 5 =15).

= 14/5 (simplify you final answer by dividing by 3)

You may want to convert your final answer back into a mixed fraction = 2 4/5.

To find the square root of a number all you need to do is to look for a number when multiplied by itself, which gives you the number that you are rooting.  Square roots and squares are opposite operations, so if you now your square numbers well enough, square roots should be straightforward to carry out.

Example 1

Find the square root of 64.

So we are looking for a number when multiplied by itself that gives 64.

The number we are looking for is 8, because 8 × 8 = 64

Example 2

Work out √49.

The symbol that is before 49 is basically a square root sign. So we need to find the square root of 49.

Again, try to think of number when multiplied by itself gives 49.

The answer is 7, as 7 × 7 = 49

Example 3

Work out √9.

All you have to do is the same as before, and look for a number when multiplied by itself which gives 9. Be careful not to square 9, as this gives 81.

The answer is therefore 3 as 3 × 3 = 9.

Sometimes we will need a calculator to find a square root, as our answer will not be a whole number.

Example 4

Work out the square root of 157.

Well we know that, 12 × 12 = 144 and 13 × 13 = 169, so our answer is going to be a decimal answer somewhere between 12 and 13.

In order to work this out, we will need a calculator (just use the root button √)

So the √157 = 12.53 (2 dp)

Extra Tips

To find the square root of a number all you need to do is look for a number when multiplied by itself which gives you the number that you are rooting.

Make sure you are rooting the number, and not squaring the number! When you are square rooting a number, the answer is always going to be smaller than the number that you started off with.

You won’t be able to square root a negative number.

The square root of 1 is 1.

The game of bingo is both very simple to play and extremely popular. As a result of these two facts, it is probably fair to say that most adults know how to play bingo, and many have actively played the game themselves. While that may be true, many people do not know, however, that many teachers are also using versions of the game of bingo as an educational activity in their classrooms.

Possibly, the most widely known variants of classroom bingo are those used for teaching English, closely followed by those used for teaching foreign languages such as French, German and Spanish. In each of these cases, the game is played using bingo cards which are printed with letters or words. As in traditional bingo, the player’s (i.e. student’s) goal is to achieve one or more lines of marked off squares across their bingo squares – however the twist is in the criteria that used to determine how squares are marked off: squares might be marked off if they contain the letter than begins the teacher’s word (“phonemic awareness bingo”), if they contain a word matching the definition given by the teacher (“vocabulary bingo”), or perhaps if they contain the appropriate foreign language translation of the English word read out by the teacher.

It would incorrect however to assume that it is only English and language teachers who introduced bingo in their classrooms.

Many math teachers have also found that educational versions of bingo can be used in their subject. These include:

* Simple math operations such as addition, subtraction, multiplication and division can be practised in an interesting way with the help of bingo. In this case, the game is typically played using bingo cards printed with numbers, and the teachers must mark off the corresponding square in response to a math problem given by the teacher (for example, marking off “42″ if asked to “multiply 6 by 7″).

* Likewise fractions and decimals can be practised using bingo.

The students’ cards contain fractions or decimals chosen by the teacher, and they must find the corresponding square in response to the teacher’s bingo calls. Some problems might be simple, such as finding the square containing “0.5″ if the teacher says “nought point five” or “five tenths”, and others might be hard, such as finding the square containing “1.25″ if the teacher says “five quarters”.

* Other math problems that can also be practised including rounding (for example finding the square containing “30″ if asked to “round 28 to the nearest multiple of ten”) – but really the only limit is the teacher’s imagination.

If you’re a teacher and interested in introducing bingo into your classes, one question that you’re probably concerned about is where to get the bingo cards? While it is possible to buy printed educational bingo cards, it can soon get expensive, particularly if you need a large number of cards, and in any case the cards may not contain the particular items you want for your class. The answer is to prepare the bingo cards yourself. No, I’m not going to suggest creating them by hand – that would be tedious and time-consuming – instead use your computer! If you use some bingo card maker software, all you need to do is enter a list of items that you want to appear on the cards, and the computer can print off as many bingo cards as you want, with just a few mouse clicks.

It’s that time of year again. On campuses all across the nation students are reporting for duty. Armed with fresh new text books thick enough to roof a building, students are stepping foot back on campus in the eternal pursuit of knowledge. Just as with the rest of the country so are students reporting back to Arizona’s three major universities for fall semester. But unlike most the nation, Arizona’s three public institutions will accommodate over 130,000 students. Arizona State University alone boasts a student population of 71,000 (more than the number of seats in Sun Devil Stadium) and saw a record freshman enrollment rate of nearly 10,000 first time students.
What these numbers show is that more and more students are seeking higher education in Arizona. With low tuition costs combined with several nationally ranked programs Arizona State, Arizona, and Northern Arizona provide alluring options for degree seekers.

Additionally, ASU and U of A consistently rank in as top tier universities in national surveys. All in all Arizona is a great place to get an education and the student populations show it.
It’s no surprise that college can be an overwhelming experience, add in numbers like these and it’s easy to see how students can begin to feel lost or neglected in the classroom. With coursework demanding and little opportunity for one on one interaction, many students get discouraged, some even drop out. Little do they know there is help out there.
One of the most common subjects students struggle with is math. While mathematics plays an important role in science and engineering, most people do not use advanced trigonometry on a daily basis. Combine that with the fact that there is zero room for error in the math world, the subject quickly becomes overwhelming. Regardless of the difficulty, almost all degrees from an Arizona university require a proficiency in some form of mathematics, from algebra to calculus to statistics.
However, students looking to stay on track towards graduation and fill their mathematics requirement have help. There are a number of excellent tutor programs available for students looking for math help. Need a calculus tutor Arizona? You’re in luck. Or are seeking a degree in economics and require the help of a statistics tutor Arizona students? No worries. You have help. Regardless of the course, a tutor like the ones provided by deanslisttutors.com can help Arizona students understand the material and pass their math course with flying colors. Even if you’re looking for a degree in Accounting and need an accounting tutor Arizona grown. No matter what your tutoring needs, companies like deanslisttutors.com make it their priority to help you pass.
So maybe math isn’t the difficult part after all. I learned all the math I needed in college, boy + girl = eventual marriage x 3 kids – all your income. That was probably the most difficult subject to master (10 years later I’m still working at it).
College life can be overwhelming at times but it can also be extremely rewarding. There is nothing greater than sitting in the student section during football games screaming so hard your voice is hoarse for three days, or cramming in library at midnight, just you, a cup of coffee, and stacks upon stacks of literary masterpieces. If you’re just starting out in college, or a semester away from graduation, my advice to you is to enjoy the experience – every little moment. And when it comes to math, take the help.

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Written below are some worked questions on how to find the area of a sector if you know the radius and the angle inside the sector.

Question 1

A sector has a radius of 3cm and an inside angle of 45⁰. Work out the area of the sector.

The area of a sector can be calculated by using the following formula:

Area of the sector = angle/360 × π × radius²

So all you need to do is substitute the radius which is 3 cm and the angle which is 45⁰ into this formula.

Area of a sector  = 45/360 × π × 3²

Now type this into you scientific calculator exactly how it appears above (use your fraction key).

Area of sector = 3.53 cm² to 3 significant figures.

Question 2

Another sector has a radius of 15 m and an inside angle of 135⁰. Work out the area of the sector.

Again, the area of a sector can be calculated by using the following formula:

Area of the sector = angle/360 × π × radius²

Next substitute the radius which is 15 m and the angle which is 135⁰ into this formula.

Area of a sector  = 135/360 × π × 15²

Now type this into you scientific calculator exactly how it appears above (use your fraction key).

Area of sector = 265.1 m² to 3 significant figures.

Question 3

A sector has a radius of 7.2 cm and an inside angle of 286⁰. Work out the area of the sector and round your final answer to the nearest integer.

Again, the area of a sector can be calculated by using the following formula:

Area of the sector = angle/360 × π × radius²

Next substitute the radius which is 7.2 cm and the angle which is 286⁰ into this formula.

Area of a sector  = 286/360 × π × 7.2²

Now type this into you scientific calculator exactly how it appears above (use your fraction key).

Area of sector = 129 cm² to the nearest integer.

Question 4

A sector has a radius of 9 mm and an inside angle of 11⁰. Work out the area of the sector and round your final answer to 3 decimal places.

Again, the area of a sector can be calculated by using the following formula:

Area of the sector = angle/360 × π × radius²

Next substitute the radius which is 9 mm and the angle which is 11⁰ into this formula.

Area of a sector  = 11/360 × π × 9²

Now type this into you scientific calculator exactly how it appears above (use your fraction key).

Area of sector = 7.775 mm² to 3 decimal places.

If you are still finding this difficult then read my other article on finding the area of a sector.

If you want some harder real life example on finding the area of a sector then click here.

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A power or index tells you how many times you multiply a number by itself. A power is written in small writing at the top right of your number.  Let’s take a look at some examples.

Example 1

Write down the meaning of 2⁵ and work out the answer.

Since the power is 5 write down 2 five times and multiply these together:

2 × 2 × 2 × 2 × 2 = 32

Example 2

Write down the meaning of 3⁴ and work out the answer.

Here the power is 4, so write down 3 four times and multiply all these together.

3 × 3 × 3 × 3 = 81

Example 3

Write down the meaning of 6⁵ and work out the answer.

This time the power is 5, so write down 6 five times and multiply all these number together.

6 × 6 × 6 ×6 × 6 = 7776

Example 4

Write down 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 in power form.

Since there are 8 fours written down, the power is 8.

So your answer is 4⁸

Example 5

Write down 7 × 7 × 7 in power form.

Since there are three 7’s being multiplies together then the power is 3.

So your answer is 7³

Example 6

Write down 4×4×6×6×6×6×4×4×4×4×4

This time we have seven 4’s and four 6’s being multiplied so we can write this as:

4⁷×6⁴

Let’s take a look at one last example which is algebra based, but the same technique can be applied.

Example 7

Write down a × a × a × b × b ×b × b × c × c × c × c × c.

This time we has three a’s,  four b’s and five c’s being multiplied together.

So we can write down our answer as :

a³ × b⁴ × c⁵

Now we can simplify this a little further by leaving out the multiply signs, as we don’t have to include these in algebra.

a³b⁴c⁵

Step 1

A quick reminder; the top number is called the numerator, and the bottom number is called the denominator. It may not seem important to you right now, but in the future you may well change your mind!

Step 2

Let’s start with the problem 2/3 + 4/9. Now, adding fractions is as simple as adding straight across, numerator to numerator and denominator to denominator. But wait; the denominators must be the same! Uh oh…ours are a 3 and a 9! So what can you do? Take a look at the 3 and the 9. Do you spot any similarities?

Step 3

That’s it! Both 3 and 9 share the factors 1 (which is a given) and 3. So therefore, 3 is their GCF, or Greatest Common Factor (pretty self-explanatory; the greatest factor that both numbers share). Now we must figure out how to get the denominators to match. Hm…so how can you get 3 to become a 9? Aha! By multiplying by 3! Be sure that you multiply both the numerator AND denominator by the same amount, so keep the fraction equivalent. Like you will learn later on (around 7th/8th grade), what you do to one side, you must do to the other.

Step 4

3*2=6, and 3*3=9, so the new fraction is 6/9. Now the problem is 6/9+4/9. Now you can add the numerators straight across! Be sure that you don’t add the denominators, though! So 6+4=10, and the fraction becomes 10/9, which, if you prefer a mixed number, is 1 1/9. Congratulations! You have just completed a fraction addition problem! Soon you will be moving on to the other operations of subtraction, multiplication, and division.

Prime factors are numbers which are factors as well as being prime.

The easiest way to find the prime factors of a number,  is to first of all find the factors of the number, and then pick out the factors that are prime.

Also make sure that you understand what a prime number is (read my other article), and knowing your first 10 prime numbers will also come in handy.

The first 10 prime numbers are:

2,3,5,7,11,13,17,19,23 and 29.

(A prime number can only be divided by 1 and itself)

Example 1

Find all the prime factors of 20.

To begin with you will need to find all the factors of 20.

These are:

1 × 20

2 × 10

4 × 5

Putting these factors into size order we get:

1,2,4,5,10 and 20.

Now from the list of factors, you need to select all the prime numbers.

The only prime numbers are 2 and 5.

Therefore the prime factors of 20 are 2 and 5.

Example 2

Find all the prime factors of 9

Again find all the factors of 9. These are:

1 × 9

3 × 3

So our factors of 9 are 1, 3 and 9.

Next we need to select all the prime numbers out of this list.

From the list of factors that we have, the only prime number in the list is 3. Therefore 3 is the only prime factor of 9.

Let’s take a look at a harder example.

Example 3

Find all the prime factors of 54.

Again, list all the factors of 54.

1 × 54

2 × 27

3 × 17

6 × 9

So the factors of 24 are 1,2,3,6,9,17,27 and 54.

Out of the list of factors all you need to know is select the prime numbers.

This time there are 3 prime numbers: 2,3 and 17.

Therefore the prime factors of 54 are 2,3 and 17.

Summary

List all the factors of your number.

Then select all the prime numbers.

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Pulling rabbits from hats and construction Statue of Liberty vanish are effective magic feats. Happen in many ways such as computer scientists are: juggler method should solve the problem, the problem being called to find rabbit appear or sculpture vanish, but without the audience realizing how it was done is. Trick magic combination of good technique is presented and, in some ways like a computer program: Computer Software should approach problem solving (in our computer science this way, or a series of steps, the algorithm) have But, unlike magic, software should offer the results to the user in order to understand them.

This is not surprising that many mathematicians and computer scientists are interested in magic tricks. Working way to solve problems, predict whether the card trick selection or how to reduce the amount of digital data in a music file MP3, without noticing the listener are very similar. Wizard wants to make sure that trick will always work. Computer scientists want to make sure that their programs always work. Difference is that computer scientists want other people How it is done. Random hiding method must clear it to keep the audience never has.

Funny story about computer discovery

Danish police computer records belonging to a man who was ‘Rottin in Denmark blog’ are involved. They used her stolen credit card to buy things online has accused. Blogger explained that he bashful to open access point, and anyone can use it. Them a long time to figure that, but at the time of your computer (your computer room and opaque) anyway.

Rottin police account of the visit is funny. But it also makes me wonder if I should open my modest network is close. I do not want cops take away my computer

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In this article I will explain how you can carry out Pythagoras’s Theorem without using the formula (a² + b² = c²). Pythagoras’s Theorem can be used to find a missing side length in a right angled triangle providing you know the two other side lengths. To do this follow these steps:

Step 1: Identify whether or not you are finding the longest side of the right angled triangle or one of the other shorter side lengths. This step is the most important!

Step 2: Take the square of your two numbers (multiply the number by itself).

Step 3: If you are finding the longest side of the right angled triangle add the two squares together (answers from step 2). If you are not finding the longest side take the two square numbers away.

Step 4: Square root the answer from step 3.

Example 1

In a right angled triangle (ABC) AB = 7cm and AC = 4cm. Find the length BC.

Step 1: BC is the longest side of the right angled triangle.

Step 2: 7 squared is 49 (since 7 × 7 = 49) and 4 squared is 16 (since 4 × 4 = 16).

Step 3: 49 + 16 = 65 (add them together as you are finding the longest side)

Step 4: The square root of 65 is 8.1 cm.

Example 2

In another right angled triangle (DEF) DE = 11 cm and EF = 13 cm. Find the length DF.

Step 1: DF is the shortest side length of the right angled triangle.

Step 2: 11 squared is 121 (since 11 × 11 = 121) and 13 squared is 169 (since 13 × 13 = 169).

Step 3: 169 – 121 = 48 (take them away as you are not finding the longest side)

Step 4: The square root of 48 is 6.9 cm.

Example 3

A ladder of length 15 m rests up against a vertical wall. The distance from the foot of the ladder to the foot of the wall is 2m. What is the distance from the bottom of the wall to the top of the ladder?

Step 1: The vertical distance up the wall is one of the shorter sides of the right angled triangle.

Step 2: 15 squared is 225 (since 15 × 15 = 225) and 2 squared is 4 (since 2 × 2 = 4).

Step 3: 225 – 4 = 221 (take them away as you are not finding the longest side)

Step 4: The square root of 221 is 14.9 m.

More Help:

More mixed Pythagoras questions.

Longest side Pthagoras questions.

Shorter side Pythagoras questions.