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Decimals to Fraction!

In math there are many things that go hand in hand, for example addition and subtraction, also multiplication and division. Another thing that goes hand in hand is fractions and decimals. We can take a fraction and make it decimal but we can also have a decimal and make it into a fraction. In order to do so we need to understand the term “rational numbers”. Rational numbers are simply decimals that are terminating or repeating.

We can take the word “rational” we can take out the word “Ratio” meaning of integers (fraction of integers).

Terminating decimals are numbers like 0.55, 0.205, and 6.1 (these are all decimals that have a clear ending). We can make these decimal into fractions by paying attention to the place values that the digits hold. For example 0.55 is in the hundredths place therefore 0.55 is 55/100.

Repeating Decimal are numbers like 0.333333….., 0.77777….,and 0.242424 (decimals that have a repetition in the number. it may start later in the number). We can make these decimals in to numbers by setting them equal to “X”. A good example is 0.333333…. because we know of the top of our heads that it is 1/3 but do we know why it is? Below are the steps to show why 0.3333…. is 1/3.

Step 1)     X=0.333333…. 

Step 2) 10X=3.333333…. (Find a number of ten that will get rid of the repeating end of the decimal. Then subtract Step 1 and Step 2.)

Step 3) 9X=3

Step 4) 9X/9=3/9 or 1/3

We can use these steps on any repeating decimals. Lets try the decimal 0.242424….! We will start the problem just like we did for 0.333……!

Step 1) X = 0.242424

Step 2) 100x = 24.2424    (We want to set it equal to 100X because it will move the decimal two places to the right and it will get rid of the repetition)

Step 3) 99X = 24

Step 4) 99X/99 = 24/99 or 8/33

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Posted by on November 3, 2011 in Decimals

 

Decimals….

First we need to know the terminology for decimals before we jump in, the terminology is very important. We can start off by understanding the meaning of the Latin word decem, which mean ten. Some of the other terms that we need to understand are decimal points, and mixed decimals.

The Decimal point is the dot between the digits in a number. For example 17.63 the dot between the 17 and the 63 is the decimal point. 17.63 can also be considered a mixed decimal! Another important thing to pay attention to is the place values when dealing with decimals.

Above is a picture with Place Values for numbers with decimals. On the Left side of the decimal we can see that the ending is “s” and that on the right side the ending are “ths”. These are very important to pay attention too.

We can also write the number in an extended form.

5(10^3)+ 4(10^2)+ 7(10)+3(1)+ 2(1/10) +8(1/100) +6(1/1000)

When we read the number we read it in a different way than what we would if just reading a whole number. When reading a decimal we say the word “and” when we come across the decimal. Below is a example of this.

 
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Posted by on November 2, 2011 in Decimals

 

Factions easy as 1,2,3!

It is important to have a sence about the size of fractions to be able to estimate what the answer is.

For example we can say that 3/5 + 1/2 is approximately equal to 1 or just over one. We can say this because 3/5 is just over a half. Therefore if we add what they are close to we can see that it will be just over 1.

Not only can we make an estimation of what the answer might be but we can use the rectangle method of multiplication for fractions!

Not only can we use this method with whole number but we can use this for fractions. The picture below shows a few examples of using this method with fractions.

When using the Rectangle Method of Multiplication for fractions you have to be able to think in parts of a whole. For example when we do 1/2 x 2/3 (the bottom problem in the picture above) we start with a 1×1 square, then we have to split the square into halves in one direction, and then into thirds in the other direction. After we do this we can shade in 2/3. By splitting the 1×1 square into half in one direction and thirds in the other we get a box that is sixths, this gives us a final answer of 2/6 because there are six parts and two of them are shaded.

We can also use this method for division of fractions if you change the division into multiplication. Here are some videos that can help explain adding and subtraction of fractions. It will also help explain multiplication and division.


 
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Posted by on October 28, 2011 in Fractions

 

Apples, Oranges, and Grapes

Fractions are part of our every day life; we use them all the time without even knowing it. A Fraction is simply when an object or a number is divide into equal parts; each part is a fraction of the whole. There are aways to parts to a fraction. The first part is the Numerator or the “number on the top”. The Numerator is the number of the shaded parts of the whole. The second part is the Denominator or the “number on the bottom”. We can think of the Denominator as units, or all the parts. The Denominator can also never be zero.

The Picture to the left is a Fraction Bar, we can use this to show a fraction with shading and to help us solve problems. This fraction happens to be fourths. Three out of the four squares are shaded therefore it is 3 fourths. This can also be written as a fraction.

To write this as a fraction you would put the 3 in the Numerator, because this is the shaded part of the whole, and you would put the 4 in the denominator because this is the whole number or the units.

This is another Fraction bar, however the size and the shading has changed. This fraction bar represents halves.1 out of two have halves are shaded therefore it is 1 half.

To write this as a fraction you would put the 1 in the numerator, the shaded part. and a 2 in the denominator because there are 2 parts or units.

Another way to use Fraction Bars are to find equivalent fractions. We can take a fraction like 2/3 and find all the fractions that are equal to it.

In the picture above we can see that 2/3 is equal to 4/6 and 8/12.

Another way that we can tell if fractions are equal is by taking the original fraction, and multiplying it by 2/2, 3/3, 4/4 and so on.

2/4 = 4/8 = 3/12 = 8/16

This is a much easier way to understand and work with fractions.

 
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Posted by on October 20, 2011 in Fractions

 

Oh No Not Them Numbers

We have many different kinds of numbers; we have Natural numbers (number {1,2,3,4,5,….} or Counting numbers), Whole number {0,1,2,3,4,….} and we have Interagers {….,-3,-2,-1,0,1,2,3,….}.

when useing negative in math we can become confused very quickly, It seem that as soon as we see the negative symbol (-) our brains freak out. This can be a easy fix if you just have the right tools. Color squares can be big help.

Red- Negative

Black- Possitive

Black + Red = 0

The Picture above are models of using red and black squares to help solve the problems. On the left we have    -3 + 5= 2 and on the right we have -5 + 1 = -4.

We can also look at these problems by creating a “sea of zeros” with problem in the center and solve the problem in a different way.

In the picture above we have -2 (the number in the center circle) and we want to take away 3. Our problem is -2 – 3 = ___. We can get an answer by takeing away three of the black squares in the “sea of zeros”, this will leave us with -5.

These are much easier ways to deal with negative numbers. Not only are the helpful but they are easy to understand!

 
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Posted by on October 19, 2011 in Uncategorized

 

GCF and LCM!

Find the Greatest Common Factor (GCF) or the Least Common Multiples (LCM) can be very intimidating and confusing. However there are tricks that can making find these things simpler.

The Greatest Common Factor can be defined as, the highest common factor between two numbers. In order to find this we need to know what all the parts are. A factor is two numbers that you can multiply together to get another number.

The Factors of 12: 1, 2, 3, 4, 6, and 12

The Factors of 30: 1, 2, 3, 5, 6, 10, 12, and 30

So we can conclude that the Greatest Common Factor is 6.

We can find the Greatest common factors by looking at factors of a number or we can find it by looking that the prime factorization. We can do this be breaking down numbers into primes.

For example:                                                 

The Prime Factors of 12 are 2 x 2 x 3

The Prime Factors of 30 are 2 x 3 x 5

12= 2 x 2 x 3

30=       2 x 3 x 5

We can find the GCF and the LCM by looking that these numbers. To find the GCF we can look at the intersection of the Prime factorization of 12 and 30.  The intersection of 12 and 30 is 2 and 3; therefore the GCF is 2 x 3= 6. We can also find the LCM by looking at these numbers, to find the LCM we look at all the number of the prime factorization (the union of the numbers). The LCM of 12 and 30 is 2^2, 3 and 5; therefor the LCM is 2 x 2 x 3 x 5 =60.

 
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Posted by on October 12, 2011 in Uncategorized

 

Factors & Multiples

Factors and multiples can be scary word if you don’t understand their meaning.

A factor is simply taking apart a number so that it is expressed as a product of the factor. Factors can also be either a composite number or a prime number (0 and 1 are neither.)

The Prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,…..

Prime numbers can be defined as a number greater than one who’s only factors are one and  itself.

The Composite number are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20,……

Composite numbers can be defined as counting number that are not prime.

For example: 16

The factors of 16 are 1,16; 2,8; and 4

therefore we can take one of these factor pairs; such as 2,8 and write a multiplication problem. 2 X 8 = 16

Multiples are a number of a product;that number and any other whole number. Zero is a
multiple of every number.

For example: 12 is a multiple of 3 because 3 divides evenly.

So 3 x 4 = 12 ; 12 is a multiple of 3 and 4.

 
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Posted by on October 8, 2011 in Uncategorized