Adding fraction

1.) Adding fraction with proper with like  denominators.

You just add both numerators.

Examples:

       7/20 + 2/20 = 9/20

2.) Adding fraction with proper with unlike denominators.

You have to make them equal by changing the denominators.For example, if it's 30 and 50, you have to make 50.

Mixed & Improper Fractions

Mixed and Improper Fractions

For mixed and improper fractions, let's start with knowing what a fraction is. A fraction is showing a division from part and whole. It shows how much the whole is divided up to in equal parts.

Numerator: In ½ , the 1 is represented as the part of the whole, meaning it's the numerator.

The numerator shows the equal parts in the fraction. 1/2 also means half because 1 is half of 2.

Denominator: In the fraction ¾, the 4 is represented as the denominator. The denominator shows how much the whole is, or the total. 

Divide: In fractions, there is the numerator ( In simplest terms, the number at the top ), and the denominator ( The number at the bottom ), but what does the line represent? The line in fractions represents divide. When you divide the numerator to the denominator, you'll turn the fraction into a decimal. If you turn a 

fraction like ¾ into a decimal, divide 3 to 4 to equal 0.75.

 Mixed Fractions:

Mixed Fractions is when there is a whole number mixed with a proper fraction. This happens when there is an improper fraction, but showed in a different way.

2¾ In this fraction, the 2 is the whole number. The 3 is the parts in the whole. The 4 is how much parts the whole is divided up to, or the total.

Improper Fractions: 

Improper Fractions is when the numerator is greater than the denominator, making it improper. You could easily convert improper fractions into mixed fractions, and vice versa.

11/4 In this fraction, you could tell it's improper by seeing that the numerator is greater than the denominator. 11 is greater than 4 so you can also tell that it's more than a whole. 4/4 is a whole, and 11/4 is greater.

Converting Mixed to Improper and Improper to Mixed:

2¾ For mixed to improper, you can take the whole number (2) and then multiply that by the denominator (4), then adding the numerator (3). Equation: 2x4+3 = 11. Once you have the answer, just simply input the denominator. Remember, the denominator never changes. Your answer should be the numerator. This equals up to 11/4.

11/4 For improper to mixed, you'll have to use your division facts. Find out how much the denominator (4) could fit into the numerator (11). So how I thought of it is 4x3 equals 12 but 12 is greater than 11, so then 2x4. 2x4 = 8. After that, figure how much you need to get to the previous numerator, so 8 to 11, you add 3. 3 is the leftover number. The leftover number will be the numerator on the new mixed number and the denominator will stay the same. The whole will be the number you multiplied by the denominator, in this case, the 2, equaling 2 3/4.

Hope this helps! ^_~~

- Pam Joseph 7-09

Converting Review ( percent,fractions,decimals)

How to convert Percent to Decimals:
Eg.
       25% and 2.5% are examples of percent.
- so we need to find the decimal form of both of 25% & 2.5%

1. To do that, we first need to find the decimal point of the percent/number.

Remember: if you can't see thr decimal point of the percent/number, the decimal point is at the right end of the number.
Eg.
        37% ( 37. <--- decimal point )

2. After we find the decimal point of the percent/number, we now move the decimal point 2x to the left then remove the percent sign.
Eg. #1
       25.%    ->      25. = 0.25 ( final answer )
           ^         <-- move the dec. p. to the left (2x)
Decimal point

Eg. # 2
       2.5%      ->   2.5 = 0.025
         ^                <-- move the dec. p. to the left (2x)
Decimal point

* always move the decimal point 2x to the left.
* if there's a gap/space when you move the decimal point like example number 2, just fill the gap with the number 0.

How to convert Decimals to Percent:
Eg.
      0.25 and 2.5
- we need to convert 0.25 and 2.5 to percent.

1. First thing we need to do is to find the decimal point.
Eg.
       0.25  2.5
         ^       ^
            \   /
  Decimal points

2. After that, we now move the decimal point 2x to the right then just add a percent sign (%).
Eg#1
       0.25         ---->           0.25 + % = 25% ( final answer )
         ^                            --->Move to the right (2x)
Decimal point

* if there's the number zero in front of the decimal numbers, just remove it.
Eg#2
          2.5     --->     2.5 = 250% ( final answer )
           ^            ---> move to the right (2x)
Decimal Point

* If there's a space when you move the decimal point just add zero to the space.

How to convert Percent to Fraction:

1. We turn the percent to decimal. ( You can see that in "How to turn Percent to Decimal".
Eg.
      3.7 = 0.037

2. Now we need to identify the place value of the last number of decimal.
Eg.
       0.037
0- tenths
3- hundredths
7- thousandths

Remember: The first number after the decimal point always starts with the place value of tenths.

3. After you 've identified the place value of the last number, we now make the decimal number a numerator and the denominator is based on the place value of the last decimal number.
Eg.
         0.037 = 37/1000
                ^
       Thousandths
* if there's a zero in front of the number, just remove it.

4. If the fraction can be simplified, simplify it. To do that, we must need to find a number that can divide both the numerator and the denomintor.
Eg.
       25/100 divided both by 25 = 1/4

How to convert Fraction to Decimal:
1. We divide the numerator by the denominator.
Eg#1
       5/8 = 5 divide by the number 8. --> 0.625
5- numerator
8- denominator

Eg#2
          3 3/5 ( mixed fraction )
= 3 divide by the number 5
= 0.6 + 3
= 3.6

Remember: if you have a mixed fraction, just add the whole number to the answer of the numerator and denominator.

3 3/5
3- whole number
3- numerator
5- denominator

How to convert Decimal to Fraction:
1. We identify the place value of the last number of decimal.
Eg.
       0.625
6- tenths
2- hundredths
5- Thousandths

2. We now place the decimal number(s) as the numerator of  the fraction and the denominator is based by the place value of the last decimal number .
Eg.
        0.625    -->            625/1000 = 5/8 ( final answer )
               ^
     Thousandths      Divide both numbers by 125

* if you can simplify the fraction, simplify.



           

Mixed Numbers and Improper Fractions

        Today, we will be talking about mixed numbers and improper fractions, but before that, lets talk about what a fraction is.

        A fraction describes a part of a whole. The number on the bottom of the fraction is called a denominator, and it denotes how many equal parts the whole is divided into. The number on the top of the fraction is called a numerator, and it denotes how many parts we are taking. For example, the fraction 3/4 denotes 3 of 4 equal parts. 3 is the numerator and 4 is the denominator.

        Now, that to know what a fraction is, we will be talking about mixed numbers.
        
        A mixed number is composed of a whole number and a fraction. 6 2/3, 18 3/4 and 2 2/5 are all examples of mixed numbers.

Converting Improper Fractions into Mixed Numbers:

        Divide the numerator by the denominator. The resultant becomes the whole number, and the remainder becomes the numerator of the new fraction. The denominator of the new fraction is the same as the old denominator. If there is no remainder, then there is no fraction, the result is simply a whole number. 

For example, we can convert 22/5 into a mixed number.
22/5= 4
Remainder= 2
Mixed Number: 4 2/5

Converting Mixed Numbers into Improper Fractions:

        To convert a mixed number into an improper fraction, multiply the whole number by the denominator and add it to the numerator. This becomes the numerator of the improper fraction; the denominator of the new fraction is the same as the original denominator.

For example, we can convert 7 8/3 into an improper fraction.
7 x 3= 21
21+8= 29
Improper Fraction: 29/3



           

Adding Fractions

There are 3 Simple Steps to add fractions:

Step 1: Make sure the bottom numbers (the denominators) are the same
Step 2: Add the top numbers (the numerators), put the answer over the denominator.
Step 3: Simplify the fraction (if needed).

Example 1:

1	+	1
4		4

Step 1. The bottom numbers (the denominators) are already the same. Go straight to step 2.

Step 2. Add the top numbers and put the answer over the same denominator:

1	+	1	=	1 + 1	=	2
4		4		4		4

Step 3. Simplify the fraction:

2	=	1
4		2

In picture form it looks like this:

1/4	+	1/4	=	2/4	=	1/2

... and do you see how ²/₄ is simpler as ¹/₂ ? (see Equivalent Fractions.)

Example 2:

1	+	1
3		6

Step 1: The bottom numbers are different. See how the slices are different sizes?

1/3	+	1/6	=	?

We need to make them the same before we can continue, because we can't add them like that.

The number "6" is twice as big as "3", so to make the bottom numbers the same we can multiply the top and bottom of the first fraction by 2, like this:

× 2

1	=	2
3		6

× 2

Important: you multiply both top and bottom by the same amount,
to keep the value of the fraction the same

Now the fractions have the same bottom number ("6"), and our question looks like this:

2/6	+	1/6

The bottom numbers are now the same, so we can go to step 2.

Step 2: Add the top numbers and put them over the same denominator:

2	+	1	=	2 + 1	=	3
6		6		6		6

In picture form it looks like this:

2/6	+	1/6	=	3/6

Step 3: Simplify the fraction:

3	=	1
6		2

In picture form the whole answer looks like this:

2/6	+	1/6	=	3/6	=	1/2

Example 3:

1	+	1
3		5

Again, the bottom numbers are different (the slices are different sizes)!

1/3	+	1/5	=	?

But let us try dividing them into smaller sizes that will each be the same:

5/15	+	3/15

The first fraction: by multiplying the top and bottom by 5 we ended up with ⁵/₁₅ :

× 5

1	=	5
3		15

× 5

The second fraction: by multiplying the top and bottom by 3 we ended up with ³/₁₅ :

× 3

1	=	3
5		15

× 3

The bottom numbers are now the same, so we can go ahead and add the top numbers:

5/15	+	3/15	=	8/15
Making the Denominators the Same In the previous example how did we know to cut them into 1/15ths to make the denominators the same? Read how to do this using either one of these methods: Common Denominator Method, or the Least Common Denominator Method They both work, use whichever you prefer! Example: Cupcakes You are going to make and sell cupcakes: A friend can supply the ingredients, if you give them 1/3 of sales And a market stall costs 1/4 of sales How much is that altogether? We need to add 1/3 and 1/4 1 + 1 = ? 3 4 ? First make the bottom numbers (the denominators) the same. Multiply top and bottom of 1/3 by 4: 1 × 4 + 1 = ? 3 × 4 4 ? And multiply top and bottom of 1/4 by 3: 1 × 4 + 1 × 3 = ? 3 × 4 4 × 3 ? Now do the calculations: 4 + 3 = 4+3 = 7 12 12 12 12 Answer: 7/12 of sales go in ingredients and market costs.

Converting Fractions, Decimals and Percents

The way to convert fractions into decimals is by dividing the numerator by the denominator. For example, ¼ = 1 ÷ 4. 1 ÷ 4 = 0.25.

The way to convert decimals into percents is by multiplying the decimal by 100. For example, 0.25 x 100 = 25%

A repeating decimal is self explanatory. It repeats itself. For example, 0.333... It could also be 2 numbers. For example, 0.4646... It could also even repeat after 1 number. For example, 3522...

A terminating decimal is just the opposite of a repeating decimal. Meaning, it has an end. For example, 0.35.