Fractions

Fractions 

• ADDING AND SUBTRACTING
• When adding and subtracting fractions you do not add the bottom (denominator) only the top (numerator)

EX. 2/6+2/6=?

You add the tops to each other and keep the bottoms.

2/6+2/6=4/6

Then you must simplify the fraction. If the numerator and the denominator have an LCD besides one then take both out and cancel.

4/6

2*2/2*3

2/3

• If the denominators are different you need to multiply them by the GCF to make them the same but by doing this you also have to multiply it to the numerator as well

EX. 2/6 + 2/3=?

The GCF of the denominators is 6 so you want to change both of the denominators to 6. You have to multiply the 6 by 1 and the 2 by 2. In the next fraction you have to multiply the denominator (3) by 2 to make it six by doing this you have to multiply the numerator (2) by 2 as well.

2/6+2/3

2*1/6*1+2*2/3*2

2/6+4/6

6/6

1

The reason 6 over 6 is equal to 1 is because a fraction bar is essentially a division bar.

• When you add one fraction with a variable (letters) you want to multiply everything in the equation by the denominator

EX. 2/6+x=3

[2/6+x=1]6

2+6x=6

-2      -2

6x=4

_    _

6    4

x=4/6

x=2/3

• Certain denominators change the fraction into a normal number. Anything with a denominator 1 is always itself because any number divided by 1 is itself. If the denominator is divisible by the numerator you divide it.

Ex. 6/1=6

6/3=2

• Equivalent fractions are fractions that equal each other. Because the fraction bar is a division bar the quotient will be the same.

EX. 3/4=6/X

There are two ways to solve this problem. 

4*6/3=x

24/3=X

8=X

or

Crossmultiply

4*6=3*X

24=3X

_     _

3     3

8=X

• Mixed fractions are fractions with a whole number out front (3 and 3/5) To change a mixed fraction into an improper fraction multiply the whole number by the denominator and add the numerator and put it all over the original denominator. To change an improper fraction into a mixed fraction you must divide the denominator into the numerator and whatever is left till you get to a multiple of the numerator.

EX. 5/2

2/5=1 and

1 and 1/2

EX.3 and 4/2

3*2+4

10

10/2

Here are some practice problems. Simplify (solve)  

1. 1/2+1/2=?
2. 6/2+4/2=?
3. 2/1+3/1=?
4. 8/1+4/1=?
5. 6/3+9/3=?

1. 2/6+2/4=?
2. 3/2+7/8=?
3. 4/6+4/12=?
4. 4/9+6/3=?
5. 4/5+6/20=?

1. 3/6+X=3
2. 4/5+5-X=5
3. 6/4-6+6+4-0+X=3
4. 1/2+2=6
5. 3/2-X=1

1. 3/6=4/X
2. X/1=4/2
3. X/4=6/1
4. 2/X=6/9
5. 2/X=7/1

Make Each Mixed Fraction Into an Improper Fraction and Each Improper Fraction Into a Mixed Number

1. 3 and 4/5
2. 9/4
3. 4/2
4. 8 and 6/1
5. 2 and 4/6

ANSWERS

1. 1
2. 5
3. 5
4. 12
5. 5

1. 5/6
2. 19/8
3. 1
4. 22/9
5. 11/10

1. 5/3 or 
2. 4/5+5-X=5
3. 6/4-6+6+4-0+X=3
4. 1/2+2=6
5. 3/2-X=1

1. X=8
2. X=1/2
3. X=2/3
4. X=3
5. X=2/7

1. 19/5
2. 2 and 1/4
3. 2
4. 14
5. 16/6

Exponents

EXPONENTS

Now exponents can be difficult but once you get used to them they are pretty easy.

The exponent of a number shows you how many times the number is to be used in a multiplication. It is written as a small number to the right and above the base number.

The exponent is also called a power or an index. When you raise a number to it's power that's how many times you are multiplying it by.

EX. 8² = 8*8 = 64 so 8² = 64

Anything to the 1^st power is equal to itself

EX. 9¹ = 9

1 to any exponent is always equaled to 1.

EX. 1⁶ = 1*1*1*1*1*1 = 1

Also anything to the zero power is one.

EX. 6⁰ = 1

7³ = 7³

7³/7³ = 1

7^(3-3) = 1

7⁰ = 1

That’s why the bas to the exponent zero is always equaled to 1.

Here are some problems to for you to try out. Simplify (solve)

1. 1⁷

2. 8³

3. 9²

4. 16⁰

5. 34¹

6. 75²

7. 91¹

8. 3²

9. 8⁴

Negative Exponents

Any negative exponent is the reciprocal or the number that cancels the original number out (9 is the reciprocal of 1/9; or 5/6 is the reciprocal of 6/5) and the denominator by the positive of the negative exponent.

EX. 9^-3 =1/9³ = 1/729

Here are some problems to for you to try out. Simplify (solve)

1. 1^-9

2. 3^-4

3. 7^-2

4. 1^-3/4

5. 3^-1/4

6. 2^-1

7. 8^-4

8. 1^-2

9. 6^-1

ANSWERS

Exponents:

1. 1
2. 512
3. 81
4. 1
5. 34
6. 5625
7. 91
8. 9
9. 4096

Negative Exponents:

1. 1
2. 1/81
3. 1/49
4. 4
5. 4/3
6. ½
7. 1/4096
8. 1
9. 1/6

Go to this link for print out worksheet:

file:///Users/ceciliamace/Desktop/Exponents%20Worksheet.htm