Crusenberry 7.16.13

Fractions

Fraction / A number that names part of a whole
Numerator / Tell the number of equal parts being described
Denominator / Tells the number of equal parts in the whole
Proper fraction / The numerator is less than the denominator
Improper fraction / The numerator is greater than the denominator; always greater than 1
Name for one (1) / Both the numerator and denominator are the same
Mixed number / A whole number combined with a fraction
Equivalent fractions / Equal in value but have different numerators and denominators
Factor / A number that is multiplied to yield a product
LCD (Least common denominator) / The smallest number that both denominators will go into
GCF (Greatest common factor) / The largest number that will go into both the numerator and denominator

Comparing fractions –

1/3 _____ 1/6 **use a pie graph or change the fractions to a decimal and then compare
1/3 = .331/6 = .16
so 1/3 > 1/6

Equivalent fractions – multiple both the numerator and the denominator by the same number to make
equivalent fractions

22 x 24
33 x 26

Renaming improper fractions–
2

125 1 2
5 -1 0
2 **this number becomes your new numerator, so your answer is 2 and 2/5

Moving between fractions and decimals -
. 2 5

1 / 4 = 4 1 . 0 0 ** 4 will not go into 1, so add a decimal and a zero
- 8
2 0
- 2 0
0

Finding common factors –

Find the factors of 12
1 x 122 x 63 x 44 x 3 **STOP, we already have a 3 and a 4

Adding and Subtracting with like denominators –

1/3 + 1/3 = 2/3

1 7/10 + 2 1/10 = 3 8/10 which reduces to 3 4/5

Regrouping to subtract –

4 – 4/5 = 3 5/5 – 4/5 = 3 1/5

**Remember that when you borrow one whole number you have to fix it on the other side. That one who number is the 5/5. We used 5/5 because that is the denominator of the fraction in the problem.

Finding common denominators –

1/5 and 2/3

First - find the multiples of 55 10 15
Second – find the multiples of 33 6 9 12 15
**When you get to a common number, that is your new common denominator

Comparing and ordering unlike fractions –

3/5 and 7/9

First- find the multiples of each till you come to a common number. In this case it is 45.
Second –make 45 the common denominator

___/45 ___/45

5 goes into 45 9 times, so 9 x 3 is 27; 9 goes into 45 5 times, so 5 x 7 is 21

21/45 < 35/45

Adding and Subtracting with unlike denominators –

1/2 + 1/5 **find the least common denominator; in this case it is 10

__/10 + __/10 **2 goes into 10 5 times and 5 x 1 is 5; 5 goes into 10 2 times, so 2 x1 is 2

5/10 + 2/10 = 7/10

4 2/3 + 2 1/6 **find the least common denominator; in this case it is 6

4 __/6 + 2 __/6 **3 goes into 6 2 times, so 2 x 2 is 4; 6 goes into 6 1 time so 1 times 1 is 1

4 4/6 + 2 1 / 6 = 6 5/6

Multiplying fractions –

1/3 x 2/3 = **multiply the numerators to get 2; multiply the denominators to get 9

2/9

Canceling before multiplying fractions –

2 3
x**3 goes into itself once and 3 goes into the 9 three times, so..
9 5

2 1
xso the answer is 2/15
3 5

Finding reciprocals – all you do is flip the numerator and the denominator

4/5 would become 5/44 ½ would become 9/2 via making improper, then the reciprocal is 2/9

Dividing fractions –

9/10 ÷ 3/8 **change the ÷ to x and flip the second fraction, so…
9/10 x 8/3 = 72/30 – 2 2/5

Dividing with Whole Numbers or Mixed Numbers -

12 ÷ 2/3 **make the whole number 12 a fraction by placing a 1 under it

12/1 ÷ 2/3 **change the ÷ to x and flip the second fraction, so…

12/1 x 3/2 = 36/2 = 18

11/3 ÷ 2/3 **change the mixed number to an improper fraction

4/3 ÷ 2/3 **change the ÷ to x and flip the second fraction

4/3 x 3/2 = 12/6 = 2