Closure for addition of fractions
The sum of any two fractions is another unique fraction.
EX: -2/3 + 4/5 = -2x5 + 4x3 = -10 + 12 = 2
3x5 5x3 15 15 15
Closure for multiplication of fractions
The product of any two fractions is another unique fraction
EX: -2/3 x 4/5 = -2x4 = -8
3x5 15
Identity for addition
The sum of any fraction and 0 is the given fraction. Zero + any integer = the given integer
EX:5/6 + 0 =5/6 + 0/6 = 5+0 = 5
6 6
Identity for multiplication
http://intermath.coe.uga.edu/dictnary/descript.asp?termID=172
EX: 1 x (-4/5) = 1x-4 = -4
5 5
Addition is commutative and associative
http://www.learningwave.com/lwonline/numbers/com_assoc_add.html
commutative: two fractions that are being added can be interchanged without changing the sum
associative: in a sum of three fractions the middle numer may be grouped with either of the other two numbers.
Multiplication is commutative and associative
http://www.learningwave.com/lwonline/numbers/com_assoc_mult.html
commutative: two fractions that are being multiplied can be interchanged without changing the product
associative: In a product of three fractions the middle number may be grouped with either of the other two numbers.
Inverses for addition and multiplication
Addition: for every fraction there is another fraction called its opposite or inverse for addition such that the sum of the two fractions is 0.
EX: 3/4 and -3/4
Multiplication: for every fraction not equal to zero there is a nonzere fraction called its reciprocal or inverse for multiplication such that the product of the two numbers is 1.
EX: 3/8 and 8/3
Mental Calculations
Compatible numbers
Numbers that can be conveniently combined in a given computation
Substitutions
EX: 2 7 + 1 = 2 7 + 1 + 1 = 3 1
8 4 8 8 8 8
Estimation
Rounding
The sum or difference of mixed numbers and fractions can be estimated by rounding each number to the nearest whole number.
Practice: http://www.ixl.com/math/practice/grade-5-round-mixed-numbers
Compatible numbers
Replacing a fraction with a reasonably close and compatible fraction can be useful when estimating
