Comparing and Order Fractions and Decimals—To compare fractions with the same denomiators, compare the numerators. To compare fractions with the same numerators, compare the denominators. When comparing mixed numbers, compare the whole numbers first. If the whole numbers are the same, then compare the fractions. If the denominators are different, find a common denominator and then compare.
5 5/8 < 5 2/3 < 6 ½
5 5/8 = 5 15/24
5 2/3 = 5 16/24
When comparing a decimal to a fraction, rewrite the fraction as a decimal, then compare.
¾ and 0.8
¾ = 0.75 and 0.8 =0.80
0.75 <0.80 so ¾ < 0.8
When multiplying fractions, multiple the numerators and then the denominators and simplify.
For example: 2/3 x 3/5 =6/15 = 2/5
When multiplying mixed numbers, change the mixed numbers to improper fractions and then multiply and simplify.
1 ¼ x 1 2/3 = 5/4 x 5/3 =25/12
25/12 = 2 1/12
Properties of Operations
Commutative Property of Addition—if the order of terms changes, the sum stays the same. 12 + a = a + 12
Associative Property of Addition—when the grouping of terms changes, the sum stays the same. 5 + (8 + b) = (5 + 8) + b
Identity Property of Addition—The sum of 0 and any number is that number.
0 + c = c
Commutative Property of Multiplication—if the order of factors changes, the product stays the same.
d x 9 = 9 x d
Associative Property of Multiplication—when the grouping of factors changes, the products stays the same.
11 x (3 x e) = (11 x 3) x e
Identity Property of Multiplication—the product of 1 and any number is that number. 1 x f = f
Distributive Property—multiplying a sum by a number is the same as multiplying each term by the number and then adding the products.
5 x (g + 9) = (5 x g) + (5 x 9)