Fractions

Fraction- a quantity that is less than a whole unit, an ordered pair of integers a&b, with b not equaling 0, written as a/b, the integer a is the numerator and b is the denominator.

Models-

• Part to Whole-
• you must agree on a unit (cups, inches, centimeters, ect.)
• you must understand that the unit is subdivided into b parts of a equal sizes
• and that you are only considering a certain number of parts
• Color Region (Area Model)-
• a shape chosen to represent unit which is visualized by coloring some of the regions.
• The Set Model-
• A finite set of objects(u) is chosen to represent the unit which is divided into n(u)= equal parts A fracction is visualized by circling the number of objects that represent numerator of fraction
• Number Line-
• portions of the number line is subdivided into equal size parts

Simplifying Fractions-

• when the numerator and the denominator of a fraction have a common factor that is greater than one they can both be divided by that common factor inorder to reduce the fraction into smallest terms.

Common Denominator-

Fraction Bars-

 This shows that 1/2 and 3/6 is equal and also that 1/3 and 2/6 are equal.

Rules of Signs for Fractions-

-7/9= -7/-9 FALSE

-5/-12= 5/-12 TRUE

3/-5=-3/5 TRUE

Mental Calculation and Estimation-

which is smaller? 1/7 or 1/10    1/10 is smaller

which is larger? 2/3 or 1/3     2/3 is larger

are they equal? 1/3 and 2/6   yes

Rounding-

9//12 almost 1

7 1/5 almost 7