Proper fractions The value of the numerator is less than the value of the denominator. Proper in this case does not mean correct or best.

Improper fractions The value of the numerator is greater than or equal to the value of the denominator.

Exploration 5.12 Drawn to scale Part 1 Use reasoning not algorithms to answer #1 Part 2 Use reasoning to answer #1 and 2

Mixed numbers Meaning of

Writing mixed numbers as improper fractions The algorithm that is taught in schools obscures the meaning. This is true for many algorithms, which are “efficient” ways of carrying out operations.

Write mixed number as improper fraction and vice versa

Adding and subtracting fractions

1/2 + 1/3

Multiplying fractions Repeated addition model Area model

Multiplication of fractions Fraction as operator The multiplication algorithm is best explained by the area model.

2/3 of 2 1/2

Mixed number times mixed number

Dividing fractions Division of fractions is most easily understood as repeated subtraction.

11 divided by 1 1/2

Multiplicative inverses The multiplicative inverse of a is 1/a

Dividing fractions Because division is the inverse operation of multiplication, dividing a number by a fraction is equivalent to multiplying the number by the multiplicative inverse, called the reciprocal, of the fraction.

Explorations 5.13 and In Class Part 1, #2, 3 –For HW4-7 and Part 2, #1 5.14#1-5