How can an understanding of multiplication be extended to fractions?

Students interpret the multiplication of natural numbers by fractions.

Multiplication of a natural number by a fraction is equivalent to multiplication by the fraction’s numerator and division by its denominator.

a x b/c = ab/c

Multiplication by a unit fraction is equivalent to division by its denominator.

a x 1/b = a/b

The product of a fraction and a natural number is the fraction with

• a numerator that is the product of the numerator of the given fraction and the natural number

• a denominator that is the denominator of the given fraction

a/b x c = ac/b

Multiplication does not always result in a larger number.

Multiplication of a natural number by a fraction can be interpreted as repeated addition of the fraction.

Multiplication of a fraction by a natural number can be interpreted as taking part of a quantity.