# The Rational Numbers

Multiplying Rational Numbers

The product of two rational numbers is the product of the numerators divided by the
product
of the denominators.

Reduce the product .

Reduced this will be

Dividing Rational Numbers

If the product of a and b is one, then a and b are reciprocals .

and are reciprocals 5 and are reciprocals

and are reciprocals

The quotient of two rational numbers is found by multiplying by the reciprocal .

Reduce the product.

Reduced this will be

To add two rational numbers that have the same denominator, add the numerators
and write the sum over the denominator.

Reduce the sum.

Reduced this will be

Playing with blocks can help us understand addition of fractions.

To add two rational numbers that have the different denominators , write the rational
numbers as equivalent fractions with the same denominators (The smallest possible
denominator will be the LCM of the two denominators ) then add the numerators
and write the sum over the denominator.

It is always true that

bd is not necessarily the smallest denominator but it will work.

Subtraction is the same as addition.

The rational numbers are dense. Between any two rational numbers there is another
rational number.

To find a rational number that is half way between two other rational numbers, add
them together and divide by 2 (find the average.) Multiplying by one half is the same
as dividing by two.

What number is half way between and

is half way between and

 A chocolate chip cookie recipe for 3 dozen cookies requires ⅔ of a cup of sugar. How many cups of sugar will be required to bake 8 dozen cookies? A chocolate chip cookie recipe for 3 dozen cookies requires 4 eggs. How many eggs will be required to bake 8 dozen cookies?

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