Multiply and divide rational numbers

key notes :

Multiplying Rational Numbers

Definition:

  • To multiply two rational numbers, multiply the numerators together and the denominators together.
  • Formula

Steps:

  • Multiply the numerators: a×c
  • Multiply the denominators: b×d
  • Simplify the resulting fraction, if possible.
  • Example:
Multiplying by a Whole Number:

When multiplying a rational number by a whole number, treat the whole number as a fraction with denominator 1.

Dividing Rational Numbers

Definition:

  • To divide two rational numbers, multiply the first rational number by the reciprocal of the second rational number.
  • Formula:

Steps:

  • Find the reciprocal of the divisor (flip the numerator and the denominator of the second fraction).
  • Multiply the first fraction by this reciprocal.
  • Simplify the resulting fraction, if possible.
  • Example:
Dividing by a Whole Number:
  • When dividing a rational number by a whole number, treat the whole number as a fraction with denominator 1 and then find its reciprocal.
Simplifying Rational Numbers
  • After multiplying or dividing rational numbers, always simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by this number.Example:
Practice Problems
  • Multiplying Rational Numbers:
  • Dividing Rational Numbers:
  • Mixed Practice:
Tips for Success

Reciprocals:

  • Remember to find the reciprocal when dividing by a fraction.

Simplifying:

  • Always simplify your answer to its lowest terms.

Multiplication and Division Rules:

  • Use the multiplication rule for both operations: multiply the numerators together and the denominators together for multiplication, and multiply by the reciprocal for division.

Check Your Work:

  • Double-check your multiplication and division to avoid small mistakes.

positive × positive = positive

positive × negative = negative

negative × positive = negative

negative × negative = positive

To multiply two fractions, multiply the numerators and multiply the denominators.

ex: 2/3 × 1/5 = 2/15

positive ÷ positive = positive

positive ÷ negative = negative

negative ÷ positive = negative

negative ÷ negative = positive

Dividing by a fraction is the same as multiplying by its reciprocal.

Ex: 2/3 ÷ 1/3 = 2/3 x 3/1 =6/3 =2

Learn with an example

🎯 Multiply.

4/5 x 1/4 =

Cancel common factors, then multiply.

4/5 x 1/4 = 1/5 x 1/1

= 1 x 1 / 5 x 1

= 1/5

🎯 Multiply.

1/2 x 2/5 =

Cancel common factors, then multiply.

1/2 x 2/5 = 1/1 x 1/5

= 1 x 1 / 1 x 5

= 1/5

🎯 Multiply.

1/4 x 2/5 =

Cancel common factors, then multiply.

1/4 x 2/5 = 1/2 x 1/5

= 1 x 1 / 2 x 5

= 1/10

Let’s Practice!