Lesson 2.

• Reducing and simplifying fractions

• Multiplying fractions

Multiplying fractions and whole numbers:

	Change the whole number into a fraction
	Then multiply.

Only the numerator is multiplied by the whole numbers.

Multiplying a fraction by a fraction: (a common denominator is not necessary) 

		First multiply the numerators
		Then multiply the denominators
2 ÷ 2 = 1	2 × 1 = 2	You can simplify before you multiply and we can cancel the common factor 2
	2 × 4 = 8

Changing  mixed numbers to improper fractions:

Example: Multiply the whole number (2) by the denominator (3) and add it to the numerator (1)

	You se that  2 × 3 + 1 = 7
	The denominator remains the same.

Mixed numbers are changed to improper fractions before multiplying. 

	Change mixed numbers into improper fractions
	Look for common factors to be canceled out
	We can cansel the factor 4 out
	Then simplify to get the correct answer

First, mixed numbers are changed into improper fractions, then simplified. 

Sometimes variables (letters) are used.

The same rules apply: first reduce, then simplify.

Dividing fractions

To divide fractions, invert the divisor (the second fraction) and multiply.

	Invert the divisor (the second fraction) and multiply
	Then simplify by canselling out the common factors, multiply and simplify.

Whole numbers must be changed into fractions.

	Change the whole number into a fraction
	Invert the divisor (the second fraction) and multiply

Mixed numbers must be changed into improper fractions.

	Change mixed number into improper fraction
	Invert the divisor (the second fraction) and multiply
	Then canselling out the common factors and simplify

Sometimes algebraic variables are used.

	Invert the divisor (the second fraction) and multiply
	Then canselling out the common factors and simplify

The same rules apply for numbers and letters.

Try Quiz 2 on Multiplying and dividing fractions.
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