Directed Numbers Multiplying Dividing Demonstration This resource provides

Directed Numbers – Multiplying & Dividing – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

Multiplication is repeated addition. How can we describe these calculations? 3 × 4 = ‘the sum of 3 lots of 4’ 4 + 4 = 12 8 × 5 = ‘the sum of 8 lots of 5’ 5 + 5 + 5 = 40 4 × − 5 = ‘the sum of 4 lots of − 5’ (− 5) + (− 5) = − 20 Would we describe − 5 × 4 differently?

What result do we expect from this calculation? Multiplying Negative Numbers positive × positive = positive 4 × 5 = 20 positive × negative = negative 4 × − 5 = − 20 − 4 × 5 = − 20 negative × negative = positive − 4 × − 5 = 20 Why?

Can you describe these statements mathematically? + + I will do my homework. − + I won’t do my homework + − I will not do my homework. − − I won’t not do my homework. = positive = negative = positive

Multiplication involves a magnitude (size) & a direction. Three times the size in the same (+) direction

Multiplication involves a magnitude (size) & a direction. Three times the size in the opposite (−) direction

Multiplication involves a magnitude (size) & a direction. Three times the size in the same (+) direction

Multiplication involves a magnitude (size) & a direction. Three times the size in the opposite (−) direction

What result do we expect from this calculation? Dividing Negative Numbers positive ÷ positive = positive 20 ÷ 5 = 4 negative ÷ positive = negative − 20 ÷ 5 = − 4 positive ÷ negative = negative 20 ÷ − 5 = − 4 negative ÷ negative = positive − 20 ÷ − 5 = 4 Why?

Division is the inverse of multiplication with a magnitude (size) & a direction. A quarter the size in the same (+) direction

Division is the inverse of multiplication with a magnitude (size) & a direction. A quarter the size in the opposite (−) direction

Division is the inverse of multiplication with a magnitude (size) & a direction. A quarter the size in the same (+) direction

Division is the inverse of multiplication with a magnitude (size) & a direction. A quarter the size in the opposite (−) direction

Describe and solve these calculations using a number line.

Multiplying Negative Numbers positive × positive = positive 4 × 5 = 20 positive × negative = negative 4 × − 5 = − 20 − 4 × 5 = − 20 negative × negative = positive − 4 × − 5 = 20 Dividing Negative Numbers positive ÷ positive = positive 20 ÷ 5 = 4 negative ÷ positive = negative − 20 ÷ 5 = − 4 positive ÷ negative = negative 20 ÷ − 5 = − 4 negative ÷ negative = positive − 20 ÷ − 5 = 4 Solve these calculations.

Multiplying Negative Numbers positive × positive = positive 4 × 5 = 20 positive × negative = negative 4 × − 5 = − 20 − 4 × 5 = − 20 negative × negative = positive − 4 × − 5 = 20 Dividing Negative Numbers positive ÷ positive = positive 20 ÷ 5 = 4 negative ÷ positive = negative − 20 ÷ 5 = − 4 positive ÷ negative = negative 20 ÷ − 5 = − 4 negative ÷ negative = positive − 20 ÷ − 5 = 4

Multiplying Negative Numbers positive × positive = positive 4 × 5 = 20 positive × negative = negative 4 × − 5 = − 20 − 4 × 5 = − 20 negative × negative = positive − 4 × − 5 = 20 Dividing Negative Numbers positive ÷ positive = positive 20 ÷ 5 = 4 negative ÷ positive = negative − 20 ÷ 5 = − 4 positive ÷ negative = negative 20 ÷ − 5 = − 4 negative ÷ negative = positive − 20 ÷ − 5 = 4

Multiplying Negative Numbers positive × positive = positive 4 × 5 = 20 positive × negative = negative 4 × − 5 = − 20 − 4 × 5 = − 20 negative × negative = positive − 4 × − 5 = 20 Dividing Negative Numbers positive ÷ positive = positive 20 ÷ 5 = 4 negative ÷ positive = negative − 20 ÷ 5 = − 4 positive ÷ negative = negative 20 ÷ − 5 = − 4 negative ÷ negative = positive − 20 ÷ − 5 = 4

Multiplying Negative Numbers positive × positive = positive 4 × 5 = 20 positive × negative = negative 4 × − 5 = − 20 − 4 × 5 = − 20 negative × negative = positive − 4 × − 5 = 20 Dividing Negative Numbers positive ÷ positive = positive 20 ÷ 5 = 4 negative ÷ positive = negative − 20 ÷ 5 = − 4 positive ÷ negative = negative 20 ÷ − 5 = − 4 negative ÷ negative = positive − 20 ÷ − 5 = 4

Multiplying Negative Numbers positive × positive = positive 4 × 5 = 20 positive × negative = negative 4 × − 5 = − 20 − 4 × 5 = − 20 negative × negative = positive − 4 × − 5 = 20 Dividing Negative Numbers positive ÷ positive = positive 20 ÷ 5 = 4 negative ÷ positive = negative − 20 ÷ 5 = − 4 positive ÷ negative = negative 20 ÷ − 5 = − 4 negative ÷ negative = positive − 20 ÷ − 5 = 4

Multiplying Negative Numbers positive × positive = positive 4 × 5 = 20 positive × negative = negative 4 × − 5 = − 20 − 4 × 5 = − 20 negative × negative = positive − 4 × − 5 = 20 Dividing Negative Numbers positive ÷ positive = positive 20 ÷ 5 = 4 negative ÷ positive = negative − 20 ÷ 5 = − 4 positive ÷ negative = negative 20 ÷ − 5 = − 4 negative ÷ negative = positive − 20 ÷ − 5 = 4

Multiplying Negative Numbers positive × positive = positive 4 × 5 = 20 positive × negative = negative 4 × − 5 = − 20 − 4 × 5 = − 20 negative × negative = positive − 4 × − 5 = 20 Dividing Negative Numbers positive ÷ positive = positive 20 ÷ 5 = 4 negative ÷ positive = negative − 20 ÷ 5 = − 4 positive ÷ negative = negative 20 ÷ − 5 = − 4 negative ÷ negative = positive − 20 ÷ − 5 = 4

Multiplying Negative Numbers positive × positive = positive 4 × 5 = 20 positive × negative = negative 4 × − 5 = − 20 − 4 × 5 = − 20 negative × negative = positive − 4 × − 5 = 20 Dividing Negative Numbers positive ÷ positive = positive 20 ÷ 5 = 4 negative ÷ positive = negative − 20 ÷ 5 = − 4 positive ÷ negative = negative 20 ÷ − 5 = − 4 negative ÷ negative = positive − 20 ÷ − 5 = 4

Multiplying Negative Numbers positive × positive = positive 4 × 5 = 20 positive × negative = negative 4 × − 5 = − 20 − 4 × 5 = − 20 negative × negative = positive − 4 × − 5 = 20 Dividing Negative Numbers positive ÷ positive = positive 20 ÷ 5 = 4 negative ÷ positive = negative − 20 ÷ 5 = − 4 positive ÷ negative = negative 20 ÷ − 5 = − 4 negative ÷ negative = positive − 20 ÷ − 5 = 4

Multiplying Negative Numbers positive × positive = positive 4 × 5 = 20 positive × negative = negative 4 × − 5 = − 20 − 4 × 5 = − 20 negative × negative = positive − 4 × − 5 = 20 Dividing Negative Numbers positive ÷ positive = positive 20 ÷ 5 = 4 negative ÷ positive = negative − 20 ÷ 5 = − 4 positive ÷ negative = negative 20 ÷ − 5 = − 4 negative ÷ negative = positive − 20 ÷ − 5 = 4

Multiplying Negative Numbers positive × positive = positive 4 × 5 = 20 positive × negative = negative 4 × − 5 = − 20 − 4 × 5 = − 20 negative × negative = positive − 4 × − 5 = 20 Dividing Negative Numbers positive ÷ positive = positive 20 ÷ 5 = 4 negative ÷ positive = negative − 20 ÷ 5 = − 4 positive ÷ negative = negative 20 ÷ − 5 = − 4 negative ÷ negative = positive − 20 ÷ − 5 = 4

Multiplying Negative Numbers positive × positive = positive 4 × 5 = 20 positive × negative = negative 4 × − 5 = − 20 − 4 × 5 = − 20 negative × negative = positive − 4 × − 5 = 20 Dividing Negative Numbers positive ÷ positive = positive 20 ÷ 5 = 4 negative ÷ positive = negative − 20 ÷ 5 = − 4 positive ÷ negative = negative 20 ÷ − 5 = − 4 negative ÷ negative = positive − 20 ÷ − 5 = 4

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