ILLUSTRATING INTEGERS Multiplication and Division INTEGERS AND MULTIPLICATION

INTEGERS AND MULTIPLICATION The University of Texas at Dallas

MULTIPLICATION Red and blue tiles can be used to model multiplication. Remember that multiplication

MULTIPLICATION 2 x -3 means 2 groups of -3 – – – 2 x

MULTIPLICATION Since 2 x 3 = 6 and 3 x 2 = 6, does

MULTIPLICATION Use your tiles to model each multiplication problem. +2 x +4 = ?

MULTIPLICATION +3 x -3 = ? – – – – – ANSWER 3 groups

MULTIPLICATION -2 – – x +4 = ? – – – ANSWER 4 –

MULTIPLICATION To model -2 x -3, think “the opposite” of 2 groups of -3,

MULTIPLICATION Use tiles to illustrate -3 x -4 =? ANSWER + + + The

INTEGERS AND DIVISION The University of Texas at Dallas

DIVISION Use tiles to model +12 ÷ +3 = ? 4 red tiles in

DIVISION Use tiles to model -15 ÷ +5 =? – Divide 15 into 5

DIVISION Write the fact family -4 x + 2 = -8 Compare your answer.

$DIVISION Three equivalent ways to write a division expression as a fraction: 12 ÷$

Mixed Practice Now try these! Use red and yellow tiles to find each answer.

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ILLUSTRATING INTEGERS Multiplication and Division

INTEGERS AND MULTIPLICATION The University of Texas at Dallas

MULTIPLICATION Red and blue tiles can be used to model multiplication. Remember that multiplication can be described as repeated addition. So 2 x 3 = ? + + + 2 groups of 3 tiles = 6 tiles The University of Texas at Dallas

MULTIPLICATION 2 x -3 means 2 groups of -3 – – – 2 x -3 = -6 The University of Texas at Dallas

MULTIPLICATION Since 2 x 3 = 6 and 3 x 2 = 6, does it make sense that -3 x 2 = -6 ? -3 x 2 = -6 is true. +2 x -3 = -6 and -3 x +2 = -6 belong to a fact family: +2 x -3 = -6 -3 x + 2 = -6 -6 ÷ + 2 = -3 -6 ÷ -3 = + 2 The University of Texas at Dallas

MULTIPLICATION Use your tiles to model each multiplication problem. +2 x +4 = ? + + 2 groups of +4 + + + +2 ANSWER x +4 = +8 The University of Texas at Dallas

MULTIPLICATION +3 x -3 = ? – – – – – ANSWER 3 groups of -3 +3 x -3 = -9 The University of Texas at Dallas

MULTIPLICATION -2 – – x +4 = ? – – – ANSWER 4 – groups of -2 -2 x + 4 = -8 Use the Commutative Property -2 x +4 = ? We can’t show -2 groups of +4 +4 x -2 = ? we can show 4 groups of -2 The University of Texas at Dallas

MULTIPLICATION To model -2 x -3, think “the opposite” of 2 groups of -3, which would be 2 groups of positive 3. -2 x -3 = + 6 The University of Texas at Dallas

MULTIPLICATION Use tiles to illustrate -3 x -4 =? ANSWER + + + The “opposite” of 3 groups of -4 -3 x -4 = +12 The University of Texas at Dallas

INTEGERS AND DIVISION The University of Texas at Dallas

DIVISION Use tiles to model +12 ÷ +3 = ? 4 red tiles in each group. + + + Divide 12 red tiles into 3 equal groups + + ++12 ÷ +3 = +4 + + The University of Texas at Dallas

DIVISION Use tiles to model -15 ÷ +5 =? – Divide 15 into 5 – equal groups – – -15 ÷ +5 = -3 – – – - The University of Texas at Dallas

DIVISION Write the fact family -4 x + 2 = -8 Compare your answer. + 2 x -4 = -8 -8 ÷ + 2 = -4 -8 ÷ -4 = + 2 The University of Texas at Dallas

$DIVISION Three equivalent ways to write a division expression as a fraction: 12 ÷$

DIVISION Three equivalent ways to write a division expression as a fraction: 12 ÷ 3 =. The University of Texas at Dallas

Mixed Practice Now try these! Use red and yellow tiles to find each answer. 1) -2 + -8 5) +3 x -4 2) +6 + -4 6) -5 x -2 3) -5 - +4 7) -12 ÷ +6 4) -6 - -7 8) -8 ÷ +2 ANSWER The University of Texas at Dallas