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

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

MULTIPLICATION – – – – -2 x +4 = -8 – – – – -2 x +4 = ? 4 groups of -2 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 + + + + + + -3 x -4 = +12 + + + + + + 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

Divide 12 red tiles into 3 equal groups 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

Divide -15 into 5 equal groups 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. -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 ÷ 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