[br]In previous lessons, you learned how to add, subtract, multiply, and divide integers.[br][br][i][color=#0000ff]Summing It Up:[/color][/i] https://www.geogebra.org/m/ryw5cfbm[br][color=#0000ff][i]Switching Directions:[/i][/color] https://www.geogebra.org/m/dkuqcztg[br][i][color=#0000ff]Getting Along:[/color][/i] https://www.geogebra.org/m/fcebgdr7[br][br]In this lesson, you're going to learn how to perform chain operations involving addition, subtraction, multiplication, division, exponents, and grouping symbols.[br][br]A common mnemonic used in performing chain operations is [color=#0000ff]PEMDAS[/color], or its expanded form, [color=#0000ff]Please Excuse My Dear Aunt Sally[/color]. The letters, in order, stand for [color=#0000ff]Parentheses[/color] (or other grouping symbols), [color=#0000ff]Exponents[/color], [color=#0000ff]Multiplication[/color] or [color=#0000ff]Division[/color] (whichever comes first from left to right) and [color=#0000ff]Addition[/color] or [color=#0000ff]Subtraction[/color] (whichever comes first from left to right). [br][br]For ease of reading, grouping symbols may be nested from innermost to outermost as follows: [color=#0000ff]Parentheses[/color], [color=#0000ff]Brackets[/color] (square brackets), [color=#0000ff]Braces[/color] (curly braces) as illustrated—{ [ ( ) ] }. Simplification begins with the innermost symbol. [br][br]Examples:[br][br] 27 - 36 ÷ 12 - 5 (2 - 7)[br] = 27 - 36 ÷ 12 - 5 (-5)[br] = 27 - 3 + 25[br] = 24 + 25[br] = [color=#ff0000]49[/color][br][br] 2 + 2 (10 - 7)[sup]2[/sup] ÷ 5 • 1 (9 - 4) - 8[br] = 2 + 2 (3)[sup]2[/sup] ÷ 5 • 1 (5) - 8[br] = 2 + 2 (9) ÷ 5 • 1 (5) - 8[br] = 2 + 18 ÷ 5 • 1 (5) - 8[br] = 2 + 3.6 • 1 (5) - 8[br] = 2 + 3.6 (5) - 8[br] = 2 + 18 - 8[br] = 20 - 8[br] = [color=#ff0000]12[/color][br]

Use the applet below to practice performing chain operations involving addition, subtraction, multiplication, division, and parentheses. Exponents will be dealt with later.[br][br]Instructions:[br][br]Solve the problems on a separate sheet of paper first, and then click the box on the right for the correct answer.[br][br]

[br]Below is a couple of problems involving chain operations with exponents.

In future lessons, you'll learn how to perform operations on rational numbers. Hope you had FUN today!