[br][color=#0000ff]IMPROPER FRACTIONS [/color]and [color=#0000ff]MIXED NUMBERS[/color] are simply two different ways of expressing the same nonintegral number. In this lesson, you'll explore this idea and learn how to change one form to the other.[br][br]Interact with the applet below to see the relationship between [color=#0000ff]IMPROPER FRACTIONS[/color] and [color=#0000ff]MIXED NUMBERS.[/color] [br][br]Start by choosing a [color=#0000ff]top-heavy[/color] fraction, a.k.a. [color=#0000ff]improper[/color] fraction. [br][br]Use the [color=#0000ff]blue[/color] slider to choose the [color=#0000ff]numerator[/color] and the [color=#ff0000]red[/color] slider to choose the [color=#ff0000]denominator[/color]. Make sure the numerator is larger than the denominator so that you'll get an [color=#0000ff]improper[/color] fraction. [br][br]Click [color=#6aa84f]Count Sectors[/color] to number and mark the parts.[br][br]Use the [color=#6aa84f]green[/color] slider to dynamically show the conversion of your chosen improper fraction to a mixed number.[br][br]Repeat as many times as needed to master the concept.

[br][color=#0000ff]EXAMPLE:[/color] What is [sub][img]data:image/png;base64,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[/img][/sub] as a mixed number?[br][br]Divide the numerator by the denominator: 16 ÷ 5 = 3 remainder 1[br][br]The quotient (3) becomes the whole number and the remainder (1) becomes the numerator of the fraction next to the whole number; the denominator (5) doesn't change. So your answer is [sub][img]data:image/png;base64,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[/img][/sub].[br][br]Use the applet below for practice. Solve the problem first on a separate sheet of paper and then verify your answer.[br][br]Repeat as many times as needed to master the concept.

[br][color=#0000ff]EXAMPLE:[/color] What is [sub][img]data:image/png;base64,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[/img][/sub] as an improper fraction?[br][br]Multiply the denominator of the fraction to the whole number (8 x 2 = 16) and then add the numerator (16 + 7 = 23).[br][br]This answer becomes the numerator of the improper fraction; the denominator stays the same: [sub][img]data:image/png;base64,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[/img][/sub].[br][br]Use the applet below for practice. Solve the problem first on a separate sheet of paper and then verify your answer.[br][br]Repeat as many times as needed to master the concept.

In future lessons, you'll learn more about operations on fractions. Hope you ENJOYED today's lesson!