Fractions and Rational Numbers

Concepts and Definitions

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Definitions

Numerator: The top number (how many pieces YOU have)

Denominator: The bottom number (how many pieces make up a Whole object-or the size of the pieces)

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Are the following Rational numbers or Fractions or Both?

both bothfraction

bothfraction fraction

= 2

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Ratios vs. Fractions

Ratios were used by the Greeks who did not have fractions.

Ratio: 2 boys to 3 girls

The format we use for fractions today is thought to have been introduced By the Hindus

and the bar introduced by the Arabs.

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Represent the fraction using the following methods:A.pictorially B.number line C.area modelsD.ratio algebra problemE.Ratio—parts and wholes

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Wholes and Parts-changing forms

What part of the day is 6 hours?

We assume the student knows there are 24 hours are in a day

We also assume the student knows how to reduce fractions

1:4

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What part of an hour is 20 minutes?

We assume the student knows there are 60 minutes in an hour

We again assume the student knows how to reduce fractions

1:3

Wholes and Parts-changing forms

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Equivalent fractions

Unit fractions have a “1” on the top.

The instructions will often want fractions converted to another form that has the same value as the original.

Equivalent fractions have equal values or represent the same amount of the whole.

Simplest form fractions have been reduced to the smallest possible value(or are relatively prime)

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Method: Calculating equivalent fractions

Equivalent fractions

Multiply the top and bottom by the same number (this is the reverse process to reducing)

This process can be done with any numbers, it doesn’t have to be 2 and 3

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Changing to a specific equivalent fraction

If a specific equivalent fraction is desired, you will set up the problem as analgebraic equivalence relation (i.e. two fractions with an equal sign between them).

The unknown piece will be represented by a variable (x, y, etc.)

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Process: Cross-Multiplication

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Cross Multiplication-practice

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Change into Unit FractionsA Unit Fraction is a special equivalence relation where

the new fraction has a numerator of “1”.This makes the new denominator your unknown variable (or “x”).

Use cross-multiplication to find unit fractions for the values below

Note: These answers oftencome out as fractions

or decimals

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