Fractions and Rational Numbers Concepts and Definitions Copyright © 2013 by Lynda Aguirre1

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) Copyright © 2013 by Lynda Aguirre2

Are the following Rational numbers or Fractions or Both? both fraction both fraction = 2 Copyright © 2013 by Lynda Aguirre3

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. Copyright © 2013 by Lynda Aguirre4

Represent the fraction using the following methods: A.pictorially B.number line C.area models D.ratio algebra problem E.Ratio—parts and wholes Copyright © 2013 by Lynda Aguirre5

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 Copyright © 2013 by Lynda Aguirre6

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 Copyright © 2013 by Lynda Aguirre7

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) Copyright © 2013 by Lynda Aguirre8

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 Copyright © 2013 by Lynda Aguirre9

Changing to a specific equivalent fraction If a specific equivalent fraction is desired, you will set up the problem as an algebraic equivalence relation (i.e. two fractions with an equal sign between them). The unknown piece will be represented by a variable (x, y, etc.) Copyright © 2013 by Lynda Aguirre10

Process: Cross-Multiplication Copyright © 2013 by Lynda Aguirre11

Cross Multiplication-practice Copyright © 2013 by Lynda Aguirre12

Change into Unit Fractions A 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 often come out as fractions or decimals Copyright © 2013 by Lynda Aguirre13