Presentation on theme: "INTRODUCTION TO FRACTIONS"— Presentation transcript:
1 INTRODUCTION TO FRACTIONS MSJC ~ San Jacinto CampusMath Center Workshop SeriesJanice Levasseur
2 Introduction to Fractions A fraction represents the number of equal parts of a wholeFraction = numerator (up North)denominator (Down south)= numerator/denominatorNumerator = # of equal partsDenominator = # of equal parts that make up a whole
3 Example: My husband and I ordered a large Papa John’s pizza Example: My husband and I ordered a large Papa John’s pizza. The large pizza is cut into 8 (equal) slices. If my husband ate 3 slices, then he ate3/8 of the pizza
4 Types of Fractional Numbers A proper fraction is a fraction whose value is less than 1 (numerator < denominator)An improper fraction is a fraction whose value is greater than or equal to 1 (numerator > denominator)A mixed number is a number whose value is greater than 1 made up of a whole part and a fraction part
5 Converting Between Fraction Types Any integer can be written as an improper fractionAny improper fraction can be written as a mixed numberAny mixed number can be written as an improper fraction
6 Integer Improper Fraction The fraction bar also represents divisionThe denominator is the divisorThe numerator is the dividendThe original integer (number) is the quotientTo write an integer as a division problem, what do we divide a number by to get the number?One n = n/1
7 Ex: Write 17 as an improper fraction 17 = 17 / ?17 divided by what is 17?1Therefore, 17 = 17 / 1
8 Improper Fraction Mixed Number Denominator: tells us how many parts make up a wholeNumerator: tells us how many parts we haveHow many wholes can we make out of the parts we have?Divide the numerator by the denominator the quotient is the whole partHow many parts do we have remaining?The remainder (over the denominator) makes up the fraction part
9 Ex: Write 11/8 as a mixed number. How many parts make up a whole?8Draw a whole with 8 parts:How many parts do we have?11To represent 11/8 we must shade 11 parts . . .But we only have 8 parts. Therefore, draw another whole with 8 parts . . .Keep shading . . .91011This is what 11/8 looks like.
10 Given the representation of 11/8, how many wholes are there? Dividing 11 parts by 8 will tell us how many wholes we can make: 11/8 =1 R ?The remainder tells us how much of another whole we have left:1 R 3Since 8 parts make a whole, we have 3/8 left.Therefore, 11/8 = 1 3/8.
11 Mixed Number Improper Fraction Denominator: tells us how many parts make up a whole. Chop each whole into that many parts. How many parts do we get?Multiply the whole number by the denominator.Numerator: tells us how many parts we already have. How many parts do we now have in total?Add the number of parts we get from chopping the wholes to the number of parts we already haveForm the improper fraction:# of parts# of parts that make a whole
12 Ex: Write 2 5/8 as an improper fraction. Draw the mixed numberLooking at the fraction, how many parts make up a whole?8Chop each whole into 8 pieces.How many parts do we now have?8+ 8+ 5= 8 * = 21= parts from whole + original parts
14 Finding Equivalent Fractions Equal fractions with different denominators are called equivalent fractions.Ex: 6/8 and 3/4 are equivalent.
15 The Magic OneWe can find equivalent fractions by using the Multiplication Property of 1: for any number a, a * 1 = 1 * a = a (magic one)We will just disguise the form of the magic oneDo you agree that 2/2 = 1?How about 3/3 = 1?4/4 = 1?25/25 = 1? /17643 = 1?1 has many different forms . . .1 = n/n for any n not 0
16 Ex: Find another fraction equivalent to 1/3 1/3 = 1/3 * 1We can write 1/3 many ways just be using the Magic One= 1/3 * 2/2= 2/6or1/3 = 1/3 * 1= 1/3 * 3/3= 3/9
17 Ex: Find a fraction equivalent to ½ but with a denominator of 8 1/2 = 1/2 * 1We can write 1/2 many ways just be using the Magic One. We want a particular denominator – 8. What can we multiply 2 by to get 8?= 1/2 * 4/4= 4/8Notice:4so choose the form of the Magic One
18 Ex: Find a fraction equivalent to 2/3 but with a denominator 12 2/3 = 2/3 * 1We can write 2/3 many ways just be using the Magic One. We want a particular denominator – 12. What can we multiply 3 by to get 12?= 2/3 * 4/4= 8/124so choose the form of the Magic One
19 Simplest Form of a Fraction A fraction is in simplest form when there are no common factors in the numerator and the denominator.
20 Ex: Simplest Form Ex: 6/8 and 3/4 are equivalent The fraction 6/8 is written in simplest form as 3/4===1 xMagic one
21 Ex: Write 12/42 in simplest form First prime factor the numerator and the denominator:12 = 2 x 2 x 3 and 42 = 2 x 3 x 7Look for Magic OnesSimplify===1 x 1 x=Notice: 2 x 3 = 6 = GCF(12, 42) factoring (dividing) out the GCF will simplify the fraction
22 Ex: Write 7/28 in simplest form What is the GCF(7, 28)?Hint: prime factor 7 = 7prime factor 28 = 2 x 2 x 7= 7===1 x=Dividing out the GCF from the numerator and denominator simplifies the fraction.
23 Ex: Write 27/56 in simplest form What is the GCF(27, 56)?Hint: prime factor 27 = 3 x 3 x 3prime factor 56 = 2 x 2 x 2 x 7= 1There is no common factor to the numerator and denominator (other than 1)Therefore, 27/56 is in simplest form.