Ms. Davis’s & Ms. Hillman’s 5th Grade Math Classes Fractions: The Basics Ms. Davis’s & Ms. Hillman’s 5th Grade Math Classes

What is a Fraction? numerator 1 3 denominator Like a decimal, a fraction is part of a whole A fraction is less than one whole A fraction has 2 parts: numerator 1 3 denominator The numerator indicates the counted parts of a fraction The denominator indicates the total parts of a fraction Give S various fractions, and have them identify the numerator and denominator.

Parts of Wholes & Sets A fraction can express part of a whole: A fraction can express part of a set 1 of 4 pieces of the whole pizza was eaten 1/4 1 of 4 cookies in the set was eaten 1/4

Numerators, Denominators, and Division A fraction is also simply a division expression The numerator is the dividend The denominator is the divisor So, the fraction 1/3 is the same as 1 divided by 3

Expressions as Fractions If we take the expression, 9 ÷ 10, we can write it as the fraction, 9/10, so 9 ÷ 10 = 9/10 Can you write each expression as a fraction? 1 ÷ 3 3 ÷ 6 2 ÷ 7 6 ÷ 13 5 ÷ 8

Proper vs. Improper A fraction is proper when its numerator is smaller than its denominator (3/4, 5/8, 6/10). A fraction is improper when its numerator is larger than its denominator (4/3, 8/5, 10/6). Which are improper fractions? 4/7 6/5 2/3 3/5 8/3 7/12 2/1 5/6

Mixed Numbers A mixed number has a whole number with a fraction: 4 The mixed number above is read, “four and two-thirds.” Mixed numbers are made by changing improper fractions. 2 3

Making Mixed Numbers To change an improper fraction to a mixed number: 1. Write the improper fraction as a division expression: = 23 ÷ 6 23 6

Making Mixed Numbers 2. Solve the expression: 6 23 3 R 5 18 5

Making Mixed Numbers 6 23 Use the quotient (3) as the whole number. 3 R 5 Use the remainder (5) as the numerator of the fraction. 6 18 5 Use the divisor (6) as the denominator of the fraction.

So, the improper fraction, 23/6 = the mixed number, 3 and 5/6! Making Mixed Numbers So, the improper fraction, 23/6 = the mixed number, 3 and 5/6! 6 23 3 R 5 3 5 6 6 18 5

Let’s Make Mixed Numbers! Convert the improper fraction, 7/5 to a mixed number. What do we do first? Write 7/5 as a division expression! Now what? Solve the expression! Finally… Use the quotient as the whole number, the remainder as the numerator, and the divisor as the denominator!

Let’s Make Mixed Numbers! Convert the improper fractions to mixed numbers. 1. 6/4 2. 12/5 3. 37/9 4. 17/7 1-2/4 2-2/5 4-1/9 2-3/7

Can You Do the Opposite? To convert a mixed number to an improper fraction: 1. Multiply the denominator by the whole number. 2. Add in the numerator. 3. Write the answer as the numerator of the improper fraction, and the original denominator as the improper fraction’s denominator. Show S how to start at the bottom (denominator) and work clockwise to the whole number, and then the numerator.

Use 17 as the numerator and Let’s Try One! Convert 5-2/3 to an improper fraction. What should we do first? Multiply 3 x 5! (denominator x whole number) Now what? Add 2 (numerator)! Finally? Use 17 as the numerator and 3 as the denominator! 5 2 3

Let’s Try Some More! Convert to improper fractions. 1. 3-4/5 2. 6-1/3 1. 3-4/5 2. 6-1/3 3. 4-5/6 4. 10-2/7 19/5 19/3 29/6 72/7

Whole Numbers to Fractions How do we show a whole number as a fraction? Think back to what we learned about fractions being division expressions. If I want to convert 3 into a fraction, I think about what I could divide into 3 so that it will still equal 3. What do you think?

Whole Numbers to Fractions Just put the whole number over 1! Convert each whole number to a fraction: 6 17 92 435 78 3 = 1 1 1 1 1 1

How do we make a fraction equivalent to the whole number, 1? Fractions Equal to 1 How do we make a fraction equivalent to the whole number, 1? Think back to what we learned about fractions being division expressions. If I want to convert 3 into the whole number, 1, I think about what I could divide into 3 so that it will equal 1. What do you think?

Fractions Equal to 1 1 = 3 Just put the whole number over itself! Convert each whole number to 1: 6 17 92 435 78 1 = 3 6 17 92 435 78

Whew! That was a lot of information! Good job!