Fractions: The BasicsFractions: The BasicsMs. Davis’s & Ms. Hillman’s 5Ms. Davis’s & Ms. Hillman’s 5thth Grade Math Classes Grade Math Classes

What is a Fraction?What is a Fraction?

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

A fraction can express part of a whole:

A fraction can express part of a set

Parts of Wholes & SetsParts of Wholes & Sets

1 of 4 pieces of the whole

pizza was eaten

1 of 4 cookies in

the set was eaten

1/4

1/4

Numerators, Denominators,Numerators, Denominators,and Divisionand Division

A fraction is also simply adivision expression

The numerator is the dividendThe denominator is the divisorSo, the fraction 1/3 is the same as 1

divided by 3

Expressions as FractionsExpressions as Fractions

If we take the expression, 9 ÷ 10, we can write it as the fraction, 9/10, so

9 ÷ 10 = 9/10Can you write each expression as a

fraction? 1 ÷ 3 3 ÷ 6 2 ÷ 7 6 ÷ 13 5 ÷ 8

Proper vs. ImproperProper 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 NumbersMixed Numbers

A mixed number has a whole number with a fraction:

4The mixed number above is read,

“four and two-thirds.”Mixed numbers are made by changing improper fractions.

2 3

Making Mixed NumbersMaking Mixed Numbers

To change an improper fraction to a mixed number:

1. Write the improper fraction as a division expression:

= 23 ÷ 623 6

6 23

Making Mixed NumbersMaking Mixed Numbers

3

18

5

R 5

2. Solve the expression:

6 23

Making Mixed NumbersMaking Mixed Numbers

3

18

5

R 5

Use the quotient (3) as the whole number.

Use the remainder (5) as the numerator of

the fraction.

Use the divisor (6) as the denominator of the fraction.

6

6 23

Making Mixed NumbersMaking Mixed Numbers

3

18

5

R 5

So, the improper fraction, 23/6 = the mixed number, 3 and 5/6!

6 3 5

6

Let’s Make Mixed Numbers!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!

Convert the improper fractions to mixed numbers.1. 6/42. 12/53. 37/94. 17/7

Let’s Make Mixed Numbers!Let’s Make Mixed Numbers!

1-2/4

2-2/5

4-1/92-3/7

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.

Can You Do the Opposite?Can You Do the Opposite?

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!

Let’s Try One!Let’s Try One!

5 23

Convert to improper fractions.

1. 3-4/52. 6-1/33. 4-5/64. 10-2/7

Let’s Try Some More!Let’s Try Some More!

19/5

19/3

29/672/7

Whole Numbers to Whole Numbers to FractionsFractions

How do we show a whole numberas 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 Whole Numbers to FractionsFractions

Just put the whole number over 1!

Convert each whole number to a fraction:6 17 92 435 78

3= 31

1 1 1 1 1

Fractions Equal to 1Fractions 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 1Fractions Equal to 1

Just put the whole number over itself!

Convert each whole number to 1:6 17 92 435 78

1=33

6 17 92 435 78

That was

a lotof information!

Good job!

Whew!Whew!