Download 3-8 Mixed Numbers and Improper Fractions

3-8 to 3-10 Mixed Numbers
and Improper Fractions
What You’ll Learn
To
write a mixed number as an improper
fraction
To write an improper fractions as a mixed
number
To relate fractions and decimals
Compare rational numbers
Mixed Numbers and Improper
Fractions



If the numerator of a fraction is less than the
denominator, the fraction is called a proper
fraction.
If the numerator is equal to or greater than the
denominator, the fraction is called an improper
fraction.
An improper fraction can be rewritten as a mixed
fraction (whole number + a proper fraction)

For example, 5/3 is an improper fraction. It can be
rewritten as 1 2/3, which is a mixed fraction.
Example 1: Writing improper
Fractions

Write 4 2/3 as an improper fraction



Multiply the denominator by the whole number
Add the numerator
The denominator remains the same
+

4 2/3 = 4
2/3
x

= (3
x
4)
3
+
2 = 14
3
Example 2: Writing a Mixed
Number

Divide the numerator by the denominator




The Quotient is the whole number
The Reminder is the numerator
The Denominator remains the same
Write 30/8 as a mixed number


3
8 30
- 24
6
30/8 = 3 6/8
Fractions and Decimals

Fractions can be written in decimal number
format, and vice versa.

For example, 1/4 = 0.25
Example 1: Write the fraction 5/8
as a decimal

Step 1: Divide the numerator by the
denominator


Step 2: Complete the division problem


(1) 5 ÷ 8 = ?
(2) 5 ÷ 8 = 0.625
Answer: 0.625
Example 2: Write the mixed
number 2 3/4 as a decimal

Step 1: Separate the mixed number 2 3/4 into a
whole number and a fraction. The whole number
will always remain a whole number, but the
fraction can be changed into a decimal.


Step 2: Write the fraction 3/4 as a decimal by
dividing the numerator by the denominator.


(1) whole number: 2; fraction: 3/4
(2) 3/4 = 3 ÷ 4 = 0.75
Step 3: Put the whole number and the decimal
back together to get the complete decimal
number

(3) 2 3/4 = 2.75
Repeating Decimals

If the same block of digits in a decimal
repeats without end, the decimal is a
repeating decimal.



Repeating block can be one or more digits
_
5.355555555 = 5.35 The digit “5” repeats
_
0.171717171 =0.17 The digits “17”
repeats
Example 3: Write 3/11 as a decimal



Divide the numerator by the denominator
0.27272727
11
3
Find the repeating digits


“27”
Record answer only to the repeating digits

0.27
Example 4: Writing 0.325 as a
Fraction

Write the decimal number over the
decimal place value


Find the GCF



0.325 = 325/1000
325: 1,5,13,25,65,325
1000: 1,2,5,10,20,25,50,100,500,1000
Reduce fraction using GCF

325/1000 = 325/25 / 1000/25

13
/
40
3-10 Rational Numbers

Ration number is a number that can be
written as a quotient of two integers,
where the divisor is not 0.




- 2/3
0.46
-6
3½