Download Converting Mixed Fractions to Improper Fractions Mixed Fraction

Name:________________________________________________________________Teacher: Ms. Kerr
Unit 3: Rational Numbers
Lesson 3 SECTION 3.3
Adding and Subtracting Fraction Notation
WARM-UP: Add or subtract the following fractions.
3 2
+ =
4 4
8 4
− =
9 9
3
7
+
=
11 11
2
1
− (− ) =
5
5
Converting Mixed Fractions to Improper Fractions
● Mixed Fraction Example:
a)
b)
● An improper fraction’s numerator is ________________________ than its denominator.
Steps to Convert:
1) Multiply the whole number by the denominator.
2) Add the product to the numerator
3) The sum is the “new” numerator. ** Keep the same denominator.
Examples
Convert each mixed fraction to an improper fraction.
3
6
a) 3 4 =
b) −8 7 =
Converting Improper Fractions to Mixed Fractions
Steps to Convert:
1) Divide the denominator into the numerator to produce the whole number.
2) Multiply the whole number times the denominator, and subtract this product from the
numerator.
3) Write the remainder in the numerator and keep the same denominator.
Examples
a)
22
4
Convert each improper fraction into a mixed fraction.
=
b)
33
7
=
Adding Fractions with Like Denominators
Steps:
1) Add the numerators
2) Keep the denominators
3) Simplify, if possible
Examples
a)
b)
5
4
3
7
Add the following: HINT when adding mixed fractions, first convert to
improper fractions.
2
5
+4
6
c) 1 9 + 4 9
5
+ (− 7) =
Subtracting Fractions with Like Denominators
Steps:
1) Subtract the numerators
2) Keep the denominator the same
3) Simplify, if possible
Examples
a)
6
7
Subtract the following:
4
− =
c)
7
2
9
10
7
− (− ) =
10
1
b) 3 5 − 1 5 =
Adding and Subtracting Fractions with UNLIKE Denominators
● Requires re-writing the fraction with a ________________ denominator
(preferably, the _______________- lowest common denominator)
Requires finding the _______________- least common multiple of all denominators
involved.
Finding the LCM of a Set of Numbers
● LCM – the smallest number that is a _________________ of each number.
● Prime Number – a number is considered to be PRIME if it is divisibly only by _____________
Example:________________________________________________________________
NOTE: ___________ is NOT prime.
Method 1: works for two or more numbers…
1) Write each number as a product of prime factors.
2) Select the greatest number of times each prime factor occurs in any one number.
3) Multiply the values
Examples
1) Determine the LCM of 24 and 36
Using a Factor Tree
2) Determine the LCM of 12, 18 and 24.
Using Division by Primes
Method 2: works only when you have two numbers…
1) Write each number as a product of prime factors.
2) Divide the GCF – Greatest Common Factor
3) Divide the product of the two numbers by the GCF.
Examples
1) Find the LCM of 36 and 48
Adding and Subtracting Fractions with UNLIKE Denominators
Examples
Find:
1
5
1) 4 3 + 1 6 =
2)
19
8
−
13
6
=
PRACTICE PROBLEMS: Section 3.3 Questions 1-10 left side, 11, 13, 15, and 17