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Fractions
Reed-Math 7C
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Sarah’s Math teacher has a new way to decide which students will present
their projects first. In groups of 10, each student pulls a slip of paper from a
jar. A fraction or mixed number is written one each slip. The student with the
fourth greatest number will present first.
2 ⅓, 8/9, 12/5, 2/9, 15/18, 7/9, ⅔, 4/6, ⅖ , ⅘
Sarah chose 8/9
The students decided to place the fractions on a number line to help them see
the order
Define
lowest terms - an equivalent form of a fraction with a numerator and a
denominator that have no common factors other than 1; for example, ¾ is the
lowest term form of 12/16, since ¾ = 12/16, and 3 and 4 have no common
factors other than 1.
common denominator - a common multiple of two or more denominators; for
example, a common denominator for ⅔ and 3/6 would be any multiple of 6. If
you use the least common multiple of the denominators, the common
denominator is called the least common denominator.
2.1 - Comparing Fractions
parts of a fraction
4
numerator
5
denominator
which of the following are in lowest terms?
4/8, ⅔, 4/6
to be in lowest terms means that the numerator and the denominator have no
common factors (other than 1).
Lowest Terms
To put a fraction into lowest terms, we divide the numerator and the
denominator by the Greatest Common Factor (GCF).
4/8 -
10/35
Common Denominator
A common denominator is when two fractions have the same denominator.
⅜ and ⅝
If two fractions do not have a common denominator, we can multiply each
fraction so that denominators equal the Lowest Common Multiple. This is the
call the Lowest Common Denominator.
For each set of fractions, first state the LCM of the denominators. Then,
change the fractions so they have the LCM.
¾, ⅝ - LCM is ___
Golden Rule of Fractions
Whatever we do to the top
we do to the bottom
Practice
⅔,⅗
¾,⅔
7/9, 5/7
⅘ , 5/8
Practice
Page 47, 1-4
2.1 - Comparing Fractions part II
Proper Fraction - 4/7
Improper Fraction - 7/4
Mixed Number - 1 ¾
Changing from an Improper Fraction to a Mixed Number
5/4
8/3
5/2
Fractions must always be
in lowest terms
From Mixed to Improper
3 ⅔ - diagram
5 ¼ - multiplication and addition
2.1 - Comparing Fractions part
III
Placing Fractions on a number line
⅚ , 2 ⅗ , 31/8 , 2/8 , 3/9 , 3/2
Step 1: Make sure all fractions are in proper form and in lowest terms
31/8 = 3 ⅞ , 2/8 = ¼ , 3/9 = ⅓ , 3/2 = 1 ½
Step 2: Decide whether the fraction is less than ½ or bigger than ½ (ignore the
whole numbers for now)
⅚ bigger , ⅗ bigger , ⅞ bigger , ¼ smaller , ⅓ smaller
Step 3: Place the original fraction on the number line
Practice
P 48-49 - 5 - 15
2.2 - Adding Fractions part I
Nayana filled a 3 x 4 grid with coloured tiles. She wrote two fraction equations
to describe how the different colours filled the space.
2/12 + 10/12 = 12/12 and 12/12 - 2/12 = 10/12
What fraction equations can you write to describe a grid covered with colored
tiles?
Practice
5/7 + ¾
LCM = 28
5/7 *4 (Golden Rule of Fractions) , ¾ * 7 = 21/28
20/28
20/28 + 21/28 = 41/28
Step 3: Change to a mixed number and reduce.
41/28 = 1 13/28
Practice
1⅔+2½
Step 1: Add the whole numbers
1+2=3
Step 2: Add the fractions
⅔+½
LCM = 6
4/6 + 3/6 = 7 /6 = 1 ⅙
Step 3: Put them together and reduce
4⅙
Practice
3¼+4⅘
3+4=7
¼ + ⅘ LCM = 20
5/20 + 16/20 = 21/20
21/20 = 1 1/20
8 1/20
Practice
P 54,55 - 1- 11
2.2 Subtracting Fractions Part II
Subtracting Fractions requires the same steps as adding fractions, except we
subtract the numerators, instead of adding them.
¾-⅔
LCM - 12
9/12 - 8/12 = 1/12
4¾-2½
4-2=2
¾ - 2/4 = ¼
2¼
LCM = 4
Practice
3⅖-1⅘
Option 1: Change to improper fractions
3 ⅖ = 17/5
1 ⅘ = 9/5
17/5 - 9/5 = 8/5
Change back to a mixed number
1⅗
Option 2
3 ⅖ = 2 7/5
2 7/5 - 1 ⅘ = 1 ⅗
Example
4⅓-2⅘
LCM = 15
4 ⅓ = 4 5/15 2 ⅘ = 2 12/15
Improper Fraction = 65/15 - 42/15
23/15 = 1 8/15
Option 2
4 5/15 = 3 20/15 - 2 12/15 = 1 8/15