Download Name

Name _____________________
Topic Guided Notes
Adding and Subtracting Fractions and Mixed Numbers
Key Words/Topic
Information, Definitions, Solutions
and Assignments
7.1 Adding & Subtracting:
Like Denominators
New Terms Fractions that have the same ________________ have like
Like Denominators denominators.
Review Terms
Denominator
Numerator
Fraction
Today’s Concept In order to add or subtraction fractions you MUST HAVE
LIKE DENOMINATORS.
Here’s how to add fractions with like denominators:
1. IF ADDITION: Add the numerators together – DO
NOT ADD THE DENOMINATORS TOGETHER.
2+1=3
4 4 4
Group Work
1-8 on page 162.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 10-26 P.
162 in textbook.
2. IF SUBTRACTION: Subtract the numerators. If the
numerator of the fraction you are subtracting is
smaller than the numerator of the fraction you are
subtracting from, use borrowing or convert any mixed
numbers to improper fractions and subtract the
numerators – DO NOT SUBTRACT THE
DENOMINATORS.
3- 1=2
4 4 4
3. IF ADDITION: Do you have whole numbers in the
problem – don’t forget to add them too, if you split the
fraction from the whole number in the beginning!
4. Simplify! If the numerator is larger than the
denominator, or the numerator and denominator have
common factors you need to simplify.
2=1
4 2
Group Work
1-8 on page 162.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 10-26 P.
162 in textbook.
1.
2.
3.
4.
5.
6.
7.
8.
Key Words/Topic
and Assignments
7.2 Least Common
Multiple
Information, Definitions, Solutions
New Terms
Common Multiple A __________ that is the same for two or _________
numbers.
Least Common Multiple This is the common multiple with the _____________
________________.
Review Terms
Today’s Concept Like finding the GCF, there are numerous methods for
finding the Least Common Multiple.
Method 1: List the common multiples of the numbers until
you find the smallest match.
Although 24 & 48 are both common multiples, we need to
pick the smallest value – 24 = LCM.
Method 2: Use factor trees to find the prime
factorization. Once you find the prime factorization, write
the factor strings of the numbers.
Group Work
1-6 on page 164.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 10-29 P.
165 in textbook.
Circle the greatest number of times a factor appears in
the different strings. Then multiply the circled factors
together. The product is the LCM.
Method 3: You can also use the CAKE method as long as
you are using it for just two numbers. It is possible to use it
for more than two numbers, but you must know the
exception.
Once you reach the point where there are no common factors
between the two numbers, you form an “L” around the
outside numbers and the lowest level of the cake. Then
multiply all of the numbers inside the “L”. This gives you
Group Work
1-6 on page 164.
the LCM.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 10-29 P.
165 in textbook.
2x3x4=24
1.
2.
3.
4.
5.
6.
Key Words/Topic
and Assignments
7.3 Adding and
Subtracting: Unlike
Denominators
Information, Definitions, Solutions
New Terms
Unlike Denominators Denominators in _____ or more ___________ that are
different.
Least Common
Denominator (LCD) The least ______________ ______________ (LCM) of the
____________________ is the least common denominator.
Review Terms
Today’s Concept
1. Find a common denominator. The least common
multiple is the same as the least common denominator
(LCD). BUT it doesn’t have to be the least common
denominator.
Example
3 2/5 + 3/7
5 x7 will give me a common denominator (it doesn’t have
to be the lowest common denominator). 35 is my new
denominator.
Multiply the numerator of the fraction by the same
number that you multiplied the denominator by to
calculate the common denominator.
2(7) + 3(5) = 14 + 15
35
35 = 35 35
Group Work
1-9 on page 167.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 12-29, 3136 P. 167 in textbook.
2. IF ADDITION: Add the numerators together – DO
NOT ADD THE DENOMINATORS TOGETHER.
29
35
3. IF SUBTRACTION: Subtract the numerators. If the
numerator of the fraction you are subtracting is
smaller than the numerator of the fraction you are
subtracting from, use borrowing or convert any mixed
numbers to improper fractions and subtract the
numerators – DO NOT SUBTRACT THE
DENOMINATORS.
4. IF ADDITION: Do you have whole numbers in the
problem – don’t forget to add them too, if you split the
fraction from the whole number in the beginning!
Add back the whole number 3 29
35
5. Simplify! If the numerator is larger than the
denominator, or the numerator and denominator have
common factors you need to simplify.
Group Work
1-9 odd on page 167.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
1.
HOMEWORK: 12-29, 3136 P. 167 in textbook.
3.
5.
7.
9.
Key Words/Topic
and Assignments
7.4 Estimating Sums and
Differences of Mixed
Numbers
Information, Definitions, Solutions
New Terms
Review Terms
Today’s Concept As we’ve learned in previous units, estimating is a good
strategy to see if your answer is reasonable or to do a quick
calculation. When we use estimations to help us with
adding/subtracting fractions and mixed numbers, it is useful
to know benchmark fractions.
Here are the benchmark fractions:
1/4 1/3 1/2 2/3 3/4
These are the decimal equivalents of the benchmark
fractions:
1/4=.25 1/3=.33 1/2=.50 2/3=.67 3/4=.75
Group Work
1-7 on page 170.
Round fractions down to the nearest whole number, if the
fraction’s value is below the benchmark fraction of 1/2.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
Round fractions up to the nearest whole number, if the
fraction’s value is equal to or above the benchmark fraction
of 1/2.
1.
HOMEWORK: 8-23 P. 171
in textbook.
2.
3.
Group Work
1-7 on page 170.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
4.
5.
HOMEWORK: 8-23 P. 171
in textbook.
6.
7.
Key Words/Topic
and Assignments
7.5 Adding Mixed Numbers
Information, Definitions, Solutions
New Terms
Review Terms
Mixed Number
Today’s Concept The process for adding mixed numbers is no different then
when we add fractions, except we need to make sure that
we had the whole numbers together and simplify in the
end.
2.
4.
Group Work
2-8 even p. 172 on page .
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
6.
HOMEWORK: 9-23 odd
25-28 P. 173 in textbook.
8.
Key Words/Topic
and Assignments
7.6 Subtracting Mixed
Numbers
Information, Definitions, Solutions
Today’s Concept Subtracting mixed numbers works the same way as
subtracting fractions EXCEPT like subtraction sometimes
you have to borrow.
Let’s look at 4 1/3 – 1 3/4.
Find a common denominator (12) and change the
numerators.
4 4/12 – 1 9/12
You can’t take 9/12 from 4/12 so you have to borrow one
whole from 4. 1 whole becomes 12/12. Add the 12/12 to the
4/12, so now the problem is
3 16/12 – 1 9/12
Group Work
2-8 even on page 175.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 12-22 even,
25-34 on page 175 in
textbook.
Subtract the whole numbers 1st
3–1=2
Then subtract the fractions
16/12 – 9/12 = 7/12
Put everything together 2 7/12.
2.
4.
6.
8.