Download Addition and Subtraction of Fractions

Math 212
Guide 6.2: Add & Subtract Fractions
6.2 SWBATS:
Book
Resources
A. Add fractions using models, properties,
theorems and approaches to justify results
B. Explain the properties of addition of
fractions
C. Subtract fractions using models, theorems
and approaches to justify results
D. Use mental math to add and subtract
fractions when possible, and estimate results
using rounded fractions and mental math
248 251
250
Model Addition (NLVM)
251 252
253
Fractions with Borrowing (TLC)
Calculators, Mental Math and Estimation
Why is the method for adding fractions used in the “Starting Point” unreasonable?
_____________________________________________________________________________________
Read pages 247 and 248 and then answer me this: Why do we simply add numerators when the
denominators are the same? _____________________________________________________________
_____________________________________________________________________________________
Add
3
4
+
5
6
by finding common denominators first. Show your work.
_____________________________________________________________________________________
Study the “Addition of Fractions with Unlike Denominators” theorem on page 248. Rewrite the proof:
Proof:
______________________________
Reason:
____________________________________________________
______________________________
____________________________________________________
Add
3
4
5
+ 6 by using this theorem. Which algorithm helps you better understand why your addition is
correct?
_____________________________________________________________________________________
_____________________________________________________________________________________
When we add fractions we can count on four properties that will always hold true:
A.
The set of fraction is _____________ under addition.
This means the sum of any two fractions is a ________________.
B. The order in which we add fractions does not matter.
Fraction addition is ____________________.
C. Changing the association of additive pairs does not change the sum.
Thus addition of fractions is ___________________ .
D. Zero can be written as a fraction in an ________________ number of ways. Zero is still the
_______________ for the addition of fractions.
SUBTRACTION makes sense only if the size of the parts is the same. This means that to subtract
fractions we still find the same _________________. Note the definition and theorem on page 252.
Once fraction addition and subtraction are well understood, all of us can add and subtract “easy”
fractions mentally. And we can estimate easily as well.
Calculate these using mental math and be
prepared to write your method on the board (and
listen to how your peers are calculating too!)
Estimate these and be prepared to write yoru
method on the board (and learn from your peers
as they explain their methods too!)
2 1
+ =
3 4
10 29
+
≈
13 45
1 2
− =
2 5
53 9
−
≈
61 29
Calculate these mixed numbers using mental math
by adding or subtracting the whole numbers first
and then the adding or subtracting the fractions.
Estimate these by rounding to the nearest whole
number and ignoring the fraction. If you want to
1
add or subtract 2 when finished, do so.
2
2
1
+3 =
3
4
4
10
29
+5
≈
13
45
2
1
2
−1 =
2
5
7
53
9
−2
≈
61
29
Watch this video, and then read the comments on the Web page (scroll down the page). Be prepared to
discuss this teacher’s work in class. https://www.teachingchannel.org/videos/fractions-with-borrowing
Calculate these using Mental Math by adding or
subtracting the whole numbers first and then the
adding or subtracting the fractions.
Estimate these by rounding to the nearest whole
number and ignoring the fraction. If you want to
1
add or subtract 2 when finished, do so.
2
2
1
+3 =
3
4
4
10
29
+5
≈
13
45
2
1
2
−1 =
2
5
7
53
9
−2
≈
61
29
Homework due Thursday, January 17
NO CALCULATOR—PRACTICE, You need this!
6.2B #1
6.2B #2
6.2B #3
6.2B #5
6.2B #6
6.2B #8
6.2B #9
6.2B #10
6.2B #21
AND:
practice fraction addition and
subtraction until you can add and
subtract automatically, and explain
both just as easily and in just as many
ways as 2 + 2. Do this now. This is
your last math content class.
Use the Web page given in these notes.
Use the method discussed in class.