Adding and Subtracting Fractions
Name:
1) Multiplying any number by one does not change the value of the number; this is called the ​Identity Property
of Multiplication
​
. When the numerator (top number) and denominator (bottom number) of a fraction are
multiplied by the same number, the fraction is multiplied by a ​GIANT ONE.​ For example:
a)​ Why is the fraction
b)​ Use a Giant One to rewrite each fraction by
multiplying each expression below.
called a Giant One?
c)​ ​What if you do not know which numbers to use in a Giant One?
​
Complete each problem below.
d. How do you decide which number to use in the Giant One?
2)​ Kayla, Lashanti, and Jean are all running a mile and each student has completed a different portion so far.​
What common denominator could they use to determine who has the most distance left to
run?​ ___________
Kayla has run
5
8
of a mile.
Lashanti has run
7
10
of a mile.
Jean has run
3
4
of a mile.
Which student has the most distance left to run? ______________ has the most distance left to
run because:
Adding Fractions Classwork
Lily: Armando: 1​)​ Before we can write the sum of two fractions, they must Josue: be rewritten so that both wholes have an equal number of parts. In other words, they must be rewritten to have a common denominator​. Three students were adding the 5
fractions​ 14 + 12
​to the left, and they each found a different common denominator: 1. Who is correct? _________________________ 2. Can any number be a common denominator? Why? ____________________________________________________________________________
_ 3. Which of their common denominators is easiest to work with? __________________ Because ______________________________________________________________ 3
List at least three different common denominators you could use to add 10
+ 15 . 1)
2)
2) ​a. Evan needs to add 38 + 56 ​. He knows that he can rewrite each fraction as a portion of 48 because 6 and 8 are each factors of 48 in his multiplication table. ​"Is there a smaller number that could work as a common denominator?" he wonders. Use the multiplication table on the right to find other number(s) you could use as a common denominator to add 38 and 56 . You could use ___________________. 7
b. If Evan 's next problem is to add 54 + 10
​, use the multiplication table to find the smallest number you could use as a common denominator, called the ​lowest common denominator​. Then, find the sum. Lowest common denominator: ___________ Sum: _____________ 3)​ One study team is trying to find the sum 56 + 34 + 15 . 1. They first tried to use 24 as a common denominator. Why does 24 not work as a common denominator? ___________________________________________________________ _______________________________________________________________________ 2. Find a common denominator for this problem and explain how you found it. Common Denominator: ___________. We found this by __________________________ _______________________________________________________________________. 3. Find the sum of 56 + 34 + 15 . 4)​ With your team, find each sum. You may want to use the multiplication table to help you find common denominators. a. b. c. d. : ​5​/​6​ + ​8​/​9 e. 23 + 12 + 16 f. Challenge: ​7​/​12​ + ​1​/​9 ​ + ​3​/​8