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© Edgenuity, Inc. 1
Warm-Up Adding and Subtracting Fractions
Lesson Goals
Solve real-world addition and subtraction problemsinvolving fractions.
Use a number line to addand subtract signedfractions.
and di�erences offractions.
EstimateUse fraction
to add and subtract signedfractions.
Lesson Question
Words to Know
Fill in this table as you work through the lesson. You may also use the glossary to help you.
the result of adding two or more numbers
the opposite of a number
(verb) to form an approximate opinion of worth, amount, size or weight; (noun) an approximate calculation
fractions that have the same numerical value
WK2
?
© Edgenuity, Inc. 2
Instruction Adding and Subtracting Fractions
2Slide
Subtracting Fractions
Use fraction bars to model subtracting fractions.
Problem: − −5
6
1
2
Find a common denominator.
Our common denominator will be , because 6 is the lowest common multiple of 2 and 6.
Rewrite the problem using the common denominator.
= + −
= − = − =
− −
−
5
65
6
3
6
8
612
6
= + −
= − = − =
− −
−
5
65
6
3
6
8
612
6
= + −
= − = − =
− −
−
5
65
6
3
6
8
612
6
Drag the fraction bars to the number line.
−126
−56
−36
−1 0 1
2 3 4 5 6 8 10 12
= + −
= − = − =
− −
−
5
65
6
3
6
8
612
6
= + −
= − = − =
− −
−
5
65
6
3
6
8
612
6
© Edgenuity, Inc. 3
Instruction Adding and Subtracting Fractions
3Slide
Adding Fractions
Problem: − − −
2
5
1
2
Use the additive inverse to rewrite the problem.
− +
2
5
1
2
The lowest common denominator is 10.
− +4
10
Drag the fraction bars to the dots on the number line.
− =5
10
4
10
−1 0 1110
− 410+ 5
10
2 3 4 5 6 8 10 12
− +4
10
− =5
10
4
10
© Edgenuity, Inc. 4
Instruction Adding and Subtracting Fractions
Adding and Subtracting Fractions on a Number Line
Find the sum p + q, where both p and q are fractions.
Locate p on thenumber line.
If q is positive…
If q is negative…the left.
Move spaces to q
qMove spaces to
the .
To find p − q, change to addition with the of q, or p + (− q).
Using a Number Line to Add Fractions
Find the using equivalent fractions.
− + = − + =11
2
3
4
3
2
3
4 − + − = − + − =
11
2
3
4
3
2
3
4
−2 −1 0−52 −94 −74 −32 −54 −34 −12 −14
− + = − + =11
2
3
4
3
2
3
4− + − = − + − =
11
2
3
4
3
2
3
4
2Slide
© Edgenuity, Inc. 5
Instruction Adding and Subtracting Fractions
Using a Number Line to Subtract Fractions
Find the by using the additive inverse.
−− = = + − = + − =
3
5
3
511
2
3
5
3
2
6
10
15
10 −− = = + − = + − =
3
5
3
511
2
3
5
3
2
6
10
15
10
0− 910
610
−− = = + − = + − =
3
5
3
511
2
3
5
3
2
6
10
15
10−− = = + − = + − =
3
5
3
511
2
3
5
3
2
6
10
15
10
2Slide
Subtracting Fractions
− − = =21
213
421
213
4
2 3
1
4214 212 23
4 314
14
14
14
312 41
4 41233
4
4
− − = =21
213
421
213
4
© Edgenuity, Inc. 6
Instruction Adding and Subtracting Fractions
7Slide
Estimating with Compatible Fractions
Marci’s Cocoa Surprise recipe calls for several ingredients, all of which are listed in fractions. Marci wants to know if the ingredients will fit in a 3-cup bowl.
The ingredients include: 3
7 cup sugar,
2
5 cup cocoa,
1
2 cup flour, and
5
8 cup milk.
What is the approximate sum of these measures?
≈3
7
1
2
2
5≈2
5≈
≈5
8
1
2
Based on the approximations, Marcy’s ingredients will fit in her 3- bowl.
Sum of these measures
+ + +1
2
1
2
1
2
1
2
cups
© Edgenuity, Inc. 7
Instruction Adding and Subtracting Fractions
9Slide
Checking a Solution
Joaquim jogged 56
mile from his home on a straight road. Then he turned around
and ran 21
8 miles in the opposite direction. How far is Joaquim from home?
−5
621
8
A common denominator for 6 and 8 is .
−= 51
24 −= 51
24
= − 3124
We know that distance is a positive value, so we’ll take the absolute value.
Joachim ran 17
24from home.
We can now check our answer using estimation.
1 − 2 = −1 =
≈17
241
Our answer is reasonable.
−= 51
24
Since we’re taking the
absolute value
© Edgenuity, Inc. 8
Summary Adding and Subtracting Fractions
? Lesson Question How do you add and subtract positive and negative fractions?
Answer
Review: Key Concepts
Adding and Subtracting Fractions
• Find a Denominator
• Adding Fractions
• Same signs: Add the absolute values. The sum has the sign as the addends.
• Different signs: Find the difference of the values. The
sum has the same sign as the addend with the greater absolute value.
Subtracting Fractions
• Add the .
2
© Edgenuity, Inc. 9
Summary Adding and Subtracting Fractions
Use this space to write any questions or thoughts about this lesson.