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Adding and Subtracting Fractions, Using GCF, and
SimplifyingAnticipatory Set / Objectives (5 min):
Introduce the concept of f raction addition and subtraction, and
teach the students how to use the greatestcommon f actor, and how
to simplif y.
Direct Instruction (40 min):
Use pie charts to help the students understand how f ractions
work.
Simple Addition:
1. Represent 1 with a circle. Split it into thirds and represent
it as 3/3.
2. Now create another circle of thirds, shade in one third, and
represent it as 1/3.
3. Add the two together to create 4/3 and explain how this
becomes 1 and 1/3.
4. Give a f ew more examples.
Simple Subtraction:
1. Represent 2 with two circles. Split them into f ourths and
represent each as 4/4.
2. Now create a pie chart representing 3/4.
3. Remove the 3/4 f rom one pie and represent the remaining pies
as 1 1/4.
4. Give a f ew more examples.
Addition using GCF:
1. Draw two pie charts: one in thirds and one in twelf ths.
2. Shade in 1/3 on the f irst, 4/12 on the second, and show how
they are same.
3. Now add the two together and shade in the second circle to
show 8/12.
4. Explain to the class that although you shaded in f our
slices, it is actually equal to a third and can beshown by
5. Now explain that the easiest way to deal with dif f erent
denominators is to make them the same. Showthat you can split each
of the thirds into f our slices and make an identical circle of
twelve slices.
6. Now show the circles in f raction f orm. Explain that
multiplying 1/3 by 4/4 will make 4/12, which then makesit easier to
manipulate the two f ractions
7. Give a f ew more examples.
Subtraction using GCF:
1. Draw two pie charts: one in f if ths and one in f if
teenths.
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2. Shade in 3/5 on the f irst, 4/15 on the second.
3. Now show the class how you cant subtract 4/15 f rom 3/5
without f irst making the denominators thesame.
4. Show that you can split each of the f if ths into f ive
slices and make an identical circle of f if teen slices.
5. Now show the circles in f raction f orm. Explain that
multiplying 3/5 by 3/3 will make 9/15, which then makesit easier to
manipulate the two f ractions.
6. Erase 4/15 of the shaded area f rom the circle that was
originally 3/5, and show that you are lef t with 5/15.
7. Represent the equation in number f orm.
8. Give a f ew more examples.
Simplif ying:
1. Using the examples f rom the previous steps, show that you
can simplif y f ractions by f inding the commondivisors between the
numerator and denominator.
2. Using the f irst step, 4/12, show that 4 and 12 have a common
divisor of 4, so this f raction can besimplif ied by dividing each
number by 4 to make 1/3.
3. Using the second step, 5/15, show that 5 and 15 have a common
divisor of 5, so this f raction can besimplif ied by dividing each
number by 5 to make 1/3.
4. Also show that if the greatest common divisor is not used,
then the f raction can be simplif ied f urther still.For example:
4/12 has a common divisor of 2, but this would make 2/6.Two and six
both have a common divisorof 2 as well, so you could simplif y f
urther to make 1/3.
Guided Practice (10 min):
1 + 3 =3D 1 + 3 =3D 1 + 4=3D5
1 + 1 =3D 1 + 1 =3D 1 + 1 =3D 1 + 2 =3D3 SIMPLIFY:3
5 3 =3D2 =3D 2 SIMPLIFY:2
4 3 =3D4 3 =3D 1 =3D 1
Closure (5 min):
Go over what weve learned about addition, subtraction, using the
greatest common f actor, and simplif ying.Ask the students if they
have any questions, and assign their homework.
Homework:
1.2 2 =3D 4/15
=3D4/15
3 5
2.2 5 =3D 1/24
=3D1/24
3 8
3.4 + 2 =3D 34/35
=3D34/35
7 5
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4.5 2 =3D 1/8
=3D1/8
8 4
5.1 1 =3D 2/63
=3D2/63
7 9
6.2 1 =3D 7/72
=3D7/72
9 8
7.5 1 =3D 16/45
=3D16/45
9 5
8.5 1 =3D 1/2 =3D
1/26 3
9.4 4 =3D 2/21
=3D2/21
6 7
10.1 + 1 =3D 7/12
=3D7/12
3 4
11.2 + 1 =3D 11/12
=3D11/12
3 4
12.3 + 4 =3D 5/4
=3D1 1/4
4 8
13.5 2 =3D 1/3
=3D1/3
9 9
14.5 + 1 =3D 7/6
=3D1 1/6
6 3
15.3 4 =3D 1/35
=3D1/35
5 7
Adding and Subtracting Fractions, Using GCF, and Simplifying
