# Adding and Subtracting Fractions, Using GCF, and Simplifying

Subject:

Math

6, 7

Anticipatory Set / Objectives (5 min):

Introduce the concept of fraction addition and subtraction, and teach the students how to use the greatest common factor, and how to simplify.

Direct Instruction (40 min):

Use pie charts to help the students understand how fractions work.

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 few more examples.

Simple Subtraction:

1.      Represent 2 with two circles. Split them into fourths and represent each as 4/4.

2.      Now create a pie chart representing 3/4.

3.      Remove the 3/4 from one pie and represent the remaining pies as 1 1/4.

4.      Give a few more examples.

1.      Draw two pie charts: one in thirds and one in twelfths.

2.      Shade in 1/3 on the first, 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 four slices, it is actually equal to a third and can be shown by

5.      Now explain that the easiest way to deal with different denominators is to make them the same. Show that you can split each of the thirds into four slices and make an identical circle of twelve slices.

6.      Now show the circles in fraction form. Explain that multiplying 1/3 by 4/4 will make 4/12, which then makes it easier to manipulate the two fractions

7.      Give a few more examples.

Subtraction using GCF:

1.      Draw two pie charts: one in fifths and one in fifteenths.

2.      Shade in 3/5 on the first, 4/15 on the second.

3.      Now show the class how you can’t subtract 4/15 from 3/5 without first making the denominators the same.

4.      Show that you can split each of the fifths into five slices and make an identical circle of fifteen slices.

5.      Now show the circles in fraction form. Explain that multiplying 3/5 by 3/3 will make 9/15, which then makes it easier to manipulate the two fractions.

6.      Erase 4/15 of the shaded area from the circle that was originally 3/5, and show that you are left with 5/15.

7.      Represent the equation in number form.

8.      Give a few more examples.

Simplifying:

1.      Using the examples from the previous steps, show that you can simplify fractions by finding the common divisors between the numerator and denominator.

2.      Using the first step, 4/12, show that 4 and 12 have a common divisor of 4, so this fraction can be simplified 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 fraction can be simplified by dividing each number by 5 to make 1/3.

4.      Also show that if the greatest common divisor is not used, then the fraction can be simplified further still. For example: 4/12 has a common divisor of 2, but this would make 2/6.Two and six both have a common divisor of 2 as well, so you could simplify further 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 we’ve learned about addition, subtraction, using the greatest common factor, and simplifying. Ask the students if they have any questions, and assign their homework.

Homework:

1.

 2 − 2 =3D 4/15 =3D 4/15 3 5

2.

 2 − 5 =3D 1/24 =3D 1/24 3 8

3.

 4 + 2 =3D 34/35 =3D 34/35 7 5

4.

 5 − 2 =3D 1/8 =3D 1/8 8 4

5.

 1 − 1 =3D 2/63 =3D 2/63 7 9

6.

 2 − 1 =3D 7/72 =3D 7/72 9 8

7.

 5 − 1 =3D 16/45 =3D 16/45 9 5

8.

 5 − 1 =3D 1/2 =3D 1/2 6 3

9.

 4 − 4 =3D 2/21 =3D 2/21 6 7

10.

 1 + 1 =3D 7/12 =3D 7/12 3 4

11.

 2 + 1 =3D 11/12 =3D 11/12 3 4

12.

 3 + 4 =3D 5/4 =3D 1 1/4 4 8

13.

 5 − 2 =3D 1/3 =3D 1/3 9 9

14.

 5 + 1 =3D 7/6 =3D 1 1/6 6 3

15.

 3 − 4 =3D 1/35 =3D 1/35 5 7