SUBTRACTION 5.NF.1
Step 3 Subtracting Fractions - Unequal Denominators
Purpose:
To subtract fractions having unequal denominators and approximate differences
Materials:
Fraction Bars, Fraction Playing Cards, and copies of Master #5 (attached)
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Using bars for fractions with unlike denominators
Fraction
Bars
pencils
and paper
. Ask students to find these bars and line them up to
compare the differences in their shaded amounts.
 How can this difference be found? (One way is to find a third bar that has the
same shaded amount as the difference. In this example, that would be an
orange bar with 7 shaded parts.) Another method is illustrated as follows:
 Find the orange bar with the same shaded amount
as the blue bar and the orange bar with the same
shaded amount as the red bar. What is the
difference of the fractions for these bars? (7/12)
3
1
9
2
7
–
=
–
=
4
6
12
12
12
 To subtract 1/6 from 3/4, you replaced 3/4 by 9/12 and 1/6 by 2/12. How can
these new fractions be found without the bars? (Multiply the numerator and
denominator of 3/4 by 3 and the numerator and denominator of 1/6 by 2.)
2. In this next example, only one fraction needs to be replaced to obtain the same
denominator for both fractions.
 Find the red bar for 5/6 and the green bar for 1/2 and replace just one of these
bars so the two fractions have the same denominator. Write the subtraction
equation. (5/6 – 1/2 = 5/6 – 3/6 = 2/6) Point out that when one denominator
divides the other (2 divides into 6) only one fraction needs to be replaced.
copies of
Master #5
3. Distribute Master #5 - "Subtracting Fractions from Fraction Bars" on page 117 to
each student. Replacing bars by bars of the same color is like replacing fractions by
fractions with the same denominator.
Activity 2 Subtracting fractions without using bars
pencils
and paper
1. Write the fraction difference 4/5 - 1/3.
 What fractions can 4/5 and 1/3 be replaced by so that both fractions have the
same denominator? (Multiply the numerator and denominator of 4/5 by 3 to get
12/15 and multiply the numerator and denominator of 1/3 by 5 to get 5/15)
 Write the equation for 4/5 – 1/3. (4/5 – 1/3 = 12/15 – 5/15 = 7/15)
2. Repeat this activity for these differences. Point out the need to compare denominators
to see if one can be divided by the other before getting common denominators.
3
1
–
5
2
2
1
–
3
8
3
1
–
5
10
1
3
–
2
8
 Look for patterns in these differences. (If one denominator divides into the other,
only one fraction needs to be replaced. Some students may remember from
addition that multiplying the two denominators of the fractions gives a common
denominator, but not necessarily the smallest common denominator.)
Activity 3 Approximating differences of fractions
1. Approximate differences by rounding fractions to 0 or 1.
Pencils
and paper
 Round each fraction to 0 or 1 and compute the difference.
7
1
–
8
5
11
9
–
12
10
5
1
–
6
8
1
1
–
4
7
2. Approximate differences by using compatible numbers.
 It is often convenient to replace a fraction by one which is approximately equal
to make the computation easier. What fraction is more compatible than 1/9 in
order to approximate 7/10 - 1/9? (1/10) So, 7/10 - 1/9 ≈ 7/10 - 1/10 = 6/10
 Approximate the following differences by using compatible numbers:
7
1
–
8
5
11
9
–
12
10
5
1
–
6
8
7
1
–
15
4
Different replacements are possible. For example, 7/8 - 1/5 ≈ 7/8 - 1/8 = 6/8, or
7/8 - 1/5 ≈ 1 - 1/5 = 4/5, where 7/8 was replaced by 1 before subtracting.
Activity 4 Activities with Fraction Playing Cards
Fraction
Playing
Cards
1. Distribute a deck of Fraction Playing Cards to each group and place students in pairs.
Ask each student to select two cards, determine the difference of the fractions, and
compare it to their partner's to see who has the smallest difference.
2. Optional: Students play Player's Choice (page 103) or Diffe (page 104), games
involving the Fraction Playing Cards and differences of fractions.
INDEPENDENT PRACTICE and ASSESSMENT
Worksheets 62-65 from the Teacher Resource Package
fractionbars.com Set 2 Rope Tug (Subtracting fractions with different denominators)
Grades 5-8 Subtraction Step 3 Master #5
Name:
______________
Turn the bars face down for all the activities on this sheet. If you select any zero
bars or whole bars, place them aside.
1. Select any two bars with the same color. Write an equation for the difference of
the two fractions. Repeat this activity for parts a, b and c.
a. ____ − ____ =
b. ____ − ____ =
c. ____ − ____ =
2. Select any bars having the first two colors and write their fractions in the first two
blanks. Find fractions that are equivalent to these two fractions and write them in
the next two blanks. Then write the difference of the two fractions. Repeat this
activity for parts a, b, c and d.
a.
blue
red
orange
orange
sum
____ − ____ = ____ − ____ =
b.
yellow
green
red
red
sum
____ − ____ = ____ − ____ =
c.
orange
blue
orange
orange
sum
____ − ____ = ____ − ____ =
d.
yellow
red
red
red
____ − ____ = ____ − ____ =
sum