SUBTRACTION 5.NF.1
Subtracting Mixed Numbers - Unequal Denominators
Purpose:
To subtract mixed numbers having unequal denominators and to approximate
differences involving mixed numbers.
Materials:
Fraction Bars
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Different denominators without regrouping
Fraction
Bars
1. Use the bars to represent the mixed numbers 3 3/4 and 2 1/3 by using the backs
of blue bars and yellow bars to represent each value of the unit.
–
3
3
4
–
2
1
3
 What bars need to be replaced so the difference can be computed? (Replace the
3/4 bar by a 9/12 bar and the 1/3 bar by a 4/12 bar.)
pencils
and
paper
 Write a subtraction equation for the difference. (Note: By removing two blue
bars and two yellow bars, the difference 3 9/12 - 2 4/12 can be replaced by the
difference 1 9/12 - 4/12.)
–
3
3
1
–2 =
4
3
1
9
12
4
12
–
= 1
5
12
2. Select from the following for computing differences. You may wish to have some of
these illustrated with the bars.
a. 4
1
3
–1
3
4
b. 3
1
5
–2
2
6
c.
5
1
2
–3
4
3
d. 4
1
1
–1
2
6
Activity 2 Different denominators with regrouping
1. Use the bars to represent the mixed numbers 3 1/6 and 2 1/2 by using the backs
of red bars and green bars to represent each value of the unit.
–
3
1
6
–
2
1
2
 How can these bars be used to compute 3 1/6 minus 2 1/2? (One possibility is to
replace the 1/6 and 1/2 bars by 2/12 and 6/12 bars. Another possibility is to replace
just the 1/2 bar by a 3/6 bar so that the difference becomes 3 1/6 − 2 3/6 . Then since
1/6 < 3/6, replace one of the whole bars for 3 1/6 by a 6/6 bar so that 3 1/6 can be
written as 2 7/6 and the difference 2 7/6 − 2 3/6 can be computed as shown below.)
–
3
1
6
–
2
3
6
=
2
7
3
4
− 2
=
6
6
6
 Replacing 3 1/6 by 2 7/6 is an example of regrouping.
2. Ask students to compute the following differences to practice regrouping. For
example, 5 1/3 - 2 5/6 = 5 2/6 - 2 5/6 = 4 8/6 - 2 5/6 = 2 3/6. Some students may find
it helpful to draw rough sketches of bars to regroup one mixed number to another.
a. 5
1
5
–2
3
6
b. 4
1
1
–1
3
2
c. 6
1
2
–2
5
3
d. 10
1
3
–7
2
4
Activity 3 Approximating differences of mixed numbers
 Round each mixed number to the nearest whole number to approximate the
following differences. (a. 1
b. 4
c. 2
d. 3)
a. 1
2
1
–1
3
5
b. 6
1
4
–1
4
7
c. 7
1
1
–5
5
8
INDEPENDENT PRACTICE and ASSESSMENT
Worksheets 5.NF.1 #11 and #12
fractionbars.com Set 2 Fraction Darts
(Players type a number between the high
and low numbers on the dart board and
click to throw a dart. In this example,
8 ½ was typed in for the first guess. A
correction can be typed by adding or
subtracting to 8 ½ or to any other
number that has been entered.
d. 3
1
2
–1
2
5