ADDITION AND SUBTRACTION 4.NF.3
Mixed Numbers with Like Denominators
Purpose:
To add and subtract mixed numbers with the like denominators
Materials:
Fraction Bars, pencils, and paper
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Adding and subtracting without using improper fractions
Illustrate the following situations using visual fraction models.
Fraction
Bars
a. If 1 7/8 quarts of milk and 1 5/8 quarts of milk are both poured into a one-gallon
container, what is the total amount of milk in the container? Illustrate each amount
and write an addition equation for the total amount.
pencils
and paper
1
1
7
8
+
1
7
5
7
5
12
4
+1 = 2+ + =2
=3
8
8
8
8
8
8
5
8
b. Since a gallon container holds 4 quarts, how much more milk can be poured into
the container? Beginning with 4 whole bars to represent 1 gallon, cross off the parts
of bars being used (taken away) and write a subtraction equation to show the amount
left. (Cross off 3 whole bars and 4 parts of another whole bar.)
4 − 3
4
4
1
=
= of a quart
8
8
2
Activity 2 Replacing mixed number by improper fractions
1. At the halfway point in their mountain hike, there is 4/5 of a quart of water in one
canteen and 3/5 of a quart of water in another canteen. Illustrate each amount and write an
addition equation for the total amount.
4
3
7
+
= quarts
5
5
5
Placing the shaded amounts of the bars end-to-end shows there is a total of 1 2/5 bars.
1
2/5
4
3
2
+ =1
5
5
5
So,
7
2
=1
5
5
Point out that in the fraction 7/5, the denominator "5" indicates 5 equal parts in a whole,
and the numerator "7" indicates 7 of these parts. So, 5 of these 7 parts can be used to
form 1 whole bar and 2 parts out of 5.
2. Replace the following mixed numbers by improper fractions. Explain your reasoning. For
example, 2 can be illustrated by 2 whole bars each with 3 equal parts. So 2 1/3 = 6/3 + 1/3.
a. 2
1
=
3
3
b. 1
5
=
6
6
c. 3
1
=
4
4
d. 1
4
=
5
5
Activity 3 Add and subtract by using improper fractions
1. On Saturday Keira practiced her piano lessons for 1 7/10 hours in the morning and 2
3/10 hours during the afternoon. What was the total time she spent practicing her lesson?
a. Sketch a visual fraction model for the mixed numbers 1 7/10 and 2 3/10.
1
7
10
2
3
10
b. Write an addition equation for the total amount of time Keira spent practicing.
1
7
4
17
24
41
1
+ 2
=
+
=
= 4
hours
10
10
10
10
10
10
c. How much longer did Keira spend practicing in the afternoon than in the morning?
2
4
7
24
17
7
−1
=
−
=
of an hour
10
10
10
10
10
Point out that when computing the difference of two mixed numbers it is
sometimes convenient to replace the mixed numbers by improper fractions.
2. Illustrate the following situation using a visual fraction model.
a. At Camp Lookout there are 2 3/5 loaves of bread. If 4/5 of a loaf is needed for
Bread Pudding and 1 2/5 loaves are needed for Egg Toast, how much bread will be
left? Explain how a visual model can be used to illustrate 2 3/5 loaves of bread, and
write a subtraction equation to show the amount that is left. (Use 2 whole bars and
a 3/5 bar and cross off the parts of the bars that will be used.)
2 3/5 - 4/5 - 1 2/5 =
13/5 - 4/5 - 7/5 = 2/5
pudding
egg toast
left
3. Compute the sums and differences of the following mixed numbers.
a. 1
3
3
+2
4
4
b. 3
1
2
−1
3
3
c. 3
2
4
+2
5
5
d. 3
1
5
−1
6
6
INDEPENDENT PRACTICE and ASSESSMENT
Worksheet: 4.NF.3 #2
fractionbars.com Set 2 Target Sums (Finding bars whose fraction sum equals 1, 1½ or 2)