Mixed-Number Subtraction
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1
2Mixed-Number Subtraction
A mixed number names one or more wholes and a fractional part of a
1 __
1 __
whole. For example, the mixed number 5
names 5 wholes and
2
2
of another whole. Therefore, when problem solvers subtract mixed
numbers, they combine the process of subtracting whole numbers and the
process of subtracting fractions.
When subtracting mixed numbers, most people prefer to subtract the
fractions first because this makes the process a bit less cumbersome when
renaming is required. However, problem solvers with good number sense
may approach such problems in either way.
Build Understanding
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Ask students to draw a picture that shows 2
. On the
3
board, draw the picture on the right and write the
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fractions below it. Explain that 2
can be written
— 3
— 1
1 +
+
—
—
3
3 __
1 __
4 __
1 __
3
3
as 1 +
+
, or 1
. Then have students rename 3
as
3
3
3
5
5 __
1 __
6 __
1 __
4 __
1 __
5 __
2 +
+
= 2
+
=
1 — 4
and 1
as
. Give students problems
—
5
5
5
4
4
4
4
3
to try on their own.
Using page 41, explain that when subtracting mixed numbers, students will
need to rename the minuend (the top number) if the minuend is a whole
number or if the fraction part of the minuend is smaller than the fraction part
of the subtrahend. In Example 1, students must rename the whole number.
Example 2 requires students first to rename the fractions so that they have
a common denominator and then rename the minuend so that subtraction
is possible. Use questions like the following to guide students through the
examples:
3 __
• In Example 1, how is the minuend (5) renamed? (as 4
, so that it has the
3
2 __
same denominator as the subtrahend 2
)
3
1 __
1 __
• In Example 2, what is the common denominator of
and
? (6)
3
2
Page 41
2 __
• In Example 2, why do you need to rename the minuend (7
) again?
6
2 __
3 __
Answer Key
(because
in the minuend is smaller than
in the subtrahend)
6
6
3 __
2 __
6 __
2 __
8 __
? (You rename it as 6 +
+
• How do you rename 7
, or 6
. )
1. 2
6
6
6
6
8
• In Examples 1 and 2, do you need to simplify the difference? (No.
2 _
2.
The difference is already in simplest form.)
5
1 __
6 __
Error Alert
Watch for students who rename a minuend like 2
as 2
4 __
5
5
3. 2
6 __
5 __
instead of 1
. Remind students that they are renaming 2 as 1
. Crossing out
7
5
5
the 2 and writing a 1 above it, similar to the way students regroup to subtract
1 __
whole numbers, might be helpful. Also, make sure students simplify the
4. 1
4
difference if necessary after they are done subtracting.
5 _
5.
Check Understanding
8
1 __
Write 7 − 4
on the board. Have a volunteer go to the board and solve the
1 __
5
6. 3
2 __
1 __
− 4
problem. Repeat the process with the following problems: 7
,
2
5
5
1 __
2 __
1 __
1 __
− 4
− 4
7
, and 7
. Continue until you are reasonably certain that most
5
5
5
3
5 __
7.
of your students understand the algorithms. Then assign the “Check Your
12
Understanding ” exercises at the bottom of page 41. (See answers in margin.)
7 __
8. 1
24
Teacher Notes
40
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