Download What does it mean to *borrow*?

Fraction Subtraction:
What does it mean to “borrow”?
You’ve used the idea of borrowing in
whole number problems…
But what does it mean
to “borrow” and how is
this idea used in
fraction problems?
If you start with
away
3
1 ,
4
1
2
4
and take
how much is left?
𝟏 rename 𝟓
𝟐
𝟏
𝟒
𝟒
𝟑
𝟑
−𝟏
−𝟏
𝟒
𝟒
Rename one of
the wholes as a
fraction.
𝟒
𝟏=
𝟒
We’re taking
away ¾ but
only have ¼ .
𝟐
𝟒
We “borrowed” from the whole number
and gave it to the fraction.
𝟏
𝟐
𝟒
=
𝟓
𝟏
𝟒
You can also think about this as regrouping.
𝟐
Rewrite 4 as 3+1
𝟐
𝟐
=𝟑
𝟑+𝟏
𝟒 =
𝟓
𝟓
𝟓
Group the 1 with the
𝟓
to create an improper
fraction.
7
Try regrouping each of these fractions.
𝟑
𝟑
𝟒
𝟓 =
=
𝟒+ 𝟏 𝟖
𝟖
𝟖
𝟏
𝟏
𝟏1+ 𝟏
𝟐 =
=
𝟗 𝟗
𝟗
11
10
Using regrouping in a subtraction problem…
𝟏
𝟏𝟎
𝟓 =𝟒
4+1
𝟗
𝟗
𝟒
−𝟐
𝟗
𝟔
=𝟐
𝟗
4
9
1
9
We need to take away from .
Rewrite the 5 as 4+1.
1
9
Group the 1 with the .
After regrouping we can rewrite
1
10
5 as 4 .
9
9
Now subtract & simplify your answer.
𝟐
=𝟐
𝟑
An Alternative to Regrouping...
THE POWER OF THE NUMBER LINE!
𝟐
𝟒
𝟑 − 𝟐
𝟓
𝟓
Subtraction is like finding the distance between the two numbers.
?
𝟐
𝟑
𝟓
𝟒
𝟐
𝟓
Use fact families to change the problem from 𝟑
𝟐
𝟓
𝟒
𝟓
𝟒
𝟓
− 𝟐 = ? to 𝟐 + ? = 𝟑
𝟐
𝟓
We need another
1
5
2
5
to make 3. Then another …
𝟒
𝟐
𝟓
𝟑
?
𝟓
+
𝟏
+
𝟓
𝟒
𝟐
𝟓
=
𝟐
𝟒
𝟑 − 𝟐
𝟓
𝟓
𝟐
𝟑
𝟓
𝟐
+
𝟓
3
𝟐
𝟑
𝟓
=
𝟑
𝟓
Try this one!
𝟏
𝟒
𝟖
−
𝟓
𝟏
𝟖
=N
Rewrite as
𝟓
𝟏
𝟖
+
𝟏
2N
𝟐
4
8
We added a total of 2 .
𝟑
+
𝟖
𝟓
𝟏
𝟖
𝟏
+
𝟖
+𝟐
2
4
𝟏
𝟒
𝟖
=
𝟏
𝟒
𝟖
Summary
• Find a partner. Decide who is Partner A and who is
Partner B.
• Partner A: Explain what it means to “borrow” in a
subtraction problem.
• Partner B: Tell which of these problems require
𝟑
𝟏
𝟏
𝟕
“borrowing” and why: 𝟐 𝟏
or 𝟐 𝟏
𝟒
𝟐
𝟒
𝟖
• Partner A: Explain how you would use borrowing in
𝟏
𝟓
the problem 𝟒  𝟐 .
𝟔
𝟔
• Partner B: Explain how you could use a number line
𝟏
𝟏
to find the difference of 𝟖  𝟓 .
𝟒
𝟐