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 2 1 4 and take away 1 3 4 , how much is left? 𝟐 𝟏 𝟒 𝟏 𝟓 𝟒 rename − 𝟏 𝟑 𝟒 − 𝟏 𝟑 𝟒 Rename one of the wholes as a fraction. We’re taking away ¾ but only have ¼ . 𝟐 𝟒 𝟏= 𝟒 𝟒

We “borrowed” from the whole number and gave it to the fraction. 𝟐 𝟏 𝟒 𝟏 𝟓 𝟒 = You can also think about this as regrouping. Group the 1 with the 𝟐 𝟓 to create an improper fraction. Rewrite 4 as 3+1 𝟒 𝟐 𝟓 𝟑 𝟓 = = 𝟑+𝟏 𝟐 𝟓 7

Try regrouping each of these fractions. =𝟒+𝟏 𝟑 𝟖 𝟓 𝟑 𝟖 𝟒 𝟖 = 11 =𝟏+𝟏 𝟏 𝟗 𝟐 𝟏 𝟗 1 𝟗 = 10

Using regrouping in a subtraction problem… 𝟓 𝟏 𝟗 =𝟒 𝟏𝟎 𝟗 We need to take 4 9 away from 1 9 . 4+1 Rewrite the 5 as 4+1. Group the 1 with the 1 9 . − 𝟐 𝟒 𝟗 After regrouping we can rewrite 5 1 9 as 4 10 9 . Now subtract & simplify your answer. =𝟐 𝟔 𝟗 =𝟐 𝟐 𝟑

An Alternative to Regrouping... THE POWER OF THE NUMBER LINE! 𝟑 𝟐 𝟓 − 𝟐 𝟒 𝟓 Subtraction is like finding the distance between the two numbers. ? 𝟑 𝟐 𝟓 𝟐 𝟒 𝟓 𝟑 𝟐 𝟓 −𝟐 𝟒 𝟓 = ? 𝟐 𝟒 𝟓 + ? = 𝟑 𝟐 𝟓 Use fact families to change the problem from to

𝟑 𝟐 𝟓 − 𝟐 𝟒 𝟓 = 𝟑 𝟓 We need another 1 5 to make 3. Then another 2 5 … 𝟐 𝟒 𝟓 + ? = 𝟑 𝟐 𝟓 𝟑 𝟓 + 𝟏 𝟓 + 𝟐 𝟓 𝟑 𝟐 𝟓 𝟐 𝟒 𝟓 3

Try this one! 𝟒 𝟏 𝟖 −𝟏 𝟓 𝟖 = N Rewrite as 𝟏 𝟓 𝟖 + N = 𝟒 𝟏 𝟖 2 𝟏 𝟐 We added a total of 2 4 8 . + 𝟏 𝟖 + 𝟑 𝟖 +𝟐 𝟒 𝟏 𝟖 𝟏 𝟓 𝟖 2 4

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 “borrowing” and why: 𝟐 𝟑 𝟒 𝟏 𝟏 𝟐 or 𝟐 𝟏 𝟒 𝟏 𝟕 𝟖 Partner A: Explain how you would use borrowing in the problem 𝟒 𝟏 𝟔  𝟐 𝟓 𝟔 . Partner B: Explain how you could use a number line to find the difference of 𝟖 𝟏 𝟒  𝟓 𝟏 𝟐 .