The idea in brief. Regroup a larger place into ten of the next place before subtracting, including across zero places. Rename from the next place whenever a column's top digit is smaller, before subtracting. In the lesson. In Primary 2, you subtracted in columns and renamed one ten as ten ones. Today, we subtract numbers up to ten thousand and rename across zeros. Start with the ones, and when a place does not have enough, rename one from the place on its left, even across zeros.
Lesson video, with the working
Subtracting and renaming through zero
5 min 49 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
How do you solve P3 subtracting across zeros questions?
This page teaches column subtraction of numbers up to 4 digits, including renaming across one or more zeros, as in 6004 minus 1758, which is 4246.
What your child learns here
This page teaches column subtraction of numbers up to 4 digits, including renaming across one or more zeros, as in 6004 minus 1758, which is 4246. It covers the MOE Primary 3 outcome on subtraction algorithms.
Set out a subtraction with the greater number on top and the places lined up from the ones.
Rename 1 ten as 10 ones, 1 hundred as 10 tens or 1 thousand as 10 hundreds when a place does not have enough.
Rename through zeros: when the hundreds and tens are both 0, rename 1 thousand as 10 hundreds, then 1 of those hundreds as 10 tens, and so on down.
Check a subtraction by adding the answer to the number that was subtracted.
Use subtraction in word problems that ask how many are left or how many more.
Does the answer make sense?
Whatever is subtracted, the answer must be smaller than the starting number on top, and your child can add back everything subtracted to rebuild that number. When the question hides a single digit, the answer is one digit from 0 to 9 that makes the finished subtraction true.
How to practise these questions
The Basic questions train column subtraction with regrouping from the next place. The Intermediate questions add renaming across a zero, where a hundred or a thousand must be broken down first. The Challenge questions first build the numbers from a set of digits, or find a missing digit in a subtraction that is already finished. If subtracting through zeros stalls, watch that question's solution film and revisit it later from Revision.
Questions parents ask
What does subtracting across zeros mean? It is a subtraction where the place your child needs to rename from holds a 0, as in 5002 minus 1347. The renaming has to reach left to the first place that is not 0, and each 0 it passes becomes 9.
Is renaming across zeros in the P3 syllabus? It is part of the Primary 3 outcome on addition and subtraction algorithms with numbers up to 4 digits. Numbers such as 6004 need renaming across zeros, so the written method has to handle them.
Should my child always put the bigger number on top? In column subtraction, the number being subtracted from goes on top, and in these questions it is the greater one. If a word problem mentions the smaller number first, your child still writes the greater one on top.
