M.1 Add and subtract numbers ending in zeros
What are numbers ending in zeros?
Numbers ending in zeros are large numbers where the final digits are zeros. These zeros are often called placeholder zeros because they show the place value of the non-zero digits. Working with these numbers is a key skill in fourth-grade math.
- 40 (4 tens, ends with one zero)
- 300 (3 hundreds, ends with two zeros)
- 5,000 (5 thousands, ends with three zeros)
- 12,000 (12 thousands, ends with three zeros)
When we say "numbers ending in zeros," we are often referring to numbers that are multiples of 10, 100, 1,000, or even 10,000. Recognizing the pattern of zeros helps us compute quickly and accurately.
Adding numbers ending in zeros
To add numbers that end in zeros, you can use a simple strategy: add the non-zero digits first, then re-attach the zeros. This is called the "basic fact" strategy. It works because the zeros represent the same place value.
- Add 40 + 30: Think: 4 tens + 3 tens = 7 tens, which is 70.
- Add 200 + 500: Think: 2 hundreds + 5 hundreds = 7 hundreds, which is 700.
- Add 3,400 + 2,100: Think: 34 hundreds + 21 hundreds = 55 hundreds, which is 5,500. Or, add 34 + 21 = 55, then attach two zeros.
- Add 12,000 + 5,000: Think: 12 thousands + 5 thousands = 17 thousands, which is 17,000.
Always align numbers by their place value before adding. When using the basic fact strategy, make sure the ending zeros are the same in both numbers. For example, you can add 400 + 300 directly, but for 400 + 3,000, you need to think carefully about place value (4 hundreds + 30 hundreds).
Subtracting numbers ending in zeros
Subtracting numbers that end in zeros follows the same principle as addition. You can subtract the non-zero digits and then re-attach the zeros. This strategy works well when both numbers have the same number of ending zeros.
- Subtract 80 - 30: Think: 8 tens - 3 tens = 5 tens, which is 50.
- Subtract 700 - 400: Think: 7 hundreds - 4 hundreds = 3 hundreds, which is 300.
- Subtract 4,500 - 2,200: Think: 45 hundreds - 22 hundreds = 23 hundreds, which is 2,300.
- Subtract 19,000 - 7,000: Think: 19 thousands - 7 thousands = 12 thousands, which is 12,000.
If the numbers have a different number of zeros, rename the larger number in terms of the smaller place value. For example, to solve 5,000 - 400, think of 5,000 as 50 hundreds, then subtract 4 hundreds to get 46 hundreds, or 4,600.
Using all types of situations
In fourth grade, you will see addition and subtraction problems with numbers ending in zeros in many different real-world situations. These are often called one-step and multi-step word problems. The key is to identify the operation needed and apply the correct strategy.
- Combining (addition): A library has 2,300 fiction books and 1,200 nonfiction books. How many books are there in total? Solution: 2,300 + 1,200 = 3,500 books.
- Comparing (subtraction): A school’s goal was to raise 10,000 dollars. They raised 7,500 dollars. How much more money do they need? Solution: 10,000 - 7,500 = 2,500 dollars.
- Finding the missing part: A farmer planted 4,800 seeds. After a week, 900 seeds did not sprout. How many seeds sprouted? Solution: 4,800 - 900 = 3,900 seeds.
- Multi-step problem: A truck driver drove 1,200 miles on Monday and 2,300 miles on Tuesday. On Wednesday, she drove 500 fewer miles than on Tuesday. How many miles did she drive in total? Solution: First find Wednesday’s miles: 2,300 - 500 = 1,800 miles. Then add all three days: 1,200 + 2,300 + 1,800 = 5,300 miles.
In multi-step problems, look for clue words. Words like "in all" or "total" often mean addition. Words like "how many more" or "difference" often mean subtraction. Always read the problem twice before solving.
Regrouping (renaming) with zeros
Sometimes, when subtracting numbers ending in zeros, you need to regroup (also called borrowing or renaming). This happens when a digit in the top number is smaller than the digit directly below it. When zeros are involved, regrouping can take multiple steps.
- Subtract 500 - 120: Write the numbers vertically. 500 has 0 tens and 0 ones. You cannot subtract 2 tens from 0 tens, so you regroup 1 hundred as 10 tens. Now you have 4 hundreds and 10 tens. Subtract 1 hundred (from 4) and 2 tens (from 10) to get 380.
- Subtract 4,000 - 1,200: Think of 4,000 as 40 hundreds. 1,200 is 12 hundreds. 40 hundreds - 12 hundreds = 28 hundreds, which is 2,800. This is a quicker way using the basic fact strategy with place value.
- Subtract 3,000 - 1,700: Regroup 1 thousand as 10 hundreds. Now you have 2 thousands and 10 hundreds. Subtract 1 thousand and 7 hundreds to get 1,300.
A helpful mental math strategy for subtraction problems like 3,000 - 1,700 is to subtract 1,000 first to get 2,000, then subtract the remaining 700 to get 1,300. This avoids complex regrouping on paper.
Estimating with numbers ending in zeros
Estimation is a powerful skill that helps you check if your exact answer is reasonable. When adding or subtracting numbers ending in zeros, you can often estimate by rounding each number to the highest place value, which usually results in numbers that also end in zeros.
- Problem: A stadium has 23,950 seats. 11,200 tickets were sold for an event. Estimate how many seats are empty. Round 23,950 to 24,000. 24,000 - 11,000 = 13,000 empty seats (estimate). The actual answer is 12,750, so 13,000 is a reasonable estimate.
- Problem: A school district ordered 4,500 notebooks for one school and 3,800 for another. Estimate the total notebooks. Round 4,500 to 5,000 and 3,800 to 4,000. 5,000 + 4,000 = 9,000 notebooks (estimate). The actual total is 8,300, so the estimate is close.
When estimating, the goal is not to find the exact answer but to find a number that is close enough to check for errors. If your exact answer is very far from your estimate, it is a sign that you should recheck your work.
Common mistakes and how to avoid them
Even strong math students can make simple errors when working with numbers that end in zeros. Recognizing these common mistakes can help you avoid them.
- Mistake: Adding 400 + 50 = 450, but incorrectly writing 4,500. Fix: Remember that 400 is 4 hundreds and 50 is 5 tens. The sum is 4 hundreds and 5 tens, which is 450, not 4,500.
- Mistake: Subtracting 7,000 - 2,000 = 5,000, but thinking it is 500. Fix: Keep track of the zeros. 7 thousands minus 2 thousands equals 5 thousands, which is 5,000, not 500.
- Mistake: Forgetting to regroup when subtracting from a number like 1,000. Fix: Remember that 1,000 is 10 hundreds, or 100 tens, or 1,000 ones. Rename it in a way that makes subtraction possible.
- Mistake: In a word problem, adding when you should subtract. Fix: Look for context clues. "How much more?" and "what is the difference?" usually mean subtraction.
A great habit is to use estimation to check your work. Also, writing numbers in a vertical format with aligned place values can prevent many of these common errors.
Common Core alignment: CCSS.MATH.CONTENT.4.NBT.B.4 – Fluently add and subtract multi-digit whole numbers using the standard algorithm. This includes numbers ending in zeros in various real-world contexts.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.4.NBT.B.4. All content is 100% free, use it for whole-class instruction, independent study and practice, or homework.