Division answers ending with zero
Grade 4 students learn that division answers can end in zero and that the division must continue through every digit of the dividend in Saxon Math Intermediate 4. When 560 is divided by 8, dividing 56 by 8 gives 7, then bringing down the 0 and dividing 0 by 8 gives 0, for a final answer of 70. A student who stops at 7 after dividing 56 is wrong because the final 0 was not processed. For 120 divided by 3: divide 12 by 3 = 4, bring down 0, divide 0 by 3 = 0, answer is 40. This Chapter 8 skill prevents the pervasive error of truncating answers prematurely.
Key Concepts
Property Sometimes division answers end with a zero. It is important to continue the division until all the digits inside the division box have been used.
Example 1: To solve $3)\overline{120}$, first divide $12$ by $3$ to get $4$. Bring down the $0$. Now divide $0$ by $3$, which is $0$. The answer is $40$. Example 2: To solve $4)\overline{200}$, first divide $20$ by $4$ to get $5$. Bring down the final $0$. Now divide $0$ by $4$, which is $0$. The answer is $50$.
Don't stop the division party early! Even if a subtraction step leaves you with a zero, you must keep going if there are still digits left to bring down from the dividend. Each digit needs its turn to be divided. Bring down that final zero and divide again; you'll often find the quotient needs a zero in that place value too.
Common Questions
Why do some division answers end in zero?
A trailing zero appears when the last digit brought down from the dividend is 0. After dividing 56 by 8 to get 7, you bring down the 0 from 560 and divide 0 by 8 = 0, making the complete answer 70, not 7.
How do you divide 560 by 8?
8 does not go into 5, so look at 56. 56 divided by 8 = 7. Bring down the 0. 0 divided by 8 = 0. Write 0 in the quotient. The answer is 70.
How do you know when you are done with long division?
You are done only when every digit in the dividend has been brought down and divided. Check that the number of digits in your quotient accounts for all the digits worked through. If you have not processed the final digit, you are not finished.
What is a quick way to check if a division answer needs a trailing zero?
Count the digits in the dividend and compare to the digits in your quotient. For 560 divided by 8, the answer should have two digits. If you have only one digit (7), you missed the final zero step.
What Saxon Math chapter covers division answers ending in zero?
Division answers ending in zero are covered in Saxon Math Intermediate 4, Chapter 8 (Lessons 71-80), emphasizing that every digit in the dividend must be processed.