Lesson 71: Division Answers Ending with Zero

New Concept

It is important to continue the division until all the digits inside the division box have been used.

What’s next

Next, you'll apply this rule to see how zeros appear in quotients, sometimes even with remainders.

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.

Property

When you bring down a digit and the new number is smaller than the divisor, you must write a zero in the quotient. The process then continues, often resulting in a remainder.

Example 1: In $3)\overline{121}$, after dividing $12$ by $3$ to get $4$, bring down the $1$. Since $1$ is less than $3$, write $0$ in the quotient. The final answer is $40 \text{ R } 1$.
Example 2: In $8)\overline{241}$, after dividing $24$ by $8$ to get $3$, bring down the $1$. Since $1$ is less than $8$, write $0$ in the quotient. The final answer is $30 \text{ R } 1$.

What happens when you bring down a digit, but it's too small to be divided by the divisor? Don't panic! You simply write a big '0' in that spot in the quotient. This zero holds the place value correctly. You then multiply the divisor by zero, subtract, and the number you couldn't divide becomes your final remainder. Easy peasy!

Property

To find 'about how many,' we can use compatible numbers to estimate. Find a number close to the dividend that is easily divisible by the divisor.

Example 1: To estimate $254 \div 5$, change $254$ to the nearby compatible number $250$. Now solve $250 \div 5 = 50$.
Example 2: To estimate how many boxes are in 6 railcars with 538 boxes total, change $538$ to $540$. Now solve $540 \div 6 = 90$. It's about $90$ boxes per car.

Why wrestle with tricky numbers when you can estimate? The secret is using 'compatible numbers'—numbers that are close to the originals but play nicely together. Swap the dividend for a nearby number that the divisor can divide cleanly. This gives you a sensible, quick answer that's perfect for figuring out 'about how many' miles per hour or boxes per car.