Unit 5, Lesson 11
Using Long Division
Grade 6
11.1
Warm-up
Here are Lin’s calculations for finding .
What do you notice? What do you wonder?
11.2
Activity
Here is how Lin found the quotient of .
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Study Lin’s steps. Then discuss with your partner:
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In the first step, Lin divided 6 by 3 to get 2. Why do you think she put the 2 over the 6?
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Lin subtracted then , and lastly . Earlier, Andre subtracted then , and lastly . Why did they have the same quotient?
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In the third step, why do you think Lin wrote the 7 next to the remainder of 2 rather than adding 7 and 2 to get 9?
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Lin’s method is called long division. Use this method to find the following quotients. Check your answer by multiplying it by the divisor.
11.3
Activity
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Use long division to calculate each quotient.
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Here is Priya’s calculation of .
Long division of 906 divided by 3. 6 rows. First row: 320. Second row: 3, long division symbol with 906 inside. Third row: minus 9. Horizontal line. Fourth row: 0 6. Fifth row: minus 6. Horizontal line. Sixth row: 0.-
Priya wrote 320 for the value of . Check her answer by multiplying it by 3. What product do you get?
- What does the product tell you about Priya’s answer? Explain your reasoning. If you think her answer is incorrect, describe the error and show the correct calculation and answer.
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Student Lesson Summary
Long division is another method for calculating quotients. It relies on place value to perform and record the division.
When we use long division, we work from left to right and with one digit at a time, starting with the leftmost digit of the dividend. We remove the largest group possible each time, using the placement of the digit to indicate the size of each group.
Here is an example of how to find using long division.
Long division of 948 divided by 3. 8 rows. First row: 316. Second row: 3, long division symbol with 948 inside. Third row: minus 9, 3 groups of 3 hundreds. Horizontal line. Fourth row: 4. Fifth row: minus 3, 3 groups of 1 ten. Horizontal line. Sixth row: 18. Seventh row: minus 18, 3 groups of 6 ones. Horizontal line. Eight row: 0.
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We start by dividing 9 hundreds into 3 groups, which means 3 hundreds in each group. Instead of writing 300, we simply write 3 in the hundreds place, knowing that it means 3 hundreds.
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There are no remaining hundreds, so we work with the tens. We can make 3 groups of 1 ten out of 4 tens, so we write 1 in the tens place above the 4 of 948. Subtracting 3 tens from 4 tens, we have a remainder of 1 ten.
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We know that 1 ten is 10 ones. Combining these with the 8 ones from 948, we have 18 ones. We can make 3 groups of 6 ones, so we write 6 in the ones place.
In total, there are 3 groups of 3 hundreds, 1 ten, and 6 ones in 948, so .
Long division is a way to show the steps for dividing numbers in decimal form. It finds the quotient one digit at a time, from left to right.
Here is the long division for .