Grade 6

2.06 Divide by a single digit

Ideas

Long division

Long division

This video looks at how we can use a long division algorithm to solve division with larger numbers. We can use the same process for division with and without a remainder.

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If we can't divide into equal groups, we end up with a remainder. Here is an example:

15 \div 4

We know that 4 goes into 15 three times, but there will be 3 leftover. We can express this remainder in three ways:

3\text{R} 3: The result of the long division, followed by \text{R}, followed by the remainder amount.
3 \dfrac{3}{4}: A fraction found by dividing the remainder by the divisor and leaving as a fraction.
3.75: A decimal found by continuing long division with the addition of zeros or converting the above fraction remainder into a decimal.

Examples

Example 1

Find the value of 228\div3.

Worked Solution

Create a strategy

Use long division.

Apply the idea

A long division with 228 being divided by 3. Ask your teacher for more information.

Set up the long division.

We cannot divide 2 by 3, so we move to the next place value and divide 22 by 3.

3 can fit into 22 \,\,\, 7 times with 1 left over. This is because 7\times 3=21. So we put a 7 in the tens place.

Multiply 7 by 3 to get 21 and put this number below 22.

Then subtract 21 from 22 to get 1, and bring down 8.

3 can fit into 18 \,\,\, 6 times since 3\times 6=18. So we put a 6 in the ones place.

Multiply 6 by 3 to get 18 and put this number below the line in the tens and ones places.

Subtract 18 from 18 to get 0.

Since the remainder is 0 and there are no more digits to divide by 3, we know that we are finished. 228\div3=76

Example 2

Find the value of 2516 \div 8.

Worked Solution

Create a strategy

Use long division, accounting for any possible remainders.

Apply the idea

A long division where 2516 is divided by 8. Ask your teacher for more information.

Set up the long division.

8 can fit into 25 \,\,\, 3 times since 8\times 3=24.

Write 3 in the hundreds column, since the 5 in 25 is in the hundreds column.

Multiply 3 by 8 to get 24 and write 24 below 25.

Subtract 24 from 25 to get 1.

Bring the 1 in the tens place down.

8 can fit into 11 \,\,\, 1 time since 8\times 1=8.

Write a 1 in the tens place at the top.

Multiply 1 by 8 to get 8 and write 8 below 11 in the tens place.

Subtract 8 from 11 to get 3.

Bring the 6 in the ones place down.

8 can fit into 36 \,\,\, 4 times since 8\times 4=32.

Write 4 in the tens place at the top.

Multiply 4 by 8 to get 32 and write 32 below 36.

Subtract 32 from 36 to get 4.

This means that 2516 \div 8=314 with a remainder of 4.

Reflect and check

The final answer with the remainder can be expressed in the following ways:

314 \text{R} 4
314 \frac{4}{8}
314.5

Idea summary

Division is when we share a total into a number of groups, or find out how many items each group has.

If we can't share a division into equal groups, we end up with a remainder. There are three ways that we can write down remainders:

\text{R}, followed by the remainder amount.
As a fraction alongside the integer answer, found by dividing the remainder by the divisor and leaving as a fraction.
As a decimal, found by continuing long division with the addition of zeros or converting the above fraction remainder into a decimal.

2.06 Divide by a single digit

Ideas

Long division

Examples

Example 1

Example 2

Outcomes

6.NS.B.2

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