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2.07 Divide by multi-digits

Long division by 2 digit numbers

We can use long division to divide by 2 digit numbers in the same way that we would divide by a single digit number.

This video looks at how we set out our work when using long division to divide by a 2 digit number.

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Similar to dividing multi-digit numbers by a single digit divisor, we follow the order of processes involved in standard algorithm in dividing numbers by two-digit divisors namely:

  1. Divide

  2. Multiply

  3. Subtract

  4. Bring Down

When we solve division, if we cannot share the total (dividend) equally, we end up with a remainder.

Examples

Example 1

Find the value of 5016\div57.

Worked Solution
Create a strategy

Use long division.

Apply the idea
A long division where 5016  is divided by 57. Ask your teacher for more information.

Set up the division.

57 doesn't fit into 5 or 50, so we need to go to the next column to the right, the tens place, and divide 501 by 57.

A long division where 5016  is divided by 57. Ask your teacher for more information.

57 fits into 501,\, 8 times, so we put an 8 above the tens place.

Then we multiply the 8 by 57 to get 456 which we write underneath the 501.

A long division where 5016  is divided by 57. Ask your teacher for more information.

Next we subtract 456 from 501 to get 45.

Since 57 doesn't fit into 45 we need to bring the 6 in the ones column down.

A long division where 5016  is divided by 57. Ask your teacher for more information.

57 fits into 456, \, 8 times, so we put an 8 above the ones place.

Multiply the 8 by 57 to get 456 which we write underneath the previous 456.

Then we subtract 456 from 456 to get 0.

5016\div57=88

Example 2

Find the value of 379\div29=⬚ with remainder .

Worked Solution
Create a strategy

Use long division.

Apply the idea
A long division where 379  is divided by 29. Ask your teacher for more information.

Set up the division.

29 doesn't fit into 3 so we need to go to the next column to the right, the tens place, and divide 37 by 29.

A long division where 379  is divided by 29. Ask your teacher for more information.

29 fits into 37 once, so we put a 1 above the tens place.

A long division where 379  is divided by 29. Ask your teacher for more information.

Multiply the 1 by 29 to get 29 which we write underneath the 37.

Then we subtract 29 from 37 to get 8.

Then we bring the 9 in the ones column down.

A long division where 379  is divided by 29. Ask your teacher for more information.

29 fits into 89,\,\,3 times, so we put a 3 above the ones place.

Multiply the 3 by 29 to get 87 which we write underneath the 89.

A long division where 379  is divided by 29. Ask your teacher for more information.

Then we subtract 87 from 89 to get a remainder of 2.

379\div29=13 with remainder 2.

Idea summary

In dividing multi-digit numbers by two-digit divisor, we follow the same processes involved in dividing by single-digit divisors:

  1. Divide

  2. Multiply

  3. Subtract

  4. Bring Down

When we solve division, if we cannot share the total (dividend) equally, we end up with a remainder.

Outcomes

6.NS.B.2

Fluently divide multi-digit numbers using the standard algorithm

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