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4.05 Division with larger numbers

Lesson

Are you ready?

Are you comfortable solving  division using the algorithm  , when there is no remainder?

Examples

Example 1

Find the value of 856 \div 8.

Worked Solution
Create a strategy

Use the short division algorithm.

Apply the idea
856 divided by 8 using short division. Ask your teacher for more information.

Set up the algorithm.

856 divided by 8 using short division. Ask your teacher for more information.

8 goes into 8 once, so we put a 1 in the hundreds column.

856 divided by 8 using short division. Ask your teacher for more information.

8 goes into 5 zero times with 5 remaining, so we put a 0 in the tens column and carry the 5 to the units column.

856 divided by 8 using short division. Ask your teacher for more information.

8 goes into 56 seven times, so we put a 7 in the units column.

856 \div 8 = 107

Idea summary

When you are dividing, you always start with the digit that is farthest to the left. If you get to a digit that you can't divide into, make sure you put a placeholder zero in the answer, before moving to the next digit.

Short division with larger numbers

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Examples

Example 2

Find the value of 3244 \div 4.

Worked Solution
Create a strategy

Use the short division algorithm.

Apply the idea
3244 divided by 4 using short division. Ask your teacher for more information.

Set up the algorithm.

3244 divided by 4 using short division. Ask your teacher for more information.

4 goes into 3 zero times with 3 remaining, so we put a 0 in the thousands column and carry the 3 to the hundreds column.

3244 divided by 4 using short division. Ask your teacher for more information.

4 goes into 32 eight times, so we put 8 in the hundreds column.

3244 divided by 4 using short division. Ask your teacher for more information.

4 goes into 4 one time, so we put a 1 in the tens column.

3244 divided by 4 using short division. Ask your teacher for more information.

4 goes into 4 one time, so we put a 1 in the units column.

3244 \div 4 = 811

Idea summary

When you are dividing, you always start with the digit that is farthest to the left.

Short division with remainders

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Examples

Example 3

Find the value of 264\div16.

Worked Solution
Create a strategy

Use the division algorithm.

Apply the idea
264 divided by 16 using short division. Ask your teacher for more information.

Set up the algorithm.

264 divided by 16 using short division. Ask your teacher for more information.

16 goes into 2 zero times with 2 remaining, so we put a 0 in the hundreds column and carry the 2 to the tens column.

264 divided by 16 using short division. Ask your teacher for more information.

16 goes into 26 one time with 10 remaining, so we put a 1 in the tens column and carry the 10 to the units column.

264 divided by 16 using short division. Ask your teacher for more information.

16 goes into 104 six times with 8 remaining, so we put a 6 in the units column and the remainder is 8.

264\div16=16 remainder 8.

Idea summary

When we solve division, if we cannot share the total (dividend) equally, we end up with a remainder. The remainder can also be expressed as a fraction or decimal.

Outcomes

MA3-6NA

selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

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