# Inside Track: Dividing by 5 & by 10 with Remainders

### Key Idea:

Dividing by 5 and 10 links with place value in the base 10 numeration system. Dividing a number which leaves a remainder requires good knowledge of the basic division facts.

Basic division facts are the reverse or inverse facts from multiplication facts, from 0x0 to 10×10 or 12×12. Dividing in this situation thus results in a whole number:

• e.g., 24 divided by 6 = 4
• 30 divided by 6 = 5

Dividing other numbers which are not whole number multiples of the divisor is more complicated. For example, dividing a number like 26 by 6 involves the following steps:

• 26 divided by 6 = ?
• Think of multiples of 6 near 26: for example, 18, 24, 30
• Find the multiple of 6 closest to 26, yet less than 26: 24
• Recall the quotient of 26 and 6: 4
• Subtract 24 from 26: 2
• State the result: 26 divided by 6 = 4 remainder 2

Students will benefit from exploring the effect of dividing various numbers in sequence by the same divisor. For example:

• 12 divided by 3 = 4
• 13 divided by 3 = 4 rem 1
• 14 divided by 3 = 4 rem 2
• 15 divided by 3 = 5
• 16 divided by 3 = 5 rem 1

### Extending These Activities:

There are thousands of division with remainder questions, even restricting the number divided to less than 100 or 144. Students who are ready for even more of a challenge can try dividing by larger divisors, such as 20 or 25, for example.