Fun facts of division
Division facts in Grade 4 math include three special rules that make certain problems instant: any number divided by 1 equals itself (8 ÷ 1 = 8), any non-zero number divided by itself equals 1 (9 ÷ 9 = 1), and zero divided by any non-zero number equals zero (0 ÷ 4 = 0). Covered in Chapter 5 of Saxon Math Intermediate 4, these 'fun facts' of division reduce calculation time and reinforce the relationship between division and the identity properties of multiplication.
Key Concepts
Property There are special rules for dividing by 1, dividing a number by itself, and dividing zero. 1. A number divided by one is itself ($8 \div 1 = 8$). 2. A non zero number divided by itself is one ($\frac{9}{9} = 1$). 3. Zero divided by a non zero number is zero ($4\overline{)0} = 0$).
Example 1. 'Twelve divided by one' is solved as $12 \div 1 = 12$. 2. 'Fifteen divided by fifteen' is solved as $\frac{15}{15} = 1$. 3. 'Zero divided by five' is solved as $5\overline{)0} = 0$.
Explanation These are division's easiest cheat codes! Any number divided by 1 is just itself, because you're just making one big group. Any number divided by itself is 1, like sharing ten cookies with ten people—everyone gets one. And if you have zero cookies to share among four friends, how many does each person get? Zero, of course!
Common Questions
What is any number divided by 1?
Any number divided by 1 equals itself. 15 ÷ 1 = 15. You are making one group that contains all items, so nothing changes.
What is any number divided by itself?
Any non-zero number divided by itself equals 1. 7 ÷ 7 = 1. You are splitting the items into groups equal to the total, so each group gets exactly 1.
What is zero divided by any number?
Zero divided by any non-zero number equals zero. 0 ÷ 5 = 0. If you have nothing to divide, each group gets nothing.
Can you divide by zero?
No. Division by zero is undefined. There is no number of groups of zero that equals a non-zero total, so the answer is meaningless.
When do Grade 4 students learn these division rules?
These special division facts are covered in Chapter 5 of Saxon Math Intermediate 4 as students build division fluency alongside multiplication.
How do these division rules connect to multiplication?
They mirror the multiplication identity properties: n × 1 = n (any number times 1 is itself) and 1 × n = n, and n × 0 = 0 (zero times anything is zero). Division reverses these relationships.