Our first assignment is to create an autobiography work to tell me about you. Some students in the past have used a collage, a theme of summer clothes, an essay, a name tag, or an oral presentation. The choice is yours. There are samples in the classroom.
The Identity Property says that multiplying or dividing a number by one does not change the value. I know what you're thinking: what's the big deal; someone call the newspaper.
Yes, you're well aware that any number multiplied or divided by one is the number.
81 x 1 = 81
78 / 1 = 78
How about 3/4 x 8/8 = 24/32 ? Wait a minute, this isn't as straightforward. Yet, it is the same property operating incognito.
3/4 does indeed equal 24/32 while they look very different.
What about 8/8 (or 8 divided by 8)? Little rascal, that is the number one in disguise. I like to call these fractions copycat fractions. It's a name Danica McKellar came up with because the denominator and numerators are copycats- they're exactly the same. So all fractions that look like 2/2, 4/4, 58/58, 1024/1024 each equal one.
Naturally, since all of these fractions are equal to one, we can multiply them by any number without changing the value of the product. You end up with an equivalent fraction- it looks different, but has the same value!
Thus, 3/4 x 8/8 is 3/4 x 1 OR 3/4 = 24/32. Therefore, as long as you multiply (or divide) the fraction's numerator and denominator by the same number, your answer (product or quotient) is the same value as the original fraction. These are equivalent fractions.
Watch Out! The expression 0/0 is not a copycat fraction, because 0/0 is undefined in math. You can never have zero as the denominator (or you can never divide by zero)-ever. Seriously, no kidding.
Let's look why: 21/3 = 7 Our check 7(3), sure enough = 21
8/0 = what? zero
Well, our check would be 0 x 0 should equal numerator (8). Far from it; simply doesn't work. Never, divide by 0!
Notice 0/8 'will work.' 0/8=0 check 0(8) = 0 Sure enough!
The inverse property works with the identity property.
Hence the inverse property at work: 1/2 of two is two 'halved.' One half of two is ONE.
1/2 x 2/1 = 2/2 = 1
2/1 is two. It means 2 'divided' by one. Any value divided by one is the same value (the identity property).
We will use the inverse and identity properties often as we solve equations.
