What property states that a divided by 2/3 = a times 3/2?

Answer 1

a / 2/3 is asking "How many times can 2/3 fit into a?"

Rewite the problem as (a/1) / (2/3).

You need to get rid of the (2/3) in the denominator.

The way to do this is by multiplying both the numerator and denominator by the multiplicative inverse of 2/3, namely 3/2

[(a/1) * (3/2)] / [(2/3) * (3.2)]

Note (2/3) * (3/2) is simply 1

Thus [(a/1)*(3/2)] / [(2/3)*(3/2)] becomes [(a/1)*(3/2)] / 1 = (a/1)*(3/2) = a*3/2

Answer 2

Recall two identities:

a / 1 = a

a (1/a) = 1

a/b ÷ c/d

a/b

c/d

a/b * d/c

c/d d/c

(a/b)(d/c)

(c/d)(d/c)

(a/b)(d/c)

1

(a/b)(d/c)

QED

Answer 3

A divided by 2/3 = A * 3/2 <---- you must change division to multiplication and multiply by the RECIPROCAL

Remember, KFC: keep, flip, change

Answer 4

The answer is the multiplicative identity property, which states that multiplying any number by 1 will give the same number.

In this case, multiply

a (3/2)

__. *. _____

(2/3). (3/2)

Note that 3/2 divided by 3/2 equals one, so we are multiplying the original expression by 1.

To evaluate, multiply the numerators together, to get a times (3/2)

Multiply the denominators together, to get (2/3)*(3/2) = 1

Divide the numerator by the denominator (1). Anything divided by 1 is equal to the same expression or number, so the answer is a times (3/2).

Answer 5

I wouldn't call it a "property" but the mnemonic for division of fractions is "invert the denominator and multiply"

a/(2/3) = a*(3/2)

P.S.

I have recently heard another mnemonic by "today's kids": Kentucky Chicken Fried...Keep Change Flip...

doesn't help me but maybe it makes sense to you!

P.P.S. Here is why the mnemonic works:

a/(2/3) = a/(2/3)*(3/2)/(3/2) because

(3/2)/(3/2) = 1

Now the original denominator and the denominator in the multiplier multiply to 1 i.e. (2/3)*(3/2)=1

and you are left with a*(3/2),

Please note: it is very hard to see this written in this editor...but if you write it by hand with horizontal bars for the fractions you will see it clearly. BTW the "horizontal bars" for the fractions are sometimes called "vincula, singular vinculum.

Answer 6

The question: What property states that a divided by 2/3 = a times 3/2?

That's a great question. We are really using the property of real numbers that states that 1*a = a. But we choose a 'sneaky' form for 1, namely, 3/2 divided by 3/2, which we know that we can do because another property says that b/b = 1, for all b (other than zero).

Answer 7

To divide by a fraction, you multiply by the reciprocal of the fraction.

2 / 3 = 2(1/3)