Answer:
0.64
Step-by-step explanation:
Let's think about a few simple examples. Once you understand them, you
will be able to put them together to make harder problems.
Ex: What is 2 divided by 1/5? Here are 2 blocks:
+---------+---------+
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
+---------+---------+
Here is 1/5 of a block (the shaded part):
+---------+
|XXXXXXXXX|
+.........+
| |
+.........+
| |
+.........+
| |
+.........+
| |
+---------+
To divide 2 by 1/5, we divide 2 blocks into pieces the size of the 1/5
block.
+---------+---------+
| | |
+.........+.........+
| | |
+.........+.........+
| | |
+.........+.........+
| | |
+.........+.........+
| | |
+---------+---------+
There are 10 pieces this size in the 2 blocks. In other words,
2 divided by 1/5 = 10
That's the same as
2 x 5 = 10
Do you see why? To make 1/5 size blocks, we had to make each whole
block into 5 pieces. In other words, we multiplied the number of
pieces by 5.
Next problem:
2 divided by 2/5 = ?
Here is 2/5 of a block (the shaded part):
+---------+
|XXXXXXXXX|
+.........+
|XXXXXXXXX|
+.........+
| |
+.........+
| |
+.........+
| |
+---------+
Let's divide the 2 blocks into pieces this size.
+---------+---------+
| | |
+ + +
| | |
+.........+.........+
| | |
+ + +
| | |
+.........+.........+
| |
+---------+---------+
The bottom block is a different shape, but it's the same size, because
it's made of 2 1/5-size pieces. Since the pieces we want are twice as
big, there are only 1/2 as many of them. The answer is
2 divided by 2/5 = 10/2 = 5
This is the same as
2 x 5/2 = 5
Do you see how the two equations are related? You take the fraction,
2/5, and "turn it upside down" (in math words, we say "invert the
fraction," or "take its reciprocal"). Then replace the division sign
by a multiplication sign.
Now we can tackle harder problems. The same method always works, even
if the answer isn't a whole number as in the simple examples. For
instance,
5 divided by 3/8 = ?
Ex: Invert the fraction 3/8; you get 8/3. Then multiply by this fraction:
5 x 8/3 = 40/3 = 13 1/3
We can even replace the whole number in the problem with a fraction,
like this:
5/7 divided by 3/8 = ?
5/7 x 8/3 = ?
5 8 40 19
--- x --- = ---- = 1 ----
7 3 21 21
If you are comfortable with multiplying fractions, then you will have
no trouble dividing fractions. Just remember: invert the fraction you
are dividing by (the divisor), and multiply instead of dividing. Hope this helps! :)
