What Does It Mean to Multiply by a Fraction?
When you multiply a number by a fraction, you are finding part of that number. For example, if you multiply 6 by 1/2, you are finding 1/2 of 6.
It gets a little trickier if both numbers are fractions, but the idea is still the same. Anytime you're multiplying a number by a fraction, you're finding part of that number. If you're multiplying 1/4 by 1/2, you're finding 1/2 of 1/4.
To figure out what 1/2 of 1/4 is, let's look at a picture of the fraction 1/4. The fraction 1/4 means the whole item has been divided equally into 4 pieces and you have 1 of those pieces:
To find 1/2 of the fraction shaded above, we need to split it down the middle. We can do this by drawing a horizontal line halfway across the box. 1/2 of 1/4 is half of the shaded part.
So what is 1/2 of 1/4? By splitting the box down the middle, we now have 8 equal boxes and want only one of them. This means the answer is one out of 8 pieces: 1/8.
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