Video Transcript
What is 0.27 as a fraction of 0.6? Circle your answer.
Starting with 0.27, “as a fraction of” indicates to us that 0.27 is the numerator out of 0.6, which is the denominator. The first thing we want to do is get rid of the decimals in this fraction. We can do that by multiplying the numerator and the denominator by 100.
0.27 times 100 equals 27, which is moving the digits to the left two times. From there, we multiply 0.6 times 100, which equals 60. Again, we’ve moved the digits to the left two times. But 27 out of 60 is not one of our four answer choices. That means we need to consider if there is anything that numerator and the denominator are both divisible by in order to simplify this fraction.
Both 27 and 60 are divisible by three. 27 divided by three equals nine, and 60 divided by three equals 20. The simplified form of this fraction is nine twentieths.
Let’s consider one other way to solve this problem. If we take 0.27, twenty-seven hundredths, we can write it as 27 over 100, which is the numerator over 0.6, which we can write as six-tenths. This is the same thing as saying 27 out of 100 divided by six out of 10.
To divide by a fraction, we multiply by its reciprocal, twenty-seven hundredths times ten sixths. We can simplify 10 out of 100 to one-tenth. 27 and six are both divisible by three, which reduces them to nine and two. From there, we multiply the numerators together and the denominators together. Nine times one equals nine. 10 times two equals 20. Both methods show the simplified form to be nine twentieths.
