Video: Comparing Decimals to the Absolute Value of Fractions

Complete 7.2 _ |−47/38|, using <, =, or >.

02:18

Video Transcript

Complete 7.2 blank the absolute value of negative 47 over 38, using less than, equal, or greater than.

The first thing to look at is actually this term which is negative 47 over 38. Well, at first glance, you think “well, this is gonna be obvious” because one of the numbers 7.2 is a positive and the other number negative 47 over 38 is negative. So therefore, the positive must be bigger. However, it isn’t just negative 47 over 38. We have these two vertical lines as well. And what these mean are the modulus or absolute value.

And the modulus or absolute value means that we’re only gonna be interested in the nonnegative value of the term inside the modulus signs. So what we’re really looking at is it’s actually how far would the value within the modulus sign be away from zero. So in this case, it’s gonna be positive 47 over 38.

So what I’ve done is I’ve actually rewritten our expression to reflect this. So it’s 7.2 blank 47 over 38. And that’s as I’ve said because we’re actually only interested in the nonnegative or positive value of the term that was inside the modulus sign. Okay, great, so now, all we need to do is see whether the right-hand term is equal to, greater than, or less than our 7.2.

Well, if we convert it into a mixed number, we’re gonna get one and nine thirty-eighths. And we get that because 38 goes into 47 once with nine left over. So therefore, we can see actually that 7.2 is gonna be greater than 47 over 38 because 7.2 is greater than one and nine over 38. So therefore, we can say that 7.2 is greater than the modulus or absolute value of negative 47 over 38.

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