Complete twelve forty-sevenths what twelve forty-sixths using the symbol for is less than, is equal to, or is greater than.
In this problem, we’re being asked to compare two fractions, twelve forty-sevenths and twelve forty-sixths. Is the first fraction less than the second? Are they both worth the same? Or is the value of the first fraction greater than the second one? We need to complete the comparison by putting the correct symbol in between the two fractions.
Let’s take a closer look at these fractions to try and identify which one is larger. What’s the same and what’s different? Well, the thing that’s the same about these fractions is the numerator. The top number of both fractions is 12. The numerator shows us the number of equal parts that we’re talking about. So if we’re talking about 12 equal parts for both fractions, we can’t identify which is larger. They’re both the same number of equal parts.
What’s different about both our fractions is the denominator. In the first fraction, the bottom number is 47. But in the second fraction, it’s 46. Now the denominator in a fraction tells us how many equal parts the whole has been split into. The more equal parts that we divide a shape into, the smaller those parts are. So in other words, the larger the denominator, the smaller the part.
Now we don’t need to draw a diagram here where we try to divide a circle into 47 equal parts or 46 equal parts. We simply need to apply what we’ve just learned about denominators. Let’s go over the rule one more time. The greater the denominator, the more parts that we’ve split the whole amount into, but also the smaller those parts are going to be.
Now if we look at our two fractions, the one with the largest denominator is the first one. 47 is larger than 46. So because the whole amount has been cut into more pieces, each piece will be smaller. And so we can say that twelve forty-sevenths is less than twelve forty-sixths. If we cut the whole amount into 46 equal pieces, they’ll be slightly larger. And so the correct symbol to write in between these fractions is the one that represents is less than.
We compared the two fractions by looking at the numerators and the denominators. The numerators were the same. So we could tell that this meant that we were talking about the same number of equal parts. But the denominators were different. So we could tell that the size of those parts were different for both fractions. We know that the larger the denominator, the smaller the part. And so twelve forty-sevenths is less than twelve forty-sixths. The correct symbol to use in between the fractions is the one that represents is less than.