How do you compare fractions? For example, is 1/8 greater than 1/5?

You remember that when numbers represent the same amount they are equal. Let’s compare 3 and 3. We know that both numbers represent the same amount or value. Therefore 3 = 3. Now let’s compare 2 and 5. You know that 2 is less than 5. So we will use the less than symbol to make this statement true, 2 is less than 5. Notice that the pointed end of the symbol is facing or pointing to the 2. This is because 2 is the smaller number. Now let’s compare 10 and 6. 10 is greater than 6, so we will use the greater than symbol. 6 is the smaller of these two numbers so the pointed end of the symbol is pointing to the 6.

A common mistake is thinking that the fraction with the largest denominator is the largest fraction. Here I have the fractions 2/4 and 2/8. If I asked you tell me which fraction is bigger you may be tempted to say that 2/8 is bigger because the denominator 8, in 2/8 is bigger than the denominator 4 in 2/4. However if we were to look at fraction models for these two fractions we would be able to see that 2/8 is not the larger fraction. 2/4 actually represents more than 2/8. Therefore 2/4 is the larger fraction even though the number in the denominator is smaller.

Let’s compare ¼ to ½. Both of these fraction have the numerator 1 Let’s compare ¼ to ½. Both of these fraction have the numerator 1. We can see that the denominator in ¼ is greater than the denominator in ½. However we must consider that since the denominators are not the same, the parts of the whole are not the same. Let’s look at a fractional model of ¼. We have a rectangle divided into four equal parts. The numerator in this fraction tells us that we are thinking of 1 part, therefore one part is shaded. Now let’s look at a fractional model for ½. We have a rectangle that is the same size as our first rectangle. This time we will divide the rectangle into two equal parts because the denominator in ½ is 2. Notice that when we only have the rectangle divided into two parts the parts are bigger. The numerator 1 tells us that we are thinking of one part out of the total two parts. Using our fraction models we can see that ¼ is less than ½.

Let’s compare3/4 to 3/8. Both of these fraction have the numerator 3 Let’s compare3/4 to 3/8. Both of these fraction have the numerator 3. We can see that the denominator in 3/4 is less than the denominator in 3/8. However we must consider that since the denominators are not the same, the parts of the whole are not the same. Let’s look at a fractional model of 3/4. We have a circle divided into four equal parts. The numerator in this fraction tells us that we are thinking of 3 parts, therefore 3 parts are shaded. Now let’s look at a fractional model for 3/8. We have a circle that is the same size as our first circle. This circle is divided into eight equal parts because the denominator is 8. Notice that when we have the circle divided into eight parts the parts are smaller. The numerator 3 tells us that we are thinking of 3 parts out of the total 8 parts. Using our fraction models we can see that 3/4 is greater than 3/8.

In a problem it may look like this. Tracy ate 1/5 of her sandwich In a problem it may look like this. Tracy ate 1/5 of her sandwich. Jim had the same size sandwich, but he ate ½ of his sandwich. Who ate the greater part of their sandwich? Since Tracy ate 1/5 of her sandwich, I will divide her sandwich into five equal parts because the denominator is 5 and that means we have a total of 5 equal parts in the whole. The numerator one tells me that we are only thinking of one part out of the five equal parts. So I will shade 1 part. Now let’s look at Jim’s sandwich. The problem says Jim at ½ of his sandwich, so I will divide his sandwich in two equal parts because the denominator is 2. Notice that since his number of equal parts is less than Tracy’s, Jim’s parts are bigger. We are only thinking of one part of Jim’s sandwich because the numerator is 1. We can clearly see that ½ is greater than 1/5. So the answer is Jim ate the greater part of his sandwich. Remember when we are comparing fractions that have the same numerator, we have to keep in mind that the more parts an object is broken into the smaller the size of the parts.

Mark walked 2/3 of a mile and then rode his scooter 2/6 of a mile Mark walked 2/3 of a mile and then rode his scooter 2/6 of a mile. Which distance is farther? Try to figure this one out on your own. Press the pause button. If you have any trouble or need to see me work the problem press the play button again. Let’s show how far Mark walked. Since the denominator is 3 we will divide the rectangle into three equal parts. The numerator is 2 so we will shade 2 of the equal parts. Now let’s show how far Mark rode his scooter. Since the denominator is 6, we will divide the rectangle into 6 equal parts. Now that we have six parts we can see that the size of the parts are smaller because we have more equal parts. The numerator tells us to shade 2 of the equal parts. We can clearly see that the distance Mark walked 2/3 is greater than the distance he rode his scooter, 2/6.