Comparing Fractions

Mentor: Any number can be made into a fraction, and many fractions can be reduced.

Student: How can a whole number, such as 4 or 5 or 20, be made into a fraction?

Mentor: By putting the number 1 as the denominator of any number, that number can be expressed as a fraction, but still keep its value. 5/1 = 5, and 20/1 = 20

Student: Could I also write a fraction that equals 5 if I expressed it as 20/4? Because 20/4 =5.

Mentor: Yes, that also works, but notice that the fraction 20/4 can be reduced by dividing the numerator and denominator by 4. Therefore, the simplest way to express the value 5 as a fraction is by writing 5/1.

Mentor: This is a helpful thing to remember when working with fractions and whole numbers, such as adding, subtracting, multiplying or dividing them. Sometimes it helps to write the whole numbers as fractions when solving the problem.

Student: The fractions 20/4 and 5/1 are equal to each other?

Mentor: Yes. Which fraction would be greater, 3/4 or 4/5?

Student: I am not sure. Can I try drawing a picture to help me see the solution?

Mentor: Good idea. First we could start by drawing two bars of equal length, but breaking one bar into four equal sections, and the other into five equal sections.

Student: I see, then we color in as many pieces as are in the numerator: 3 for the bar with four segments and 4 for the one with five. They now show what 3/4 and 4/5 looks like.

Student: OK, now I can easily see that the fraction 4/5 is greater than 3/4.

Mentor: Good. So which fraction is less, 1/6 or 1/8?

Student: Well, let me start by drawing two bars of equal length, dividing them into as many pieces as are in the denominator, and .....

Can you finish this student's work? Which fraction is less?