Fraction divided by a Whole Number

Today we will be focusing on a fraction being divided by a whole number.  I will be using Fraction Tiles which can be purchased here, or you can print and laminate a set of fractions tiles for free here.

Let’s look at the problem 6/8 ÷ 2.  Have students represent 6/8 with their fraction tiles.

We could say, “How many times can 2 fit in to 6/8?”  Have students ponder that question and have a discussion about it.  Students may be puzzled because it can’t fit in at all.  Therefore, it makes sense that our answer is going to be a fraction.  Have students line up 16/8 to represent 2 wholes.  We could say we have 6/8 out of 16/8.  Therefore, 6/16 which simplifies to 3/8.  So, 6/8 divided by 2 = 3/8.

Another way to look at the same problem is with partitive division.  If we have 6/8 ÷ 2, we could say, “What is 6/8 divided into two groups?”  Students can easily split their pieces into to groups to see that there are 3/8 in each group.

Let’s look at another problem, 1/3 ÷ 2.  Have students represent one-third.  We could say, “How many times can 2 fit into 1/3?”  Have students line up 6/3 to represent 2.  We have 1/3 out of 6/3.  Therefore, we have 1/6.  1/3 ÷ 2 = 1/6.

If you want to see the same problem using partitive division, have students represent 1/3.  We can’t break 1/3 into two pieces, but if we look at our fraction tiles, 2/6 = 1/3.  Therefore, 1/3 ÷ 2 = 1/6.

Let’s try one more, 3/5 ÷ 2.  “How many times can we fit 2 into 3/5.”  Have students line up 10/5 to represent 2.  We have 3/5 out of 10/5.  Therefore we have 3/10.  3/5 ÷ 2 = 3/10.

Using partitive division, have students represent 3/5.  We can’t break 3/5 into two pieces, but if we use our tenth pieces, we can see that 3/5 = 6/10 and 6/10 divided by 2 = 3/10.

Students may start to see that you can just multiply the whole number by the denominator.  That is a beautiful thing, because they are starting to see why multiplying by the reciprocal works!!  Don’t let them take short cuts yet!  We are building their fraction sense so when you finally teach the rule, they will have that deep understanding!!

~MN

 

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