Fractions Operations Using Rectangles

A few days ago, Mary had replied to Nat’s tweet.

God, I love Mary. She sent me a decadent chocolate bar from 2,800 miles away. She remembers my birthday when 2/3 of my children did not.

I am queen only in my own head, and no, I did not have a blog post on adding fractions. I thought surely there must be a wide assortment of videos on adding fractions using rectangles. But the very first two that I’d clicked on - this and this - really astonished me. They both used grid papers without using the grids. Like, what the heck.

Say we want to add 2/3 and 4/5, same two fractions that popped in my head when I replied to Mary.

Draw two same-size rectangles using the denominators as dimensions.

2021-05-17_14-00-00.png

Students will ask, “Why 3 by 5?” If they don’t, you ask why. And you answer them by asking them to shade in 2/3 for one rectangle and 4/5 for the other. Give them a few seconds to do this and they’ll understand why the 3 by 5 rectangles work pretty well here.

2021-05-17_14-24-36.png

We’re adding the fractions, so let’s combine them.

2021-05-17_14-19-16.png

Similarly with subtraction of fractions.

For multiplication, the word “of” is useful. Of course, the commutative property of multiplication applies too.

To take 2/3 of 4/5, we’d look along the height in this rectangle as we can see the thirds and just grab two of the sections.

2021-05-17_14-47-43.png

Likewise, taking 4/5 of 2/3 is to look along the width of 5 and grab 4 sections of it.

2021-05-17_14-55-06.png

I’ve written about division of fractions previously:

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