Question Video: Visualizing the Commutative Property of Addition and Multiplication Mathematics • 6th Grade

What equivalent expression to 𝑎 + 𝑏 − 𝑐 does the diagram show?

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Video Transcript

What equivalent expression to 𝑎 add 𝑏 subtract 𝑐 does the diagram show?

In order to answer this question, we are firstly gonna consider diagram one. If we label the shaded section 𝑥, we can see that the top rectangle, 𝑎 add 𝑏, is the same as the bottom rectangle, 𝑥 add 𝑐. We are then gonna balance the equation by subtracting 𝑐 from both sides of the equation. This leaves us with 𝑎 add 𝑏 subtract 𝑐 on the left-hand side and the letter 𝑥 on its own on the right-hand side. Therefore, the shaded region is 𝑎 add 𝑏 subtract 𝑐, as stated in the question.

Let us now consider the second diagram. Well, once again, we have labelled the shaded section 𝑥. Once again, we have an equation where the top rectangle, 𝑏 plus 𝑎, is equal to the bottom rectangle, 𝑥 plus 𝑐. We can then subtract 𝑐 from both sides of the equation to balance it, leaving us with 𝑏 add 𝑎 subtract 𝑐 on the left-hand side and 𝑥, once again, on the right-hand side. Therefore, the shaded section in this case can be written as 𝑏 add 𝑎 subtract 𝑐.

This gives us the overall answer to the question which is that 𝑏 add 𝑎 subtract 𝑐 is equivalent to 𝑎 add 𝑏 subtract 𝑐.

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