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How do you explain how the product of 16 times 34 is like the product of 6 times 34 plus 10 times 34

if you have 6 apples and 10 apples, you add them up to have 16 apples.

Same for anything else that is alike.

In this case, you are adding 34's.
6 34's plus 10 34's makes 16 34's. Or, more symbolically,

6(34)+10(34) = (6+10)(34) = 16(34)

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