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3-107.

Simplify each of the following expressions without using a calculator. Draw diagrams or use words to show your thinking.

1.  $4 ( - 2 ) + 7$

Remember that terms are separated by addition symbols ($+$).

Can you draw or explain how you separate these terms?
You should simplify these terms before adding them together.

1.  $-8+-2\left(3\right)$

to draw a diagram like the tightropes used in previous lessons?

The product of this expression is $−14$.

1.  $4 + - 5 ( - 3 ) + ( - 7 )$

Reminder: Multiplying two negative numbers results in a positive number. Can you find the product and explain why this is so?

The expression simplifies to $12$. Don't forget to show your thinking!

1.  $( - 4 ) ( 2 ) + ( - 4 ) ( - 2 )$

Mara used this expression to explain part of her reasoning. Does this help you to solve the problem?

$( - 4 ) ( 2 )=-8 \qquad ( - 4 ) ( - 2 )=8\\ \enclose{circle}{-4}+\enclose{circle}{-4} \qquad -\enclose{circle}{-4}-\enclose{circle}{-4}$

Can you think of another way to show your thinking?