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Big Ideas Math: Modeling Real Life, Grade 7

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Big Ideas Math: Modeling Real Life, Grade 7 View details

Cumulative Practice

Exercise 3 Page 121

Instead of subtracting a negative number, you can add.

- 24

We want to find the value of the given expression. - 38-(- 14) We can recall to subtract a number we can add its opposite. Let's rewrite the difference as a sum! - 38-(- 14) ⇔ - 38+14 Finally, we can calculate the value of our expression. - 38+14 = - 24 We can see that subtracting a negative number is the same as adding its positive counterpart. Below we will demonstrate by finding - 38 and moving 14 units to the right on the number line.

The resulting position, after moving to the right on the number line, is the sum. - 38+14=- 24

Extra

Properties of Real Numbers

When we are performing mathematical operations using real numbers, we always need to make sure that we are following the Properties of Real Numbers.

Distributive Property
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication

These properties tell us the legal moves we can make when adding or multiplying numbers.

But why aren't there properties for subtraction or division?

Some mathematicians refuse to acknowledge that subtraction and division are even operations! Subtraction is the same thing as adding a negative and division is the same thing as multiplying by a fraction. a-b=a+(- b) and a/b=a* 1/b Therefore, we can use the Properties of Real Numbers for subtraction and division, but we need to change our way of thinking.

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