Core Connections: Course 1
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Chapter Closure

Exercise 140 Page 159

When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with different denominators. - 2/7 + 3/5Since 35 is a common multiple of 7 and 5, we can multiply both the numerator and denominator of - 27 by 5 and both the numerator and denominator of 35 by 7 to create a common denominator.

- 2/7 + 3/5
- 2* 5/7* 5+3/5
- 2* 5/7 * 5+ 3* 7/5* 7
- 10/35+21/35

Now that we have a common denominator, we can proceed to simplifying the expression.

- 10/35+21/35
- 10/35+21/35
- 10 +21/35
11/35

Let's perform the addition.

1.4+(-2.3)
1.4-2.3
- 0.9

We can see that adding a negative number is the same as subtracting its positive counterpart. Below we will demonstrate by finding - 1.4 and moving 2.3 units to the left on the number line.

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.

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.

Let's perform the addition.

- 5.2 +(- 8.39)
- 5.2 -8.39
- 13.59

Let's perform this addition using a calculator.

We want to compute the given sum. 3/10 + 4.29 We will start by rewriting the fraction as a decimal. To do os, we can divide the numerator by the denominator.

3/10 + 4.29
(3÷ 10) + 4.29
0.3 + 4.29

Now, we let's perform the addition. 0.3+4.29 = 4.59 We can check if this is true by using a calculator.