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Extra resources for California Algebra I
0: Students identify and use the arithmetic pr oper ties of subsets of proper operties integers and rational, umber s, number umbers irrational, and real n including closure properties for the four basic arithmetic operations where applicable. What it means for you: Comm uta ti ve La ws — the Or der Doesn tter Commuta utati tiv Laws Order Doesn’’ t Ma Matter It doesn’t matter which order you add two numbers in — the result is the same. This is called the commutative property (or law) of addition.
Finding the difference between two numbers means you subtract them. For example, the difference between a and b would be a – b or b – a. Since subtraction is a type of addition, and R is closed under addition, R must be closed under subtraction. Key words: • • • • difference quotient reciprocal commutative Subtraction is not commutative (meaning that a – b π b – a). 7 for more on what “commutative” means. 1 Show that a – b π b – a for any a π b. Solution Write both subtractions as additions: a – b = a + (–b) b – a = b + (–a) = (–a) + b The two subtractions “a – b” and “b – a” contain different addends when they’re written as additions — so a – b π b – a.
1. 2 4 ⋅ 3 5 2. 3 1 ⋅ 5 2 3. 6 3 ⋅ 7 7 4. 3 1 ⋅ 10 8 5. 7 3 ⋅ 8 4 6. 5 5 ⋅ 8 8 7. 8 3 ⋅ 11 5 8. 9 3 ⋅ 10 5 9. 2 5 ⋅ 7 11 10. 3 15 ⋅ 8 2 11. 5 4 ⋅ 9 7 12. 3 — Exponents, Roots, and Fractions 49 Al ways Gi ve Solutions in the Simplest F or m Alw Giv For orm You should always give your answer in its simplest form — so with more complicated examples, factor the numerators and denominators and cancel common factors. It’ll save time if you do this before you compute the products. Example Check it out: If there are two fractions multiplied together, you can cancel a factor from anywhere in the numerator with a matching factor in the denominator.
California Algebra I by CGP Education