Mary Jane Sterling - Algebra I All-in-One For Dummies

13 47.Regroup so that the first two numbers are together. Their sum is 0!

14 5.Regroup so that the second two numbers are together.

15 70.Regroup so that the first two numbers are together. The fraction reduces to make the multiplication easier.

16 110.Regroup so that the second two numbers are together. The multiplication is simple!

17 5.Switch the order of the second and third numbers.

18 470.Switch the order of the second and third numbers.

19 78.Switch the order of the second and third numbers.

20 8.Switch the order of the second and third numbers.

21 560.There’s a lot of switching that goes on here to make the problem easier. Your goal is to be able to multiply fractions times numbers that will eliminate their denominators. In this particular problem, I’m bringing the up next to the 16 and the up next to the 18.

Then I group, reduce, multiply, and find the product of the three “nice” numbers!

22 –11 and .The sum of 11 and –11 is 0; the product of 11 and is 1.

23 and –3.The sum of and is 0; the product of and –3 is 1.

24 and .The sum of and is 0; the product of and is 1.

25 1 and –1.The sum of –1 and 1 is 0; the product of –1 and –1 is 1. The number is its own multiplicative inverse.

26 and or .The sum of and 4.5 is 0. The product of 4.5 and is 1. You usually don’t want to write decimals in fractions, so you can change by writing it with a fractional denominator and simplifying:

You’ll see more on working with fractions in Chapter 4.

27 and .The additive inverse is just the positive version of the same number. To write the multiplicative inverse, you change the mixed number to an improper fraction and just flip it:

There’s a full coverage of fractions in Chapter 4.

28 Use 8.The additive inverse of –8 is 8. If you add 8 to the expression, you have . Use the associative property to group the –8 and 8 together: . The sum of a number and its additive inverse is 0, so the expression becomes . Because 0 is the additive identity, .