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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, .
29 Use –6. The additive inverse of 6 is –6. If you add –6 to the expression, you have . Use the associative property to group the 6 and –6 together: . The sum of a number and its additive inverse is 0, so the expression becomes 0 – 3x. Because 0 is the additive identity, .
30 Use . The multiplicative inverse of –7 is . If you multiply the expression by , you have . Use the commutative property to rearrange the factors and the associative property to group the –7 and together: . The product of a number and its multiplicative inverse is 1, so the expression becomes 1x. Because 1 is the multiplicative identity, .
31 Use 4. The expression can be written as . The multiplicative inverse of is 4. If you multiply the expression by 4, you have
An added bonus here is that the constant also becomes an integer.
32 6.
33 6. By definition, the value of 0! is 1.
34 639,200.
35 147. The 9, which will be dropped with the 5 following it, is greater than 5. Round the 6 in the ones place to a 7.
36 146. The greatest integer smaller than 146.95 is 146.
If you’re ready to test your skills a bit more, take the following chapter quiz that incorporates all the chapter topics.
Whaddya Know? Chapter 3 Quiz
Quiz time! Complete each problem to test your knowledge on the various topics covered in this chapter. You can then find the solutions and explanations in the next section.
1
2 Which is larger: 5.932 rounded to the nearest integer or ?
3
4 Distribute:
