Middle School Math & Grammar

home *** CD-ROM | disk | FTP | other *** search

/ Middle School Math & Grammar / ProOneSoftware-MiddleSchoolMath&Grammar-Win31.iso / math / chapter8.1b < prev next >

Wrap

Text File | 1994-09-09 | 4.7 KB | 330 lines

328 àï8.1èAdding Rational Numbers. äèPlease add the following Rational Numbers. âSêè1)ê 3 + 4è=è7 êêè 2)ê -5 + (-6)è=è-11 êêè 3)ê 8 + (-5)è=è3 êêè 4)ê -7 + 5è=è-2 éSëThe Whole Numbers were introduced in Chapter 1.ïThis set was extended to the Positive Fractions in Chapter 2.ïThe next step is to extend this set to the set of Rational Numbers.ïThe Rational Numbers include all of the negative fractions, zero, and the positive fractions.êêèRational Numbers #êê - ╦ï- ╩ï- ╔è ╚è ╔è ╩è ╦è ╠ êï. . .è1è 1è 1è 1è 1è 1è 1è 1ï. . . #êê - ╦ï- ╩ï- ╔è ╚è ╔è ╩è ╦è ╠ êï. . .è2è 2è 2è 2è 2è 2è 2è 2ï. . . #êê - ╦ï- ╩ï- ╔è ╚è ╔è ╩è ╦è ╠ êï. . .è3è 3è 3è 3è 3è 3è 3è 3ï. . . êêê .êêêè. êêê .êêêè. (the pattern continues) We would like to look at the Addition Operation on this important set of numbers which is sometimes called the "signed numbers".ïThe Addition Operation is broken down into two cases.ïThe first case occurs when adding two numbers from the same side, i.e. when both numbers are positive or when both numbers are negative.ïThis case is covered in Rule 1. RULE 1ïTo add two numbers that are either both positive or both negative, think of them as both positive and add them together as we did positive numbers in Chapters 1 and 2.ïThen attach the original "sign" that they both had in common.èExamplesï3 + 4 = 7ë-5 + (-6) = -11 The second case involves adding two numbers when one number is positive and the other number is negative.ïThis case is covered by Rule 2. RULE 2ïTo add two numbers with different signs, think of them as both positive and subtract the smaller from the larger as we did positive numbers in Chapters 1 and 2.ïThen attach the original "sign" of the larger number.ê Examplesè 8 + (-5) = 3,è -7 + 5 = -2 ï1 êêêë Add,è4 + 16. êA)ï-12êè B)ï20êëC)ï12êè D)ïå ü êêêê4 + 16è=è20 ÇïB ï2 êêêë Add,è-5 + (-12). êA)ï-17êè B)ï17êëC)ï-7êè D)ïå ü êêêè -5 + (-12)è=è-17 ÇïA ï3 êêêë Add,è9 + (-3). êA)ï-6êëB)ï12êëC)ï6êëD)ïå ü êêêë 9 + (-3)è=è6 ÇïC ï4 êêêë Add,è6 + (-8). êA)ï-14êè B)ï-2êëC)ï14êè D)ïå ü êêêë 6 + (-8)è=è-2 ÇïB ï5 êêêë Add,è-12 + 8. êA)ï4êë B)ï20êëC)ï-4êè D)ïå ü êêêë -12 + 8è=è-4 ÇïC ï6 êêêë Add,è-7 + 9. êA)ï2êë B)ï-16êè C)ï-2êè D)ïå ü êêêë -7 + 9è=è2 ÇïA ï7 êêêë Add,è-6 + (-15). êA)ï-21êè B)ï-9êëC)ï9êëD)ïå ü êêêë -6 + (-15)è=è-21 ÇïA ï8 êêêë Add,è-14 + (-23). êA)ï-9êëB)ï-37êè C)ï9êëD)ïå ü êêêë -14 + (-23)è=è-37 ÇïB ï9 êêêë Add,è(.6) + (-1.4). êA)ï.8êëB)ï2.0êè C)ï-.8êèD)ïå ü êêêë (.6) + (-1.4)è=è-.8 ÇïC ï10 êêêë Add,è-4.5 + 2.7. êA)ï2.3êè B)ï-1.8êèC)ï-7.2êïD)ïå ü êêêë -4.5 + 2.7è=è-1.8 ÇïB ï11 êêêë Add,è14 + 0. êA)ï14êëB)ï15êëC)ï0êëD)ïå üè Zero is called the "additive identity".ïIt has the property that when it is added to any number, you get the original number. êêêê14 + 0è=è14 ÇïA ï12 êêêë Add,è-8 + 8. êA)ï-16êè B)ï0êë C)ï8êëD)ïå üè The two numbers "8" and "-8" are "additive inverses" of each other.ïAdditive inverses cancel each other out when added and you get zero. êêêê-8 + 8è=è0 ÇïB #ï13êêêï3è┌ï2 ┐ #êêêë Add,è─ + │- ─ │ #êêêêë 5è└ï5 ┘ êêêêè3êê 1 #êA)ï1êë B)ï- ─êè C)ï─êëD)ïå êêêêè5êê 5 ü #êêêê3è┌ï2 ┐ê 1 #êêêê─ + │- ─ │è=è ─ #êêêê5è└ï5 ┘ê 5 ÇïC #ï14êêêï3è┌ï5 ┐ #êêêë Add, - ─ + │- ─ │ #êêêêë 8è└ï8 ┘ êêêêè5êêè5 #êA)ï-1êëB)ï- ─êè C)ï- ─êèD)ïå êêêêè8êêè8 ü #êêêê3è┌ï5 ┐êï8 #êêêë- ─ + │- ─ │è=è- ─ = -1 #êêêê8è└ï8 ┘êï8 ÇïA #ï15êêêï4è┌è8 ┐ #êêêë Add,ï── + │- ── │ #êêêêë15è└ï15 ┘ êë 12êêè4êê16 #êA)ï- ──êèB)ï- ──êèC)ï──êè D)ïå êë 15êêï15êê15 ü #êêêê4è┌è8 ┐êè4 #êêêë ── + │- ── │è=è- ── #êêêë 15è└ï15 ┘êï15 ÇïB ï16êêêï2è11 #êêêë Add, - ─ + ──. êêêêë 3è15 êë 2êêï1êêè4 #êA)ï- ─êè B)ï──êëC)ï──êè D)ïå êë 3êê 15êêï15 ü êêêë 2è11êè10è11ë 1 #êêêè - ─ + ──è=è - ── + ──ï=ï── êêêë 3è15êè15è15ë15 ÇïB ï17êêêï3è1 #êêêë Add,è─ + ─ . êêêêë 4è3 êê1êê5êêè11 #êA)ï1 ──êèB)ï─êë C)ï──êè D)ïå êë 12êê4êêè12 ü êè 3è1ê 9è 4ê13êë 1 #êè ─ + ─è=è── + ──è=è──è orè 1 ── êè 4è3ê12è12ê12êë12 ÇïA #ï18êêêï3è┌è2 ┐ #êêêë Add, - ─ + │- ── │. #êêêêë 5è└ï15 ┘ êè 1êêë11 #êA)ï─êë B)ï- ──êèC)ï- 3êèD)ïå êè 5êêë15 ü #êè 3è┌è2 ┐êè9è┌è2 ┐êï11 #êï- ─ + │- ── │è=è- ── + │- ── │è=è- ── #êè 5è└ï15 ┘êï15è└ï15 ┘êï15 ÇïB ï19 êêêë Add,è-3 + 5 + (-8). êA)ï12êëB)ï-16êè C)ï- 6êèD)ïå ü êêêê -3 + 5 + (-8) êêêêè 2 + (-8) êêêêë -6 ÇïC ï20êêêë1ê2 #êêêë Add,è-3 ─ï+ï2 ─. êêêêêï8ê3 êë 11êêè5êêï7 #êA)ï- ──êèB)ï-2 ─êèC)ï- ─êèD)ïå êë 24êêè8êêï8 ü êè 1ê2êï25è 8êï75ë64êï11 #ê -3 ─ï+ï2 ─è=è- ──ï+ ─è=è- ──ï+ï──è=è- ── êè 8ê3êè8è 3êï24ë24êï24 ÇïA