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- 282
- àï2.7èExponents and the Order of Operations.
- äèPlease insert the correct symbol between the two numbers
- êê to make a true sentence.
- âSêêêï2ë1êë13ë19
- #ê 1)ï3ï?ï27ê2)ï─ï?ï─ê 3)ï──ï?ï──
- êêêêè3ë2êë14ë21
- êë3ï<ï27
- êêêêè2ë1êë13ë19
- #êêêêè─ï>ï─êë──ï>ï──
- êêêêè3ë2êë14ë21
- éS The number that occurs further to the left on the number line
- is the smaller of the two numbers.ïThe symbol, "<" , is used to
- represent "smaller than".ïThus, since 3 occurs to the left of 27 on
- the number line, the correct symbol is "<".
- êêêêè 3ï<ï27
-
- Since 1/2 occurs to the left of 2/3 on the number line, it is the
- smaller of the two numbers. The symbol, ">" ,is used to represent
- "larger than".ïThus, the number 2/3 is larger than 1/2.
- êêêêè 2ë1
- #êêêêè ─ï>ï─
- êêêêè 3ë2
-
- This can be seen more clearly by expressing the numbers as equivalent
- fractions with common denominators.ïSince 2/3 is equal to 4/6 and
- 1/2 is equal to 3/6, it is seen that 2/3 is greater than 1/2.
- êêë 2ê4ë3ê1
- #êêë ─è=è─ï>ï─è=è─
- êêë 3ê6ë6ê2
- 1êêêêêè13ê19
- #êëInsert the correct symbol betweenï──ïandï──.
- êêêêêêë20ê20
-
- ë 13ë19êè 13ë19êë19ë13
- #ïA)ï──ï>ï──êB)ï──ï<ï──ê C)ï──ï<ï──êD)ïå
- ë 20ë20êè 20ë20êë20ë20
- ü
-
- êêêêè13ë19
- #êêêêè──ï<ï──
- êêêêè20ë20
- Ç B
- 2êêêêêè3ê 6
- #êëInsert the correct symbol betweenï─ïandï──.
- êêêêêêë8ê15
-
- ê6ë3êè 3ë 6êë3ë 6
- #ïA)ï──ï>ï─êB)ï─ï>ï──ê C)ï─ï<ï──êD)ïå
- ë 15ë8êè 8ë15êë8ë15
- ü
- êè The least common denominator of 8 and 15 is 120.
-
- ë 3ë 6êï45ë 48êï45ë 48ê 3ë 6
- #ë ─ï?ï── ,ë ───ï?ï─── ,ë ───ï<ï───è soï─ï<ï──
- ë 8ë15ê 120ë120ê 120ë120ê 8ë15
- Ç C
- 3êêêêêè3ê5
- #êëInsert the correct symbol betweenï─ïandï─.
- êêêêêêë4ê8
-
- ê3ë5êè 3ë5êë 5ë3
- #ïA)è─ï>ï─êB)ï─ï<ï─êïC)ï─ï>ï─ê D)ïå
- ê4ë8êè 4ë8êë 8ë4
- ü
- êëThe least common denominator of 4 and 8 is 8.
-
- ë 3ë5êè 6ë5êë6ë5êï3ë5
- #ë ─ï?ï─ ,êï─ï?ï─ ,êè─ï>ï─ësoï─ï>ï─
- ë 4ë8êè 8ë8êë8ë8êï4ë8
- Ç A
- 4êêêêêè2ê3
- #êëInsert the correct symbol betweenï─ïandï─.
- êêêêêêë5ê8
-
- ê2ë3êè 3ë2êë 2ë3
- #ïA)è─ï>ï─êB)ï─ï>ï─êïC)ï─ï<ï─ê D)ïå
- ê5ë8êè 8ë5êë 5ë8
- ü
- êëThe least common denominator of 5 and 8 is 40.
-
- ë 2ë3êè16ë15êè16ë15ê 2ë3
- #ë ─ï?ï─ ,ê ──ï?ï──,êï──ï>ï──è soï─ï>ï─
- ë 5ë8êè40ë40êè40ë40ê 5ë8
- Ç A
- 5êêêêêè5ê 7
- #êëInsert the correct symbol between ──ïandï──.
- êêêêêêè 24ê30
-
- ê7ë 5êè 5ë 7êë 5ë 7
- #ïA)ï──ï<ï──ë B)ï──ï>ï──ê C)ï──ï<ï──êD)ïå
- ë 30ë24êè24ë30êë24ë30
- ü
- êëThe least common denominator of 24 and 30 is 120
-
- ë 5ë 7êï25ë 28êï25ë 28ê5ë 7
- #ë──ï?ï──,ê───ï?ï───,ê───ï<ï───èso ──ï<ï──
- ë24ë30ê 120ë120ê 120ë120ë 24ë30
- Ç C
- äè Please simplify the following fractions with exponents.
- â
-
- êêêêêêêè 1∙1∙1∙3∙3ë 9
- # (1/2)Ä∙(3/5)ìï=ï(1/2)∙(1/2)∙(1/2)∙(3/5)∙(3/5)ï=ï─────────ï=ï───
- êêêêêêêè 2∙2∙2∙5∙5ë200
- #éS In order to simplify the expression,ï(1/2)Ä∙(3/5)ì, it is
- necessary to write 1/2 as a factor three times and 3/5 as a factor
- two times.êê 1è1è1è3è3
- #êêêè ─ ∙ ─ ∙ ─ ∙ ─ ∙ ─
- êêêè 2è2è2è5è5
-
- Then, you can write this product as one fraction.
- êêêêè1∙1∙1∙3∙3
- #êêêêè─────────
- êêêêè2∙2∙2∙5∙5
-
- Finally, you can reduce and multiply the remaining factors.
- êêêê3∙3êè 9
- #êêêè ─────────è=è───
- êêêè 2∙2∙2∙5∙5ê200
- 6
- #êêêë Simplifyè (1/2)Ä
-
- êè1êêè1êêè1
- #ë A)ï─êë B)ï─êë C)ï─êë D)ïå
- êè4êêè8êêè6
- ü
-
- êêêë 1è1è1êï1∙1∙1êï1
- #êë(1/2)Äè =è ─ ∙ ─ ∙ ─è =è ─────è =è ─
- êêêë 2è2è2êï2∙2∙2êï8
- Ç B
- 7
- #êêêë Simplifyè (3/4)ì
-
- êè 9êêï6êêè9
- #ë A)ï──êëB)ï─êë C)ï─êë D)ïå
- êè16êêï8êêè4
- ü
-
- êêêë 3è3êï3∙3êè9
- #êë(3/4)ìè =è ─ ∙ ─è =è ───è =è ──
- êêêë 4è4êï4∙4êï16
- Ç A
- 8
- #êêêèSimplifyè (2/5)(1/3)ì
-
- êè 4êêè8êêè2
- #ë A)ï──êëB)ï──êëC)ï──êëD)ïå
- êè15êêï15êêï45
- ü
-
- êêêë 2è1è1ê 2∙1∙1êè2
- #ê(2/5)(1/3)ìè =è ─ ∙ ─ ∙ ─è=è ─────è =è ──
- êêêë 5è3è3ê 5∙3∙3êï45
- Ç C
- 9
- #êêê Simplifyè (5/9)ì(18/25)ì
-
- êè24êêêêê4
- #ë A)ï──êëB)ï4êë C)ï──êëD)ïå
- êè81êêêêë 25
- ü
-
- êêêêï5è5è18è18ê 2∙2êè4
- #ê(5/9)ì(18/25)ìè =è ─ ∙ ─ ∙ ── ∙ ──è=è ───è =è ──
- êêêêï9è9è25è25ê 5∙5êï25
- Ç C
- 10
- #êêë Simplifyè (2/7)ì(7/8)ì(8/9)
-
- êè7êêè 1êêï56
- #ë A)ï─êë B)ï──êëC)ï──êëD)ïå
- êè9êêè18êêï89
- ü
-
- êêêê2è2è7è7è8êï1êè 1
- #ï(2/7)ì(7/8)ì(8/9)è =è ─ ∙ ─ ∙ ─ ∙ ─ ∙ ─è=è ───è =è ──
- êêêê7è7è8è8è9ê 2∙9êï18
- Ç B
- äè Please simplify the following expressions using the
- êêïcorrect Order of Operations.
- #âêêê 27ï÷ï(2ìï+ï5)
-
- êêêêï27ï÷ï(4ï+ï5)
-
- êêêêë27ï÷ï9
-
- êêêêêï3
- éSè Operations should be done in the following order:
- êè 1)ïFirst, you should work inside any parençs.
- êè 2)ïEvaluate any exponents.
- êè 3)ïPerform all multiplication and division first come first
- êê serve in order from left to right.
- êè 4)ïFinally, perform all addition and subtraction first come
- êê first serve in order from left to right.
-
- #To simplify the expression, 27ï÷ï(2ìï+ï5), you would first work
- inside the parençs and evaluate the exponent.
- êêêê 27ï÷ï(4ï+ï5)
-
- The next operation in the parençs is the addition.
- êêêêè 27ï÷ï9
-
- Since the operations inside the parençs have been completed, we can
- perform the division.êï27ï÷ï9è=è3
-
- #Thus, 27ï÷ï(2ìï+ï5)è=è3.ïThe same Order of Operations is used
- when the numbers are fractions.
- 11
- êêë Simplifyë10 - 18 ÷ 3 + 4
-
-
- ë A)ï4êë B)ï8êêC)ï6êë D)ïå
- üêêê 10 - 18 ÷ 3 + 4
-
- êêêêè10 - 6 + 4
-
- êêêêë 4 + 4
-
- êêêêê 8
- Ç B
- 12
- #êêè Simplifyë(2Ä + 7) ÷ 5 + 4
-
- êêêêêêë13
- #ë A)ï7êë B)ï6êêC)ï──êëD)ïå
- êêêêêêë 5
- #üêêê(2Ä + 7) ÷ 5 + 4
-
- êêêê(8 + 7) ÷ 5 + 4
-
- êêêêï15 ÷ 5 + 4
- êêêêë3 + 4
- êêêêê7
- Ç A
- 13êêê3ë 3ë2
- #êêè Simplifyë─ï+ï──ï-ï─
- êêêêè5ë10ë3
- êè 7êêè4êêè 3
- #ë A)ï──êëB)ï──êë C)ï──êëD)ïå
- êè30êêï15êêè10
- üë3è 3è2ê6 3è3ï3è10 2ê18è 9è20
- #êè ─ + ── - ─è=è─∙─ + ─∙── - ──∙─è=è── + ── - ──è=
- êè 5è10è3ê6 5è3 10è10 3ê30è30è30
-
- êêï18 + 9 - 20ê27 - 20ê 7
- #êêï───────────è=è───────è=è──
- êêê30êê30êï30
- Ç A
- 14êêê3ë 6ë4
- #êêè Simplifyë─ï÷ï──ï+ï─
- êêêêè5ë11ë5
-
- êè13êêï17êêè19
- #ë A)ï──êëB)ï──êë C)ï──êëD)ïå
- êè10êêï10êêè10
- ü
-
- ë 3è 6è4ê3è11è4ê11è4ê11 + 8ê19
- #ë ─ ÷ ── + ─è=è─ ∙ ── + ─è=è── + ─è=è──────è=è──
- ë 5è11è5ê5è 6è5ê10è5êï10êï10
- Ç C
- 15
- #êêèSimplifyè (2/3)ì∙(1/5 + 3/10) ÷ 6/15
-
- êè3êêè5êêè 2
- #ë A)ï─êë B)ï─êë C)ï──êëD)ïå
- êè7êêè9êêè15
- #üêêï(2/3)ì∙(1/5 + 3/10) ÷ 6/15
-
- #êêê (2/3)ì∙(2/10 + 3/10) ÷ 6/15
-
- #êêêè (2/3)ì∙(5/10) ÷ 6/15
-
- êêêè(4/9) ∙ (5/10) ÷ 6/15
-
- êêêë4/9 ∙ 5/10 ∙ 15/6
- êêêêè 4∙5∙15êï5
- #êêêêè ──────è =è ─
- êêêêè 9∙10∙6êï9
- Ç B
-
-