Middle School Math & Grammar/ProOneSoftware-MiddleSchoolMath&Grammar-Win31.iso/math/chapter2.5b

Text File | 1993-09-25 | 6.5 KB | 336 lines

 334
àï2.5èMultiplying Fractions.
äèPlease Multiply the following Fractions.
â

#è 4ë5ê 4∙5ê 2∙2∙5êï2∙╖∙║êï2ê 2
#è──ï∙ï─è=è────è=è───────è=è───────è=è───è=è─
#è15ë6ê15∙6ê3∙5∙2∙3ê3∙║∙╖∙3ê3∙3ê9
éS To multiply the two fractions,ï4/15ïandï5/6, you should
first multiply the two numerators and the two denominators.
êêêê4ë5ê 4∙5
#êêêë ──ï∙ï─è=è────
êêêë 15ë6ê15∙6

Next, you should express each number in prime factored form.
êêêë 4∙5ê 2∙2∙5
#êêêë────è=è───────
êêêë15∙6ê3∙5∙2∙3
Then, cancel out any like factors that occur on both the top and bottom.
#êêêï2∙2∙5êï2∙╖∙║êï2
#êêê ───────è=è───────è=è───
#êêê 3∙5∙2∙3ê3∙║∙╖∙3ê3∙3

Finally, you should multiply any remaining factors.
êêêêè2ê 2
#êêêêï───è=è─
êêêêï3∙3ê9

Thus the product ofï4/15ïandï5/6ïis the fractionï2/9.ïYou should
always check the final answer to make sure the it is completely reduced.
Note that multiplication can be indicated by the symbols "∙", "x", or
by parençs.
 1êêêë4ë 3
#êêêMultiplyë──ï∙ï──
êêêêë 15ë12

êë1êêè2êêè3
#êA)ï──êëB)ï──êëC)ï──êëD)ïå
êè 15êêï15êêï28
ü

#êè4ë 3ê 4∙3êè╖∙╖∙╕êè1êï1
#êï──ï∙ï──è=è─────è=è─────────è=è───è=è──
#êï15ë12ê15∙12ê╕∙5∙╖∙╖∙3ê3∙5ê15
Ç A
 2êêêë3ë7
#êêêMultiplyë ─ï∙ï─
êêêêê7ë6

êè 2êêè5êêè1
#êA)ï─êë B)ï─êë C)ï─êë D)ïå
êè 7êêè6êêè2
ü

#êêè3ë7ê3∙7ê ╕∙╝ê 1
#êêè─ï∙ï─è=è───è=è─────è=è─
#êêè7ë6ê7∙6ê╝∙2∙╕ê2
Ç C
 3êêêë1ë5
#êêêMultiplyë ─ï∙ï─
êêêêê5ë8

êë5êêï1êêè1
#êA)ï──êëB)ï─êë C)ï─êë D)ïå
êè 40êêï8êêè2
ü

#êè1ë5ê1∙5êï1∙║êè 1êï1
#êè─ï∙ï─è=è───è=è───────è=è─────è=è─
#êè5ë8ê5∙8ê║∙2∙2∙2ê2∙2∙2ê8
Ç B
 4êêêë5ë15
#êêêMultiplyë ─ïxï──
êêêêê9ë25

êè 2êêè1êêè2
#êA)ï─êë B)ï─êë C)ï─êë D)ïå
êè 5êêè3êêè3
ü

#êêè5ë15ê5∙15ê ║∙╕∙║ê 1
#êêè─ïxï──è=è────è=è───────è=è─
#êêè9ë25ê9∙25ê╕∙3∙║∙║ê3
Ç B
 5êêêè 2ë 5
#êêë Multiplyë──ï∙ï──
êêêêë15ë12

êë1êêï3êêè3
#êA)ï──êëB)ï─êë C)ï─êë D)ïå
êè 18êêï5êêè4
ü

#êè2ë 5ê 2∙5êè ╖∙║êë1êè1
#êï──ï∙ï──è=è─────è=è─────────è=è─────è=è──
#êï15ë12ê15∙12ê3∙║∙╖∙2∙3ê3∙2∙3ê18
Ç A
 6êêêè 7ë 6
#êêë Multiplyë ─ï∙ï──
êêêêë 2ë14

êè 5êêè 3êêï3ë 1
#êA)ï─êë B)ï──êëC)ï─ or 1 ─ë D)ïå
êè 7êêè14êêï2ë 2
ü

#êêè7ë 6ê╝∙╖∙3ê3ê 1
#êêè─ï∙ï──è=è─────è=è─ïorï1 ─
#êêè2ë14ê╖∙2∙╝ê2ê 2
Ç C
 7êêêë4ë1
#êêêMultiplyë ─ï∙ï─
êêêêê7ë5

êè 3êêè2êêè 4
#êA)ï─êë B)ï─êë C)ï──êëD)ïå
êè 7êêè5êêè35
ü

êêï4ë1ê4∙1ê2∙2∙1ê 4
#êêï─ï∙ï─è=è───è=è─────è=è──
êêï7ë5ê7∙5ê 7∙5ê 35
Ç C
 8êêêè 14ë27
#êêêMultiplyë──ï∙ï──
êêêêê9ë 2

êêêê 9ë 4
#êA)ï21êëB)ï─ or 1 ─ë C)ï3êë D)ïå
êêêê 5ë 5
ü

#êè14ë27ê14∙27ê╖∙7∙╕∙╕∙3ê21
#êè──ï∙ï──è=è─────è=è─────────è=è──è=è21
#êè 9ë 2ê 9∙2êè╕∙╕∙2êè1
Ç A
 9êêêë3ë12
#êêêMultiplyë──ï∙ï──
êêêêë 16ë17

êë3êêè9êêè1
#êA)ï──êëB)ï──êëC)ï──êëD)ïå
êè 17êêï68êêï34
ü

#ê 3ë12ê 3∙12êï3∙╖∙╖∙3êè3∙3êï9
#ê──ï∙ï──è=è─────è=è──────────è=è──────è=è──
#ê16ë17ê16∙17ê╖∙╖∙2∙2∙17ê2∙2∙17ê68
Ç B
 10êêêè18ë22
#êêêMultiplyë──ï∙ï──
êêêêë 44ë 6

êè 4ë 1êè3ë 1êè5ë 2
#êA)ï─ or 1 ─ë B)ï─ or 1 ─ë C)ï─ or 1 ─ë D)ïå
êè 3ë 3êè2ë 2êè3ë 3
ü

#êè18ë22ê18∙22ê╖∙╕∙3∙╖∙╢╢ê3ê1
#êè──ï∙ï──è=è─────è=è──────────è=è─ïor 1 ─
#êè44ë 6ê44∙6ê ╖∙╖∙╢╢∙2∙╕ê2ê2
Ç B
äèPlease Multiply the following Mixed Numbers.
â

#è1ë3ê7è15ê7∙15ê7∙╕∙5ê7∙5ê35ë 3
# 2 ─ ∙ 3 ─è=è─ ∙ ──è=è────è=è─────è=è───è=è── or 8 ─
#è3ë4ê3è 4ê 3∙4ê╕∙2∙2ê2∙2ê 4ë 4
éS To multiply the two Mixed Numbers,ï2 1/3ïandï3 3/4, you
should first express each mixed number as an improper fraction.
êêêè1ê3ê7ë15
#êêê 2 ─ï∙ï3 ─è=è─ï∙ï──
êêêè3ê4ê3ë 4

At this point you can multiply the tops and the bottoms and reduce just
as we did in the above problems.
#êï7è15ê7∙15ê7∙╕∙5ê7∙5ê35ê 3
#êï─ ∙ ──è=è────è=è─────è=è───è=è──ïorï8 ─
#êï3è 4ê 3∙4ê╕∙2∙2ê2∙2ê 4ê 4

Therefore, the product ofï2 1/3ïandï3 3/4ïisï35/4ïorï8 3/4.
 11êêêè 1ê1
#êêë Multiplyë3 ─ï∙ï2 ─
êêêêê7ê8

êë 19êêï1êêè5
#êA)ï6 ──êèB)ï7 ─êè C)ï6 ─êè D)ïå
êë 28êêï7êêè7
ü

#è1ë1ê22ë17ê22∙17ê╖∙11∙17ê187ë 19
# 3 ─ ∙ 2 ─è=è──ï∙ï──è=è─────è=è───────è=è─── or 6 ──
#è7ë8ê 7ë 8ê 7∙8ê 7∙╖∙2∙2ê 28ë 28
Ç A
 12êêêè 3ê3
#êêë Multiplyë1 ─ï∙ï2 ─
êêêêê4ê5

êë 1êêè11êêï3
#êA)ï4 ─êè B)ï4 ──êèC)ï5 ─êè D)ïå
êë 4êêè20êêï5
ü

ï3ë3ê7ë13ê7∙13ê 7∙13ê91ë 11
#1 ─ ∙ 2 ─è=è─ï∙ï──è=è────è=è─────è=è── or 4 ──
ï4ë5ê4ë 5ê 4∙5ê2∙2∙5ê20ë 20
Ç B
 13êêêè 3ê1
#êêë Multiplyë3 ─ï∙ï1 ─
êêêêê4ê5

êë 1êêè3êêè1
#êA)ï5 ─êè B)ï3 ──êèC)ï4 ─êè D)ïå
êë 4êêè4êêè2
ü

#ë 3ë1ê15ë6ê15∙6ê3∙║∙╖∙3ê9ê1
#è 3 ─ ∙ 1 ─è=è──ï∙ï─è=è────è=è───────è=è─ïor 4 ─
#ë 4ë5ê 4ë5ê 4∙5ê ╖∙2∙║ê 2ê2
Ç C
 14êêêë1
#êêêMultiplyë2 ─ïxï3
êêêêê 2

êêêêè3êêè1
#êA)ï7êë B)ï6 ─êè C)ï7 ─êè D)ïå
êêêêè4êêè2
ü

êë 1êë 5ë3ê5∙3ê 15ê1
#êè 2 ─ïxï3è=è─ïxï─è=è────è=è──ïor 7 ─
êë 2êë 2ë1ê2∙1êï2ê2
Ç C
 15êêêë3ê3
#êêêMultiplyê─ïxï3 ─
êêêêê 8ê7

êë 2êêè1êêè2
#êA)ï1 ─êè B)ï4 ─êè C)ï3 ─êè D)ïå
êë 7êêè8êêè7
ü

#ë3ê3ê3ë24ê3∙╖∙╖∙╖∙3ê3∙3ê9ë 2
#ë─ïxï3 ─è=è─ïxï──è=è─────────è=è───è=è─ or 1 ─
#ë8ê7ê8ë 7ê ╖∙╖∙╖∙7êï7ê 7ë 7
Ç A
 16êêêè 1ê2
#êêë Multiplyë3 ─ïxï4 ─
êêêêê2ê3

êë 5êêè 1
#êA)ï7 ─êè B)ï16 ─êèC)ï8êë D)ïå
êë 6êêè 3
ü

#ë1ê2ê7ë14ê7∙14ê7∙╖∙7ê49ê1
#è3 ─ïxï4 ─è=è─ïxï──è=è────è=è─────è=è── or 16 ─
#ë2ê3ê2ë 3ê 2∙3ê ╖∙3êï3ê3
Ç B
 17êêêè1ê1
#êêëMultiplyë4 ─ïxï2 ─
êêêêë 3ê4

êë 1êêè3êêè3
#êA)ï8 ─êè B)ï8 ─êè C)ï9 ─êè D)ïå
êë 4êêè4êêè4
ü

#ë1ê1ê13ë9ê13∙9ê13∙╕∙3ê39ë 3
#è4 ─ïxï2 ─è=è──ïxï─è=è────è=è──────è=è── or 9 ─
#ë3ê4ê 3ë4ê 3∙4ê ╕∙2∙2ê 4ë 4
Ç C
 18êêêêè 1
#êêêMultiplyë4ïxï6 ─
êêêêêê2

êê1êêêêê1
#êA)ï12 ─êèB)ï26êëC)ï24 ─êèD)ïå
êê2êêêêê2
ü

#êë 1ê4ë13ê4∙13ê╖∙2∙13ê26
#ë4ïxï6 ─è=è─ïxï──è=è────è=è──────è=è── or 26
#êë 2ê1ë 2ê 1∙2ê 1∙╖êè1
Ç B
 19è A person can row a boatï2 1/2ïmiles in one hour.ïHow
êêfar can he row inï1 1/3ïhours?

êë3êêè1êêï4
#ë A)ï2 ─ mi.êB)ï3 ─ mi.ë C)ï2 ─ mi.êD)ïå
êë5êêè3êêï5
ü

#ë 1ë1ê5è4ê5∙4ê5∙╖∙2ê10ë 1
#è 2 ─ ∙ 1 ─è=è─ ∙ ─è=è───è=è─────è=è── or 3 ─ miles
#ë 2ë3ê2è3ê2∙3ê ╖∙3êï3ë 3
Ç B
 20èA car getsï25 2/5ïmiles per gallon.ïHow far can it
êë travel on 4 gallons of gas?

êêêêè1êêï3
#ëA)ï105 mi.êB)ï103 ─ mi.è C)ï101 ─ mi.ëD)ïå
êêêêè5êêï5
ü

êë2êè 127è4ê127∙4ê508êè3
#êï25 ─ ∙ 4è=è─── ∙ ─è=è─────è=è───ïorï101 ─ mi.
êë5êë5è 1ê 5∙1êï5êè 5
Ç C
 21è A worker earnsï6 1/2ïdollars per hour.ïHow much does
he earn inï4 1/3ïhours?

êë1êêêêë 1
#ëA)ï28 ─ dollarsïB)ï32 dollarsèC)ï29 ─ dollarsïD)ïå
êë6êêêêë 3
ü

ê 1ë1ê13è13ê13∙13ê169êï1
#ë 6 ─ ∙ 4 ─è=è── ∙ ──è=è─────è=è───ïorï28 ─ dollars
ê 2ë3ê 2è 3ê 2∙3êï6êè6
Ç A
 22è A boardï6 2/3ïfeet long is cut intoï4ïequal parts.
êêWhat isï1/4ïof 6 2/3?

êè 1êêè2êêï1
#ëA)ï2 ─ ft.êB)ï1 ─ ft.ë C)ï2 ─ ft.êD)ïå
êè 4êêè3êêï3
ü

#ê 1ë2ê1è20ê1∙╖∙╖∙5ê5ê 2
#ê ─ ∙ 6 ─è=è─ ∙ ──è=è───────è=è─ïorï1 ─ïfeet
#ê 4ë3ê4è 3ê ╖∙╖∙3ê 3ê 3
Ç B