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CHAPTER1.1T
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à 1.1ïFractions
äïPlease write each fraction in lowest terms.
â
êêêê 18è9 ∙ 2è2
êêêê ── = ───── = -
êêêê 27è9 ∙ 3è3
éS
êTo write a fraction in lowest terms, first factor both the
ênumerator and denominator.
êi.e.ï28è 2∙2∙7
êë ── = ───────
êë 36è2∙2∙3∙3
êThen cancel like factors that occur on both the top and bottom.
êè 2∙2∙7ë 7ë Finally multiplyë 7ë7
êè───────ï= ───ëremaining factors.è───ï= ─
êè2∙2∙3∙3è 3∙3êêêë3∙3è 9
1
êë 9è?êA)ï1ëB)è2ëC)ï1è D) å
êë── = ─êè ─êè─êï─ê of
êë18è?êè 2êè3êï3êç
ü
êêêè9ê3 ∙ 3ê1
êêêï──ï=ï─────────ï=ï─
êêêï18ë2 ∙ 3 ∙ 3ë2
Ç A
2
êë22ë?è A)ï11ë B)ï12è C)ï11è D) å
êë──ï=ï─ê ──êè──ê ──ê of
êë28ë?ê 12êè14ê 14êThese
ü
êêêë22ë2 ∙ 11ë11
êêêë──ï=ï──────ï=ï──
êêêë28ë2 ∙ 14ë14
Ç C
3
êë96ë?è A)ï4êB)ï4ëC)ï2ëD) å
êë─── =ï─ê ─êè ─êï─êïof
êë120è ?ê 6êè 5êï3ê ç
ü
êêê 96ë4 ∙ 6 ∙ 4ë4
êêê ─── =ï─────────ï=ï─
êêê 120è 4 ∙ 6 ∙ 5ë5
Ç B
äïFind the products or quotients. Write answers in lowest
êêterms.
âSêêêêêë 2
êêêêêêê─
êè5è 6ê 5 ∙ 6ê1êë3ë 2è5è10
êè── ∙ ── = ───────────── = ──êè───ï=ï─ ∙ ─ = ──
êè12è25è2 ∙ 6 ∙ 5 ∙ 5è10êè 9ë 3è9è27
êêêêêêê─
êêêêêêê5
éS
To multiply twoë5è 6ë5∙6ëthen factor allè5∙6ë 2∙3∙5
fractions expressï── ∙ ──ï= ─────è parts of theë───── =ï───────
the productê 12è25è 12∙25è numerator andè 12∙25è 2∙2∙3∙5
as one fractionêêêèdenominator.
Next cancel likeêï2∙3∙5ë 1ëFinally, multiplyë1ë1
factors that occur onï───────── = ───è remaining factors.è─── = ──
the top and bottom.è 2∙2∙3∙5∙5è2∙5êêêè 2∙5è10
To divide two fractionsï2è9è2è5èThen treatë 2è5è2∙5è1
invert the secondê ─ ÷ ─ = ─ ∙ ─èthe problemë─ ∙ ─ = ─── = ─
fraction and multiply.è3è5è3è9èas a multi-ë3è9è3∙9è2
êêêêêë plication problem.
4
êë 4è1è?è A)ï2ë B)ï4ëC)ï5ëD) å
êë ─ ∙ ─ = ─ê ──êï──ê ─êïof
êë 5è2è?ê 5êè10ê 7ê ç
ü
êêêï4è1ë4 ∙ 1è 2 ∙ 2ë2
êêêï─ ∙ ─ =è─────ï= ─────ï=ï─
êêêï5è2ë5 ∙ 2è 5 ∙ 2ë5
Ç A
5
êë 7è21è?è A)ï1ë B)ï28è C)ï1ëD) å
êë── ÷ ── = ─ê ─êè──ê ─êïof
êë12è 4è?ê 9êè16ê 8ê ç
ü
êêè7è 21è 7è 4ë7ï∙ 4ê1ë 1
êêè── ÷ ── =ï── ∙ ──ï= ───────ï= ─────ï= ─
êêè12è4ë12è21è 12 ∙ 21è 3 ∙ 3è 9
Ç A
6
êë 7ë5è?è A)ï12ëB)ï23è C)ï14è D) å
êè 2 ─ï÷ï─ = ─ê ──êï──ê ──ê of
êë 8ë4è?ê 5êè10ê 5ê ç
ü
êêêï7ë5è23è5è23è4è23
êêê2 ─ï÷ï─ = ── ÷ ─ = ── ∙ ─ = ──
êêêï8ë4è 8è4è 8è5è10
Ç B
äïAdd or Subtract and write answers in lowest terms.
â
êêêë3è2è 3 + 2è 5
êêêë─ + ─ï= ─────ï= ─
êêêë8è8ë 8ë 8
éS
èTo add two fractions, make sure that the denominators are the
èsame.
êë 2è1ë2è4ë1è3ë 8ë 3
êë ─ + ─ï=ï─ ∙ ─ï+ï─ ∙ ─ï=ï──ï+ï──
êë 3è4ë3è4ë4è3ë12ë12
èAdd the numerators and write the denominator once.
êë 8è 3è8 + 3è11
êë── + ── = ───── = ──
êë12è12è 12ë12
7
êë1è 7è ?è A)ï4ë B)ï8ëC)ï8ëD) å
êë── + ── = ─ê ─êï──êï──êof
êë10è10è?ê 5êï10êï20êç
ü
êêêï1è 7è 1 + 7è 8è 4
êêê ── + ── =ï───── = ── =ï─
êêê 10è10ë10ë10è 5
Ç A
8
êë 3è1è ?è A)ï3ë B)ï4ëC)ï5ëD) å
êë ─ + ── = ─ê ──êï──ê ─êïof
êë 4è12è?ê 48êï16ê 6ê ç
ü
êè3è1ë 3è3è1ë9è 1ë9 + 1è 10è 5
êè─ + ── =è─ ∙ ─ + ── =ï── + ──ï= ─────ï= ──ï= ─
êè4è12ë4è3è12è 12è12ë12ë 12è 6
Ç C
äïAdd or Subtract and write answers in lowest terms.
â
ë 1è1ë 1è4ê1è3ê 4è 3ê4 - 3ë 1
ë ─ - ─è=ï- ∙ -è-è─ ∙ ─è=è── - ──è=è─────ï=ï──
ë 3è4ë 3è4ê4è3ê12è12ê 12ê12
éS
ïTo subtract two fractions, make sure that the denominators are
ïthe same.
êë2è1ë2è4ë1è3ë 8ë 3
êë─ - ─ï=ï─ ∙ ─ï-ï─ ∙ ─ï=ï──ï-ï──
êë3è4ë3è4ë4è3ë12ë12
ïThen subtract the numerators and write the denominator once.
êë8è 3è8 - 3è 5
êè ── - ── = ───── = ──
êè 12è12è 12ë12
ïFinally check the fraction to make sure that it is in lowest terms.
9
êë 3è1è ?è A)ï4ë B)ï11è C)ï1ëD) å
êë ─ - ── = ─ê ──êï──ê ─êïof
êë 8è10è?ê 18êï40ê 4ê ç
ü
êë3è1ë 3è5è1è 4è 15è4ë15-1è 11
êë─ - ── =è─ ∙ ─ - ── ∙ ─ï= ── - ──ï= ────ï= ──
êë8è10ë8è5è10è4è 40è40ë40ë40
Ç B
10
êë5ê1è?è A)ï14ëB)ï54è C)ï27è D) å
êè6 ─ï-ï2 ─ = ─ê ──êï──ê ──ê of
êë6ê6è?êï3êè6êï3êç
ü
ê 5ê1ë41è13ë41 - 13è 28è2∙2∙7è2∙7è14
ë 6 ─ï-ï2 ─ï=ï── - ──ï=ï───────ï= ── = ───── = ─── = ──
ê 6ê6ë 6è 6ê 6ê 6è 2∙3ë3ë3
Ç A