Middle School Math & Grammar

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319 àï4.1è Introduction to Ratios. äè Please write the following ratios in simplest form. âïWrite the ratio of 20 ft. to 24 ft. using three different notations. è Fraction Notationê Colon Notationê "is to" Notation è 20 ft.è20è5êè20 ft. : 24 ft.ê20 ft. is to 24 ft. #è ────── = ── = ─êê20 : 24êê 20 is to 24 è 24 ft.è24è6êê 5 : 6êêè5 is to 6 éS A ratio is a comparison of two numbers that have the same units.ïThe two quantities "20 ft." and "24 ft." have the same units since they are both in "feet".ïThese two quantities can be compared three differentïways.ïProbably the most frequent method of comparison is as a fraction. êêêè20 ft.ë20ë5 #êêêè──────ï=ï──ï=ï─ êêêè24 ft.ë24ë6 êêêêêêêêï20 #Note that the units, "ft.", cancel out and the fraction,ï── , is êêêêêêêêï24 reduced to simplest form. ëThe second method of comparison is done by using a colon, ":". êêè20 ft. : 24 ft.ï=è20 : 24è=è5 : 6 è The third method of comparison is by using the expression, "is to". êè20 ft. is to 24 ft.è=è20 is to 24è=è5 is to 6 èThese methods of comparison of two numbers having the same units are the three ways you can express a ratio. ï1 êê Write the ratio of 5 to 7 using the Fraction Notation. êë7êê5 #ê A)ï─êèB)ï─êèC)ï5 : 7ê D)ïå êë5êê7 ü êêêêê5 #êêêêê─ êêêêê7 ÇïB ï2 êê Write the ratio of 25 to 40 in simplest form using the êê Fraction Notation. êë8êêêê 5 #ê A)ï─êèB)ï8 : 5ë C)ï─êëD)ïå êë5êêêê 8 ü êêêêè25ë 5 #êêêêè──ï=è─ êêêêè40ë 8 ÇïC ï3 êê Write the ratio of 50 cm to 40 cm in simplest form using êê Fraction Notation. êë5 #ê A)ï─êèB)ï50 is to 40èC)ï5 : 4êïD)ïå êë4 ü êêêë50 cmë50ë 5 #êêêë─────ï=ï──ï=è─ êêêë40 cmë40ë 4 ÇïA ï4 êëWrite the ratio of 20 ft. to 28 ft. in simplest form using êëFraction Notation. êêêêêêë5 #ê A)ï7 : 5ë B)ï20 is to 28ëC)ï─êèD)ïå êêêêêêë7 ü êêêë20 ft.è 20ë 5 #êêêë─────ï=ï──ï=è─ êêêë28 ft.è 28ë 7 ÇïC ï5 êëWrite the ratio of 8 in. to 2 ft. in simplest form using the êëFraction Notation. êë1êê4 #ê A)ï─êèB)ï─êê C)ï8 : 2ë D)ïå êë3êê1 üê Since ratios must have the same units, it is necessary to change 2 ft. to 24 inches before reducing. êêï8 in.ë8 in.ë 8ë1 #êêï─────ï=ï─────ï=ï──ï=ï─ êêï2 ft.ë24 in.è 24ë3 ÇïA ï6 ïWrite the ratio of 4 dimes to 16 nickels in simplest form using the ïFraction Notation. êë1êê1êêë1 #ê A)ï─êèB)ï─êê C)ï─êèD)ïå êë2êê4êêë8 üê Since ratios must have the same units, it is necessary to change 4 dimes to 8 nickels before reducing. êè4 dimesê 8 nickelsë 8ë1 #êï──────────ï=ï──────────ï=ï──ï=ï─ êï16 nickelsë16 nickelsë16ë2 ÇïA ï7 êê Write the ratio of 5 to 4 in simplest form using the êê Colon Notation. ê A)ï5 : 4ë B)ï4 : 5ê C)ï5 is to 4ëD)ïå ü êêêêè 5 : 4 ÇïA ï8 êê Write the ratio of 20 to 16 in simplest form using the êê Colon Notation. êêêêêêï10 #ê A)ï10 : 8ëB)ï5 : 4ê C)ï──êèD)ïå êêêêêêè8 ü êêêë20 : 16ï=è5 : 4 ÇïB ï9 êWrite the ratio of 14 lbs. to 35 lbs. in simplest form using the êColon Notation. ê A)ï35 : 14è B)ï2 : 5ê C)ï14 is to 35èD)ïå ü êè 14 lbs. : 35 lbs.ï=ï14 : 35ï=ï2 : 5 ÇïB ï10 êWrite the ratio of 14 oz. to 21 oz. in simplest form using the êColon Notation. êë14êë 2 #ê A)ï──êïB)ï─êëC)ï2 : 3êïD)ïå êë21êë 3 ü êêè 14 oz. : 21 oz.ï=ï14 : 21ï=ï2 : 3 ÇïC ï11 êWrite the ratio of 8 oz. to 2 lbs. in simplest form using the êColon Notation. ê A)ï1 : 4ë B)ï4 : 1ê C)ï8 is to 32è D)ïå ü êêSince ratios must have the same units, it is necessary to change 2 lbs. to 32 oz. è 8 oz. : 2 lbs.ï=è8 oz. : 32 oz.ï=ï8 : 32ï=ï1 : 4 ÇïA ï12 êWrite the ratio of 8 ft. to 4 yds. in simplest form using the êColon Notation. ê A)ï8 : 4ë B)ï2 : 3ê C)ï2 : 1êïD)ïå ü êêSince ratios must have the same units, it is necessary to change 4 yds. to 12 ft. è 8 ft. : 4 yds.ï=è8 ft. : 12 ft.ï=ï8 : 12ï=ï2 : 3 ÇïB ï13 êêïWrite the ratio of 5 to 7 in simplest form using the êêï"is to " Notation. êêêêêêë 5 #ëA)ï5 is to 7ëB)ï7 is to 5ê C)ï─ê D)ïå êêêêêêë 7 ü êêêêè5 is to 7 ÇïA ï14 êêWrite the ratio of 26 to 14 in simplest form using the êê"is to " Notation. êêêêè 7 #êA)ï7 is to 13ë B)ï──êC)ï13 is to 7è D)ïå êêêêè13 ü êêêï26 is to 14ï=ï13 is to 7 ÇïC ï15 êïWrite the ratio of 12 mi. to 16 mi. in simplest form using the êï"is to " Notation. êè 4 #êA)ï─êïB)ï3 is to 4êC)ï3 : 4êD)ïå êè 3 ü êë12 mi. is to 16 mi.ï=è12 is to 16ï=ï3 is to 4 ÇïB ï16 êïWrite the ratio of $36 to $24 in simplest form using the êï"is to " Notation. êêêêï3 #êèA)ï3 : 2êB)ï─êïC)ï3 is to 2èD)ïå êêêêï2 ü êê $36 is to $24ï=ï36 is to 24ï=ï3 is to 2 ÇïC ï17 ëWrite the ratio of 24 hours to 4 days in simplest form using the ë"is to" Notation. è A)ï1 is to 4ëB)ï6 is to 1ëC)ï4 is to 9ëD)ïå ü êïSince ratios must have the same units, it is necessary to change 24 hours to 1 day. ê24 hours is to 4 daysï=ï1 day is to 4 daysï=ï1 is to 4 ÇïA ï18 ëWrite the ratio of 3 quarts to 2 gal. in simplest form using the ë"is to" Notation. êêêêêêï3 #è A)ï3 is to 8ëB)ï3 : 8êïC)ï─êèD)ïå êêêêêêï8 ü êïSince ratios must have the same units, it is necessary to change 2 gal. to 8 quarts. ë3 quarts is to 2 gal.ï=ï3 quarts is to 8 quartsï=ï3 is to 8 ÇïA