# Proportions: Measurement Conversions

1. 52 ounces \eqalign{\dfrac{1 \text{ pound}}{16 \text{ounces}}&=\dfrac{3.25 \text{ pounds}}{x \text{ ounces}}\\x&=52}

2. 18 inches \eqalign{\dfrac{1 \text{ foot}}{12 \text{inches}}&=\dfrac{1.5 \text{ feet}}{x \text{ inches}}\\x&=18}

3. 22 fluid ounces \eqalign{\dfrac{1 \text{ cup}}{8 \text{fl. ounces}}&=\dfrac{2.75 \text{ cups}}{x \text{ ounces}}\\x&=22}

4. 3 pounds\eqalign{\dfrac{1 \text{ pound}}{16 \text{ounces}}&=\dfrac{x \text{ pounds}}{48 \text{ ounces}}\\48&=16x\\3&=x}

5. $7.\overline{33}$ feet \eqalign{\dfrac{1 \text{ foot}}{12 \text{inches}}&=\dfrac{x \text{ feet}}{88 \text{ inches}}\\12x&=88\\x&=7.\overline{33}}

6. 20.25 feet \eqalign{\dfrac{1 \text{ yard}}{3 \text{feet}}&=\dfrac{6.75 \text{ yards}}{x \text{ feet}}\\x&=20.25}

7. 210 minutes \eqalign{\dfrac{1 \text{ hour}}{60 \text{minutes}}&=\dfrac{3.5 \text{ hours}}{x \text{ minutes}}\\x&=210}

8. 2.15 hours\eqalign{\dfrac{1 \text{ hour}}{60 \text{minutes}}&=\dfrac{x \text{ hours}}{129 \text{ minutes}}\\60x&=129\\x&=2.15}

9. 6.3 kilometers

\eqalign{\dfrac{1 \text{ km}}{1000 \text{m}}&=\dfrac{x \text{ km}}{900 \text{ m}}\\1000x&=900\\x&=.9}
Then, you multiply the number of kilometers per day ($0.9$) by the number of days in a week ($7$).
$0.9$ kilometers $\times$ $7$ days each week = 6.3 kilometers

10. .7 meters \eqalign{\dfrac{1 \text{ m}}{100 \text{cm}}&=\dfrac{x \text{ m}}{70\text{ cm}}\\70&=100x\\x&=.7}

11. 2.4167 hours

6:10 - 3:45 = 2 hours and 25 minutes.  We know it's 2 hours, so just convert the 25 minutes to hours and add to 2.

\eqalign{\dfrac{1 \text{ hour}}{60 \text{minutes}}&=\dfrac{x \text{ hours}}{25 \text{ minutes}}\\60x&=25\\x&=.4167}

$2 + .4167 = 2.4167$ hours

12. 72 seconds \eqalign{\dfrac{1 \text{ minute}}{60 \text{seconds}}&=\dfrac{1.2 \text{ minutes}}{x \text{ seconds}}\\x&=72}