Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

1. $20$ to $36$
   Show Solution

   $\Large\frac{5}{9}$
2. $20$ to $32$
3. $42$ to $48$
   Show Solution

   $\Large\frac{7}{8}$
4. $45$ to $54$
5. $49$ to $21$
   Show Solution

   $\Large\frac{7}{3}$
6. $56$ to $16$
7. $84$ to $36$
   Show Solution

   $\Large\frac{7}{3}$
8. $6.4$ to $0.8$
9. $0.56$ to $2.8$
   Show Solution

   $\Large\frac{1}{5}$
10. $1.26$ to $4.2$
11. $1\Large\frac{2}{3}$ to $2\Large\frac{5}{6}$
    Show Solution

    $\Large\frac{10}{17}$
12. $1\Large\frac{3}{4}$ to $2\Large\frac{5}{8}$
13. $4\Large\frac{1}{6}$ to $3\Large\frac{1}{3}$
    Show Solution

    $\Large\frac{5}{4}$
14. $5\Large\frac{3}{5}$ to $3\Large\frac{3}{5}$
15. ${$18}$ to ${$63}$
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    $\Large\frac{2}{7}$
16. ${$16}$ to ${$72}$
17. ${$1.21}$ to ${$0.44}$
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    $\Large\frac{11}{4}$
18. ${$1.38}$ to ${$0.69}$
19. $28$ ounces to $84$ ounces
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    $\Large\frac{1}{3}$
20. $32$ ounces to $128$ ounces
21. $12$ feet to $46$ feet
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    $\Large\frac{6}{23}$
22. $15$ feet to $57$ feet
23. $246$ milligrams to $45$ milligrams
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    $\Large\frac{82}{15}$
24. $304$ milligrams to $48$ milligrams
25. total cholesterol of $175$ to HDL cholesterol of $45$
    Show Solution

    $\Large\frac{35}{9}$
26. total cholesterol of $215$ to HDL cholesterol of $55$
27. $27$ inches to $1$ foot
    Show Solution

    $\Large\frac{9}{4}$
28. $28$ inches to $1$ foot
29. $28$ to $40$$56$ to $32$
    Show Solution

    $\Large\frac{7}{4}$
30. $3.5$ to $0.5$
31. $1.2$ to $1.8$
    Show Solution

    $\Large\frac{2}{3}$
32. $1\Large\frac{3}{4}\normalsize\text{to}1\Large\frac{5}{8}$
33. $2\Large\frac{1}{3}\normalsize\text{to}5\Large\frac{1}{4}$
    Show Solution

    $\Large\frac{4}{9}$
34. $64$ ounces to $30$ ounces
35. $28$ inches to $3$ feet
    Show Solution

    $\Large\frac{7}{9}$

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction.

1. $140$ calories per $12$ ounces
   Show Solution

   $\Large\frac{\text{35 calories}}{\text{3 ounces}}$
2. $180$ calories per $16$ ounces
3. $8.2$ pounds per $3$ square inches
   Show Solution

   $\Large\frac{\text{41 lbs}}{\text{15 sq. in}.}$
4. $9.5$ pounds per $4$ square inches
5. $488$ miles in $7$ hours
   Show Solution

   $\Large\frac{\text{488 miles}}{\text{7 hours}}$
6. $527$ miles in $9$ hours
7. ${$595}$ for $40$ hours
   Show Solution

   $\Large\frac{{$119}}{{8 hours}}$
8. ${$798}$ for $40$ hours
9. $180$ calories per $8$ ounces
10. $90$ pounds per $7.5$ square inches
    Show Solution

    $\Large\frac{90\text{pounds}}{7.5\text{square inches}}$
11. $126$ miles in $4$ hours
12. ${$612.50}$ for $35$ hours
    Show Solution

    $\Large\frac{$612.50}{35\text{hours}}$

Find Unit Rates

Exercise 1

In the following exercises, find the unit rate. Round to two decimal places, if necessary.

1. 1. $140$ calories per $12$ ounces
      Show Solution

      11.67 calories/ounce
   2. $180$ calories per $16$ ounces
   3. $8.2$ pounds per $3$ square inches
      Show Solution

      2.73 lbs./sq. in.
   4. $9.5$ pounds per $4$ square inches
   5. $488$ miles in $7$ hours
      Show Solution

      69.71 mph
   6. $527$ miles in $9$ hours
   7. ${$595}$ for $40$ hours
      Show Solution

      $14.88/hour
   8. ${$798}$ for $40$ hours
   9. $576$ miles on $18$ gallons of gas
      Show Solution

      32 mpg
   10. $435$ miles on $15$ gallons of gas
   11. $43$ pounds in $16$ weeks
       Show Solution

       2.69 lbs./week
   12. $57$ pounds in $24$ weeks
   13. $46$ beats in $0.5$ minute
       Show Solution

       92 beats/minute
   14. $54$ beats in $0.5$ minute
   15. $180$ calories per $8$ ounces
   16. $90$ pounds per $7.5$ square inches
       Show Solution

       12 pounds/sq.in.
   17. $126$ miles in $4$ hours
   18. ${$612.50}$ for $35$ hours
       Show Solution

       $17.50/hour

Exercise 2

1. 1. The bindery at a printing plant assembles $96,000$ magazines in $12$ hours. How many magazines are assembled in one hour?
      Show Solution

      8,000
   2. The pressroom at a printing plant prints $540,000$ sections in $12$ hours. How many sections are printed per hour?

Find Unit Price

Exercise 1

In the following exercises, find the unit price. Round to the nearest cent.

1. 1. Soap bars at $8$ for ${$8.69}$
      Show Solution

      $1.09/bar
   2. Soap bars at $4$ for ${$3.39}$
   3. Women’s sports socks at $6$ pairs for ${$7.99}$
      Show Solution

      $1.33/pair
   4. Men’s dress socks at $3$ pairs for ${$8.49}$
   5. Snack packs of cookies at $12$ for ${$5.79}$
      Show Solution

      $0.48/pack
   6. Granola bars at $5$ for ${$3.69}$
   7. CD-RW discs at $25$ for ${$14.99}$
      Show Solution

      $0.60/disc
   8. CDs at $50$ for ${$4.49}$
   9. t-shirts: $3$ for ${$8.97}$
   10. Highlighters: $6$ for ${$2.52}$
       Show Solution

       $0.42
   11. An office supply store sells a box of pens for ${$11}$. The box contains $12$ pens. How much does each pen cost?
   12. Anna bought a pack of $8$ kitchen towels for ${$13.20}$. How much did each towel cost? Round to the nearest cent if necessary.
       Show Solution

       $1.65

Exercise 2

1. 1. The grocery store has a special on macaroni and cheese. The price is ${$3.87}$ for $3$ boxes. How much does each box cost?
      Show Solution

      $1.29/box
   2. The pet store has a special on cat food. The price is ${$4.32}$ for $12$ cans. How much does each can cost?

Exercise 3

In the following exercises, find each unit price and then identify the better buy. Round to three decimal places.

1. 1. Mouthwash, ${50.7-ounce}$ size for ${$6.99}$ or ${33.8-ounce}$ size for ${$4.79}$
      Show Solution

      The 50.7-ounce size costs $0.138 per ounce. The 33.8-ounce size costs $0.142 per ounce. The 50.7-ounce size is the better buy.
   2. Toothpaste, $6$ ounce size for ${$3.19}$ or $7.8-ounce$ size for ${$5.19}$
   3. Breakfast cereal, $18$ ounces for ${$3.99}$ or $14$ ounces for ${$3.29}$
      Show Solution

      The 18-ounce size costs $0.222 per ounce. The 14-ounce size costs $0.235 per ounce. The 18-ounce size is a better buy.
   4. Breakfast Cereal, $10.7$ ounces for ${$2.69}$ or $14.8$ ounces for ${$3.69}$
   5. Ketchup, ${40-ounce}$ regular bottle for ${$2.99}$ or ${64-ounce}$ squeeze bottle for ${$4.39}$
      Show Solution

      The regular bottle costs $0.075 per ounce. The squeeze bottle costs $0.069 per ounce. The squeeze bottle is a better buy.
   6. Mayonnaise ${15-ounce}$ regular bottle for ${$3.49}$ or ${22-ounce}$ squeeze bottle for ${$4.99}$
   7. Cheese ${$6.49}$ for $1$ lb. block or ${$3.39}$ for $\Large\frac{1}{2}$ lb. block
      Show Solution

      The half-pound block costs $6.78/lb, so the 1-lb. block is a better buy.
   8. Candy ${$10.99}$ for a $1$ lb. bag or ${$2.89}$ for $\Large\frac{1}{4}$ lb. of loose candy
   9. Shampoo: $12$ ounces for ${$4.29}$ or $22$ ounces for ${$7.29}?$
   10. Vitamins: $60$ tablets for ${$6.49}$ or $100$ for ${$11.99}?$
       Show Solution

       $0.11, $0.12; 60 tablets for $6.49

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

1. 1. $793$ miles per $p$ hours
      Show Solution

      $\Large\frac{\text{793 miles}}{p \text{hours}}$
   2. $78$ feet per $r$ seconds
   3. ${$3}$ for $0.5$ lbs.
      Show Solution

      $\Large\frac{{$3}}{{0.5 lbs}.}$
   4. $j$ beats in $0.5$ minutes
   5. $105$ calories in $x$ ounces
      Show Solution

      $\Large\frac{\text{105 calories}} {x \text {ounces}}$
   6. $400$ minutes for $m$ dollars
   7. the ratio of $y$ and $5x$
      Show Solution

      $\Large\frac{y}{5x}$
   8. the ratio of $12x$ and $y$
   9. $535$ miles per $h\text{hours}$
   10. $a$ adults to $45$ children
       Show Solution

       $\Large\frac{a\text{adults}}{45\text{children}}$
   11. the ratio of $4y$ and the difference of $x$ and $10$
   12. the ratio of $19$ and the sum of $3$ and $n$
       Show Solution

       $\Large\frac{19}{3+n}$

Everyday Math

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