4.02 Writing proportions
Complete the following equivalent ratios:
Complete the ratio table for the ratio 6 : \dfrac{2}{3}.
| 6 | 12 | 18 | |
|---|---|---|---|
| \dfrac{2}{3} | \dfrac{8}{3} |
Complete the ratio table for the ratio \dfrac{1}{5} : \dfrac{2}{5}.
| \dfrac{1}{5} | \dfrac{2}{5} | \dfrac{3}{5} | \dfrac{4}{5} | |
|---|---|---|---|---|
| \dfrac{2}{5} | \dfrac{4}{5} | \dfrac{6}{5} | 2 |
Simplify the following ratios:
Determine whether the following pairs of fractions are equal:
\dfrac{7}{20}, \, \dfrac{2}{5}
\dfrac{4}{5}, \, \dfrac{12}{20}
\dfrac{39}{52}, \, \dfrac{57}{76}
\dfrac{9}{5}, \, \dfrac{74}{40}
\dfrac{19}{10}, \, \dfrac{171}{90}
\dfrac{5}{16}, \, \dfrac{20}{64}
\dfrac{7}{12}, \, \dfrac{35}{64}
\dfrac{18}{11}, \, \dfrac{72}{55}
Determine whether the following proportions are true or false:
\dfrac{2}{3} = \dfrac{6}{9}
\dfrac{5}{4} = \dfrac{60}{42}
\dfrac{2\dfrac{3}{4}}{3\dfrac{2}{3}} = \dfrac{3}{4}
\dfrac{6\dfrac{1}{10}}{3\dfrac{3}{5}} = 2\dfrac{2}{3}
19:76 = 5:20
11:20 = 99:180
\dfrac{\text{12 nurses}}{\text{5 doctors}} = \dfrac{\text{36 nurses}}{\text{16 doctors}}
3 \text{ gal} is to 4 \text{ ft}^2 as 12 \text{ gal} is to 16 \text{ ft}^2
Find the missing value in each case, given that the two quantities are in proportion:
\dfrac{⬚}{10}:\dfrac{35}{50}
\dfrac{⬚}{6}:\dfrac{2}{3}
\dfrac{12}{20}:\dfrac{⬚}{10}
\dfrac{16}{⬚}:\dfrac{8}{10}
\dfrac{2}{⬚}:\dfrac{10}{15}
\dfrac{⬚}{32}:9
\dfrac{15}{⬚}:3
\dfrac{6}{⬚}:\dfrac{12}{16}
If the following ratios are equivalent to 5:8, find the missing value:
⬚ : 32
400 : ⬚
10 : ⬚
⬚ : 96
125 : ⬚
⬚ : 112
⬚ : 168
150 : ⬚
If the following ratios are equivalent to 5:28, find the value of x:
80:x
50:x
x:84
60:x
x:252
x:504
110:x
To make 2 cups of rice, Dylan needs 5 cups of water. To make 10 cups of rice, he needs 25 cups of water. Complete the following proportion:
\dfrac{2\text{ cups rice}}{⬚ \text{ cups water}}=\dfrac{⬚ \text{ cups rice}}{⬚ \text{ cups water}}Glen and Fred are professional tennis players. This year, Glen has won 22 out of his 40 matches, while Fred has won 16 out of his 28 matches. Is the ratio of wins to losses the same for both players? Explain your answer.
In a particular country, there are 11\,200 registered female football players and 16\,000 registered male football players. In another country, there are 9800 registered female football players and 14\,000 registered male football players. Is the ratio of female players to male players the same for both countries? Explain your answer.
The ratio of cats to dogs is 56:231. If there are 33 dogs, find the number of cats.
The ratio of men to women at a concert is 15:45. If there are 15 women, how many men are there?
The ratio of bikes to helmets is 7:4. If there are 21 bikes, how many helmets are there?
Two types of pine trees, type A and type B, are planted in rows. In each row, the ratio of type A to type B is 7:10. If 490 of type A are planted, how many of type B are planted?
At a sporting event, the ratio of security personnel to spectators is 1:220. If 24\,200 spectators attend the event, how many security personnel will be required?
The number of students and teachers competing in a charity race is in the ratio 5:3. If 25 students take part in the race, how many teachers are there?
Homer is making perfume to sell. He is using sandalwood and rose oils in the ratio 1:\dfrac{1}{8}. How much sandalwood oil will he need if he wants to use 1 cup of rose oil?
Tricia is making a dress that uses two materials. She wants to use the materials in the ratio \dfrac{1}{3} \text{ yd} of gray for every \dfrac{7}{10} \text{ yd} of blue. If she knows she needs 1 \text{ yd} of gray material, how many yards of blue material will she need?
A painter wants to create a certain color by mixing two different colors of paint, Vespa and Nitro, in the ratio 6:1. He uses 4 \text{ L} of the Nitro color.
How many liters of the Vespa color must he use?
How many liters of paint will he have altogether once the two colors are combined?
Beth competed in a race and found that her times for the swimming, cycling, and running legs were in the ratio 3:1:2. If the quickest leg took 7 minutes, how many minutes did she take to complete the whole race?
A fruit punch recipe states that 5 cups of apple juice should be mixed with a \dfrac{4}{5} of a cup of lemonade.
Complete the given table.
| Apple Juice | Lemonade |
|---|---|
| 5 | \dfrac{4}{5} |
| 10 | \dfrac{8}{5} |
| 15 | \dfrac{12}{5} |
| 20 | |
| 25 |
To convert US dollars, USD (\$), to Japanese yen, JPY (\yen), we can use the ratio table below:
| \text{USD } (\$) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| \text{JPY } (\yen) | 320.40 |
Complete the ratio table.
How many Japanese yen will you be able to buy for \$20?
Beth wants to buy a pair of jeans that costs \yen 4272. What is this equivalent to in US dollars?
To convert US dollars, USD (\$), to British pounds, GBP (\pounds), we can use the ratio table below:
| \text{USD } (\$) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| \text{GBP } (\pounds) | 0.60 |
Complete the ratio table.
How many pounds will you be able to buy with \$11?
Justin has just returned from holiday with £15.00. How many US dollars can he exchange this for?
To convert US dollars, USD (\$), to Australian dollars, AUD (\$), we can use the ratio table below:
| \text{USD } (\$) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| \text{AUD } (\$) | 2.34 |
Complete the ratio table.
How many Australian dollars will you be able to buy for \$100 USD?
Hannah has just returned from holiday with \$93.60 AUD. How many US dollars can she exchange this for?
To convert US dollars, USD (\$), to Japanese yen, JPY (\yen), we can use the ratio table below:
| \text{USD } (\$) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| \text{JPY } (\yen) | 305.40 |
Complete the ratio table.
Oriana has \$40.00, and wants to buy a dress that costs \yen 4080. Explain whether she can afford the dress.
The cost of different amounts of pens is shown in the ratio table below:
| \text{No. of pens} | 10 | 20 | 30 | 40 | 50 | |
|---|---|---|---|---|---|---|
| \text{Cost }(\$) | 11.60 | 29.00 | 58.00 |
Complete the ratio table.
Find the cost of buying 90 pens.
How much would you expect to pay for 5 pens?