Question

1. a mechanic has 2/3 foot of hose. if each cut is 1/9 foot, how many pieces are possible?
2. a sheet of gasket material is 4/5 foot long. if each piece is 2/25 foot, how many pieces are cut?
3. a mechanic pours 5/6 gallon of oil. if each bottle holds 1/12 gallon, how many bottles can be filled?
4. a chain measures 7/12 meter. if each repair needs 1/24 meter, how many repairs can be done?
5. a mechanic has 2/3 quart of oil. if each test uses 1/18 quart, how many tests can be run?
6. a gasket roll is 3/4 foot long. if each gasket uses 1/16 foot, how many gaskets are possible?
7. a mechanic has 5/8 gallon of fuel. if each job takes 1/16 gallon, how many jobs can be completed?
8. a repair requires dividing 9/10 foot of tubing into sections of 3/50 foot. how many sections are made?
9. a mechanic has 11/12 gallon of oil. if each bottle holds 1/6 gallon, how many bottles can be filled?

Explanation:

Step1: Recall division of fractions rule

To find the number of pieces/repairs/jobs etc., we divide the total amount by the amount per piece/job/repair. The rule for dividing fractions is $\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$.

Step2: Solve problem 7

We have $\frac{2}{3}\div\frac{1}{9}=\frac{2}{3}\times\frac{9}{1}=6$.

Step3: Solve problem 8

$\frac{4}{5}\div\frac{2}{25}=\frac{4}{5}\times\frac{25}{2}=10$.

Step4: Solve problem 9

$\frac{5}{6}\div\frac{1}{12}=\frac{5}{6}\times\frac{12}{1}=10$.

Step5: Solve problem 10

$\frac{7}{12}\div\frac{1}{24}=\frac{7}{12}\times\frac{24}{1}=14$.

Step6: Solve problem 11

$\frac{2}{3}\div\frac{1}{18}=\frac{2}{3}\times\frac{18}{1}=12$.

Step7: Solve problem 12

$\frac{3}{4}\div\frac{1}{16}=\frac{3}{4}\times\frac{16}{1}=12$.

Step8: Solve problem 13

$\frac{5}{8}\div\frac{1}{16}=\frac{5}{8}\times\frac{16}{1}=10$.

Step9: Solve problem 14

$\frac{9}{10}\div\frac{3}{50}=\frac{9}{10}\times\frac{50}{3}=15$.

Step10: Solve problem 15

$\frac{11}{12}\div\frac{1}{6}=\frac{11}{12}\times\frac{6}{1}=\frac{11}{2} = 5.5$, but since we are talking about number of bottles, we take the whole - number part, so 5 bottles can be filled (with some oil left over).

Answer:

1. 6
2. 10
3. 10
4. 14
5. 12
6. 12
7. 10
8. 15
9. 5