# Exercises on division and multiplication of fractions

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Practice multiplication and division of fractions with the template exercises. Clear your doubts with the step-by-step commented resolutions.

## Exercise 1

Multiply the fractions .

To multiply fractions, we multiply numerator by numerator and denominator by denominator.

## Exercise 2

divide the fractions .

To divide fractions, we repeat the first and multiply by the inverse of the second. Inverting the fraction means swapping the denominator and numerator.

## Exercise 3

solve the expression .

calculate .

## Exercise 5

Calculate:

At this point, you can simplify the expression to make the calculation easier.

Again, it is possible to simplify.

## Exercise 6

The quarter of a number divided by 7/3 is equal to 9/8. What number is this?

## Exercise 7

A survey carried out with students at a college found that 3/4 play sports. Of these, 2/6 play basketball. If the survey was conducted with 60 students, how many play basketball?

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First we define how many students practice sport.

45 students play sports, of these, 2/6 play basketball. Now we define the number of students who play basketball.

## Exercise 8

A new soda industry has just launched 2/5 and 3/4 liter cans. In its reservoirs there are 5,400 liters ready to be filled and sold. With which of the two can options will there be more units of the product? What is the difference between the number of units in the two can options?

Answer: 2 160 units with 2/5 cans and 4 050 units with 3/4 cans. The difference is 1 890 units.

Calculation for the 2/5 liter reservoir:

2160 units will be filled with 2/5 liter cans.

Calculation for the 3/4 liter reservoir:

4,050 units will be filled with 3/4 liter cans.

To calculate the difference between the quantities, we do:

4 050 - 2 160 = 1 890

## Exercise 9

At a business presentation, coffee will be served in cups with a capacity of 2/40 of a liter. There are 43 participants, five of whom warned that they do not drink coffee. If a bottle of coffee has a capacity of 3/4 of a liter and each participant will be served a cup, how many bottles, at least, will be needed to serve the participants?

Answer: At least 2.5 bottles of coffee.

The number of people who will drink coffee is:

43 - 5 = 38

The total amount of coffee served will be:

Dividing the total amount of coffee by the capacity of each bottle, we will have:

Dividing the numerator by the denominator:

We concluded that to serve all participants it will be necessary to prepare a little more than two and a half bottles of coffee.

## Exercise 10

(Enem 2015 modified) Alcohol used as automotive fuel (hydrated ethanol) must have a maximum rate of water in its composition so as not to harm the engine's operation. A simple and quick way to estimate the amount of ethanol in a mixture with water is to measure the density of the mixture. The graph shows the variation of the density of the mixture (water and ethanol) with the percentage fraction of the mass of ethanol (fe), given by the expression

where me and ma are the masses of ethanol and water in the mixture, respectively, at a temperature of 20 °C.

Available at: www.handymath.com. Accessed on: 8 Aug. 2012.

Suppose that in a routine inspection carried out at a certain station, it was found that 50.0 of fuel alcohol have a mass of 45.0 g. What is the percentage fraction of ethanol in this mixture? What is the proportional relationship between the mass of water and ethanol present in the fuel sample?

Answer: fe = 55; ma = 0.81m and.

The graph gives the change in density with the change in percent fraction fe.

Density is calculated by dividing mass by volume.

Following the line of density 0.9 g/cm³ horizontally, we cross with f equal to 55. Thus, the percentage fraction of ethanol in this mixture is 55.

Using the formula, substituting the values ​​and solving for ma, we have:

Substituting the value of f into the formula:

Study more exercises on:

• Fractions Exercises
• Exercises on generating fraction and repeating decimal

• Fractions
• What is fraction?
• Fraction simplification
• Equivalent Fractions
• Generating Fraction
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