Multiplying Fractions Exercises

Fractionsare quotients between two whole numbers and the multiplication of fractions It is a basic operation, in which you multiply numerator by numerator and denominator by denominator.

$\dpi{120} \mathrm{\frac{a}{b}\cdot \frac{c}{d} \frac{a\cdot c}{b\cdot d}}$

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The results of multiplying fractions can be simplified or, equivalently, cancellation techniquecan be used before calculating the product.

Next, see a list of multiplication fractions exercises, all resolved so you can check your answers and ask questions.

List of fraction multiplication exercises

Question 1. Do the multiplications and, if possible, simplify:

The) $\dpi{120} \frac{2}{5}\cdot \frac{6}{7}$

B) $\dpi{120} \frac{1}{9}\cdot \frac{9}{10}$

w) $\dpi{120} \frac{3}{4}\cdot \frac{2}{3}$

Question 2. Determine the value of x in the multiplications below:

The) $\dpi{120} \mathrm{\frac{7}{4}\cdot \frac{x}{5} \frac{21}{20}}$

B) $\dpi{120} \mathrm{\frac{3}{2}\cdot \frac{5}{x} \frac{15}{16}}$

w) $\dpi{120} \mathrm{\frac{7}{x}\cdot \frac{1}{6} \frac{7}{6}}$

Question 3. Solve the multiplications and simplify if possible:

The) $\dpi{120} 2\cdot \frac{9}{7}$

B) $\dpi{120} 4\cdot \frac{3}{20}$

w) $\dpi{120} \frac{8}{9}\cdot 9$

Question 4. How much is it:

The) $\dpi{120} \frac{1}{3}$ from 6?

B) $\dpi{120} \frac{1}{4}$ in $\dpi{120} \frac{2}{7}$ ?

w) $\dpi{120} \frac{3}{4}$ from 12?

Question 5. There are a total of 150 vegetables in a stall. Of these, one-third are potatoes and one-fifth are carrots. Reply:

a) How many potatoes are in the bank?
b) How many carrots are there in the bank?
c) Are there any other types of vegetables on the stand?

Question 6. What is one-sixth of two-thirds of 240?

Question 7. In a parking lot for cars and motorcycles there are 49 vehicles, of which two sevenths are motorcycles. How many cars are there in the parking lot?

Question 8. Using fractions express the following quantities:

a) half of half
b) half of half of half
c) twice as many as two sevenths

Question 9. How many minutes corresponds $\dpi{120} \frac{1}{2}$ in $\dpi{120} \frac{3}{5}$ of time?

Question 10. How many days corresponds $\dpi{120} \frac{3}{4}$ in $\dpi{120} \frac{2}{3}$ a month?

Resolution of question 1

The) $\dpi{120} \frac{2}{5}\cdot \frac{6}{7} \frac{2\cdot 6}{5\cdot 7} \frac{12}{35}$

B) $\dpi{120} \frac{1}{9}\cdot \frac{9}{10} \frac{1}{\cancel{9}^1}\cdot \frac{\cancel{9}^1} {10} 1\cdot \frac{1}{10} \frac{1}{10}$

w) $\dpi{120} \frac{3}{4}\cdot \frac{2}{3} \frac{\cancel{3}^1}{\cancel{4}^2}\cdot \frac{\cancel {2}^1}{\cancel{3}^1} \frac{1}{2}\cdot 1 \frac{1}{2}$

Resolution of question 2

The) $\dpi{120} \mathrm{\frac{7}{4}\cdot \frac{x}{5} \frac{21}{20}}$

Like 7. 3 = 21, so x = 3.

B) $\dpi{120} \mathrm{\frac{3}{2}\cdot \frac{5}{x} \frac{15}{16}}$

Like 2. 8 = 16, so x = 8.

w) $\dpi{120} \mathrm{\frac{7}{x}\cdot \frac{1}{6} \frac{7}{6}}$

Like 1. 6 = 6, so x = 1.

Resolution of question 3

The) $\dpi{120} 2\cdot \frac{9}{7} \frac{2\cdot 9}{7} \frac{18}{7}$

B) $\dpi{120} 4\cdot \frac{3}{20} \cancel{4}^1\cdot \frac{3}{\cancel{20}^5} 1\cdot \frac{3}{5} \frac{3}{5}$

w) $\dpi{120} \frac{8}{9}\cdot 9 \frac{8}{\cancel{9}^1}\cdot \cancel{9}^1 8$

Resolution of question 4

The) $\dpi{120} \frac{1}{3}$ from 6?

$\dpi{120} \frac{1}{3}\cdot 6 \frac{1}{\cancel{3}^1}\cdot \cancel{6} ^2 2$

Therefore, $\dpi{120} \frac{1}{3}$ of 6 is equal to 2.

B) $\dpi{120} \frac{1}{4}$ in $\dpi{120} \frac{2}{7}$ ?

$\dpi{120} \frac{1}{4}\cdot \frac{2}{7} \frac{1}{\cancel{4}^2}\cdot \frac{\cancel{2}^1} {7} \frac{1}{2}\cdot \frac{1}{7} \frac{1}{14}$

Therefore, $\dpi{120} \frac{1}{4}$ in $\dpi{120} \frac{2}{7}$ it's the same as $\dpi{120} \frac{1}{14}$ .

w) $\dpi{120} \frac{3}{4}$ from 12?

$\dpi{120} \frac{3}{4}\cdot 12 \frac{3}{\cancel{4}^1}\cdot \cancel{12}^3 3\cdot 39$

Therefore, $\dpi{120} \frac{3}{4}$ of 12 equals 9.

Resolution of question 5

a) There are a third of potatoes, so we must calculate $\dpi{120} \frac{1}{3}$ out of 150:

$\dpi{120} \frac{1}{3}\cdot 150 50$

So there are 50 potatoes in the bank.

b) There are one fifth of carrots, so we must calculate $\dpi{120} \frac{1}{5}$ out of 150:

$\dpi{120} \frac{1}{5}\cdot 150 30$

So there are 30 carrots in the bank.

c) Subtracting the number of potatoes and carrots from the total number of vegetables, we can see that there is another type of vegetable:

150 – 50 – 30 = 70

That is, there are 70 units of other vegetable(s).

Resolution of question 6

We want to know how much $\dpi{120} \frac{1}{6}$ in $\dpi{120} \frac{2}{3}$ out of 240:

$\dpi{120} \frac{1}{6}\cdot \frac{2}{3}\cdot 240 \frac{1}{\cancel{6}^3}\cdot \frac{\cancel{2} ^1}{\cancel{3}^1}\cdot \cancel{240}^{80} \frac{1}{3}\cdot 80 \frac{80}{3}$

Therefore, $\dpi{120} \frac{1}{6}$ in $\dpi{120} \frac{2}{3}$ of 240 is $\dpi{120} \frac{80}{3}$ .

Resolution of question 7

We need to know how much $\dpi{120} \frac{2}{7}$ of 49:

$\dpi{120} \frac{2}{7}\cdot 49 \frac{2}{\cancel{7}^1}\cdot \cancel{49}^7 2\cdot 7 14$

So there are 14 motorcycles in the parking lot.

49 – 14 = 35

So there are 35 cars in the lot.

Resolution of question 8

a) half of half is the same as $\dpi{120} \frac{1}{2}$ in $\dpi{120} \frac{1}{2}$ :

$\dpi{120} \frac{1}{2}\cdot \frac{1}{2} \frac{1}{4}$

b) half of half of half is the same as $\dpi{120} \frac{1}{2}$ in $\dpi{120} \frac{1}{2}$ in $\dpi{120} \frac{1}{2}$ :

$\dpi{120} \frac{1}{2}\cdot \frac{1}{2}\cdot \frac{1}{2} \frac{1}{8}$

c) the double of two sevenths is the same as 2 of $\dpi{120} \frac{2}{7}$ :

$\dpi{120} 2\cdot \frac{2}{7} \frac{4}{7}$

Resolution of question 9

How many minutes corresponds $\dpi{120} \frac{1}{2}$ in $\dpi{120} \frac{3}{5}$ of time?

One hour equals 60 minutes, so we must calculate $\dpi{120} \frac{1}{2}$ in $\dpi{120} \frac{3}{5}$ from 60:

$\dpi{120} \frac{1}{2}\cdot \frac{3}{5}\cdot 60 \frac{3}{\cancel{10}^1}\cdot \cancel{60}^6 3 \cdot 618$

Therefore, it corresponds to 18 minutes.

Resolution of question 10

How many days corresponds $\dpi{120} \frac{3}{4}$ in $\dpi{120} \frac{2}{3}$ a month?

Considering a month of 30 days, we must calculate $\dpi{120} \frac{3}{4}$ in $\dpi{120} \frac{2}{3}$ from 30:

$\dpi{120} \frac{3}{4}\cdot \frac{2}{3}\cdot 30 \frac{\cancel{3}^1}{\cancel{4}^2}\cdot \frac {\cancel{2}^1}{\cancel{3}^1}\cdot 30 \frac{1}{2}\cdot 30 15$

Therefore, it corresponds to 15 days.

You may also be interested:

Exercises on Equivalent Fractions
Exercises on generating fractions
Use of fractions in everyday life
Rationalization of denominators

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