Multiplication of Decimal Fractions - Examples, Exercises and Solutions

In the number -0.3, there is one digit after the decimal point: 3.

In the number 2.15, there are two digits after the decimal point: 15.

Therefore, we have three digits after the decimal point.

To find the answer, we will count three decimal places to the left, which gives us -0.645.

In the number -3.5, there is one digit after the decimal point: 5.

In the number 2.4, there is one digit after the decimal point: 4.

In other words, we have two digits after the decimal point.

Therefore we will move the decimal point two places to the left to get our answer: 8.40.

Whilst adhering to the rules of the order of operations, the exercise can be solved from left to right, given that it only contains multiplication.

Proceed to solve the left exercise vertically in order to avoid confusion as shown below:

$4.5\\\times3.2\\=14.40$

It is important to maintain correct positioning of the exercise, with the decimal point serving as an anchor.
Then we can multiply in order, first the ones digit of the first number by the ones digit of the second number,
then the tens digit of the first number by the ones digit of the second number, and so on.

We should obtain the following exercise:

$14.40\times5.6=$

Remember that:

$14.40=14.4$

We will once again solve the exercise vertically whilst remembering the rules of maintaining the decimal point and multiplying in order (ones, tens, and so on)

As shown below:

$14.4\\\times5.6\\=80.64$

Adhering to the rules of the order of operations, the exercise can be solved from left to right, given that it only contains multiplication.

Proceed to solve the left exercise vertically in order to avoid confusion as shown below:

$11.2\\\times5.6\\=62.72$

It's important to maintain correct positioning of the exercise, with the decimal point serving as an anchor.
Then we can multiply in order, first the ones digit of the first number by the ones digit of the second number,
then the tens digit of the first number by the ones digit of the second number, and so on.

We should obtain the following exercise:

$62.72\times7.3=$

Remember that:

$7.3=7.30$

We will once again solve the exercise vertically whilst maintaining the decimal point and multiplying in order (ones, tens, and so on)

As shown below:

$457.856$

Upon observing the exercise note that we have two "regular" numbers and one number with a variable.
Given that this is a multiplication exercise, multiplying a number with a variable by a number without a variable doesn't present a problem.

In fact, it's important to remember that a variable attached to a number represents multiplication by itself, for example in this case: $2\times x$
Therefore, we can apply the distributive property in order to separate the variable, and come back to it later.
Solve the exercise from left to right.

Solve the left exercise by breaking down the decimal number into an addition problem of a whole number and a decimal number as follows:

$2\times(4+0.65)=$

Multiply 2 by each term inside of parentheses:

$(2\times4)+(2\times0.65)=$

Solve each of the expressions inside of the parentheses as follows:

$8+1.3=9.3$

We obtain the following exercise:

$9.3\times6.3=$

Solve the exercise vertically in order to simplify the solution process.

It's important to be careful with the proper placement of the exercise, using the decimal point as an anchor.
Then we can proceed to multiply in order, first the ones digit of the first number by the ones digit of the second number. Then the tens digit of the first number by the ones digit of the second number, and so on.

$9.3\\\times6.3\\=58.59$

Don't forget to add the variable at the end resulting in the following answer:

$58.59x$

Adhering to the rules of the order of operations the exercise can be solved from left to right given that it only contains multiplication

The exercise on the left hand side should be solved vertically in order to avoid confusion as shown below:

$0.5\\\times6.7\\=3.35$

It is important to maintain correct positioning of the exercise, with the decimal point serving as an anchor.
Then we can multiply in order, first the ones digit of the first number by the ones digit of the second number,
then the tens digit of the first number by the ones digit of the second number, and so on.

This should result in the following exercise::

$3.35\times6.31=$

We will once again solve the exercise vertically whilst maintaining the decimal point and multiplying in order (ones, tens, and so on)

As shown below:

$3.35\\\times6.31\\=21.1385$

Upon observing the exercise note that we have two "regular" numbers and one number with a variable.
Given that this is a multiplication exercise, multiplying a number with a variable by a number without a variable doesn't present a problem.

In fact, it's important to remember that a variable attached to a number represents multiplication by itself, for example in this case: $5.2\times x$
Therefore, we can apply the distributive property in order to separate the variable, and come back to it later.
Proceed to solve the exercise from left to right.

Solve the left exercise vertically in order to avoid confusion as shown below:

$~~~~~15.6 \\\times~~~~5.2 \\=~81.12$

It's important to be careful with the correct placement of the exercise, where the decimal point serves as an anchor.
Then we can multiply in order, first the ones digit of the first number by the ones digit of the second number.
Next the tens digit of the first number by the ones digit of the second number, and so on.

We should obtain the following:

$81.21\times0.3=$

Remember that:

$0.3=\text{0}.30$

Calculate:

$24.336$

Let's not forget to add the variable at the end resulting in the following answer:

$24.336 x$

We begin by converting the decimal numbers into mixed fractions:

$4\frac{1}{10}\times1\frac{6}{10}\times3\frac{2}{10}+4\frac{7}{10}=$

We then convert the mixed fractions into simple fractions:

$\frac{41}{10}\times\frac{16}{10}\times\frac{32}{10}+\frac{47}{10}=$

We solve the exercise from left to right:

$\frac{41\times16}{10\times10}=\frac{656}{100}$

This results in the following exercise:

$\frac{656}{100}\times\frac{32}{10}+\frac{47}{10}=$

We solve the multiplication exercise:

$\frac{656\times32}{100\times10}=\frac{20,992}{1,000}$

Now we get the exercise:

$\frac{20,992}{1,000}+\frac{47}{10}=$

We then multiply the fraction on the right so that its denominator is also 1000:

$\frac{47\times100}{10\times100}=\frac{4,700}{1,000}$

We obtain the exercise:

$\frac{20,992}{1,000}+\frac{4,700}{1,000}=\frac{20,992+4,700}{1,000}=\frac{25,692}{1,000}$

Lastly we convert the simple fraction into a decimal number:

$\frac{25,692}{1,000}=25.692$