Multiplication of Decimal Fractions - Examples, Exercises and Solutions

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.

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.

According to the order of operations rules, we will solve the exercise from left to right since multiplication is the only operation in it.

We will solve the left exercise vertically to avoid confusion and get:

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

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.

Now we will get the exercise:

$14.40\times5.6=$

Let's remember that:

$14.40=14.4$

We will solve the exercise vertically as well, and remember the rules of keeping the decimal point and multiplying in order (ones, tens, and so on)

And we will get:

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

According to the order of operations rules, we will solve the exercise from left to right since multiplication is the only operation in it.

We will solve the left exercise vertically to avoid confusion and get:

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

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.

Now we'll get the exercise:

$62.72\times7.3=$

Let's remember that:

$7.3=7.30$

We will solve the exercise vertically as well, remembering the rules about keeping the decimal point aligned and multiplying in order (ones, tens, and so on)

And we'll get:

$457.856$

Let's look at the exercise, and we'll see that we have two "regular" numbers and one number with a variable.
Since this is a multiplication exercise, there's no problem multiplying a number with a variable by a number without a variable.

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 use the distributive property to separate the variable, and come back to it later.
We'll solve the exercise from left to right.

We'll solve the left exercise by breaking down the decimal number into an addition problem of a whole number and a decimal number as follows:

$2\times(4+0.65)=$

We'll multiply 2 by each term in parentheses:

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

We'll solve each of the expressions in parentheses and get:

$8+1.3=9.3$

Now we'll get the exercise:

$9.3\times6.3=$

We'll solve the exercise vertically to make the process easier for ourselves.

It's important to be careful with the proper placement of the exercise, using the decimal point 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.

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

Don't forget to add the variable at the end, and the answer will be:

$58.59x$

According to the order of operations rules, we will solve the exercise from left to right since multiplication is the only operation in it.

We will solve the left exercise vertically to avoid confusion and get:

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

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.

Now we will get the exercise:

$3.35\times6.31=$

We will solve the exercise vertically as well, remembering the rules of keeping the decimal point and multiplying in order (ones, tens, and so on)

And we will get:

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

Let's look at the exercise, and we'll see that we have two "regular" numbers and one number with a variable.
Since this is a multiplication exercise, there's no problem multiplying a number with a variable by a number without a variable.

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 use the distributive property to separate the variable, and come back to it later.
We'll solve the exercise from left to right.

We'll solve the left exercise vertically to avoid confusion and get:

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

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,
then the tens digit of the first number by the ones digit of the second number, and so on.

Now we'll get the exercise:

$81.21\times0.3=$

Let's remember that:

$0.3=\text{0}.30$

And we'll get:

$24.336$

Let's not forget to add the variable at the end, and thus the answer will be:

$24.336 x$

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:

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