Examples with solutions for Multiplication of Decimal Fractions: More than two fractions

Exercise #1

Calculate the following exercise:

4.5×3.2×5.6= 4.5\times3.2\times5.6=

Video Solution

Step-by-Step Solution

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:

4.5×3.2=14.40 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:

14.40×5.6= 14.40\times5.6=

Remember that:

14.40=14.4 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:

14.4×5.6=80.64 14.4\\\times5.6\\=80.64

Answer

80.64 80.64

Exercise #2

Solve the following problem:

11.2×5.6×7.3= 11.2\times5.6\times7.3=

Video Solution

Step-by-Step Solution

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:

11.2×5.6=62.72 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:

62.72×7.3= 62.72\times7.3=

Remember that:

7.3=7.30 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:

457.856 457.856

Answer

457.856 457.856

Exercise #3

Solve the following problem:

0.5×6.7×6.31= 0.5\times6.7\times6.31=

Video Solution

Step-by-Step Solution

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:

0.5×6.7=3.35 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::

3.35×6.31= 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:

3.35×6.31=21.1385 3.35\\\times6.31\\=21.1385

Answer

21.1385 21.1385

Exercise #4

Solve the following problem:

15.6×5.2x×0.3= 15.6\times5.2x\times0.3=

Video Solution

Step-by-Step Solution

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×x 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×    5.2= 81.12 ~~~~~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:

81.21×0.3= 81.21\times0.3=

Remember that:

0.3=0.30 0.3=\text{0}.30

Calculate:

24.336 24.336

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

24.336x 24.336 x

Answer

24.336x 24.336x