Examples with solutions for Associative Property: Decimal numbers

Exercise #1

Solve the following problem:

2x×4.65×6.3= 2x\times4.65\times6.3=

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: 2×x 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×(4+0.65)= 2\times(4+0.65)=

Multiply 2 by each term inside of parentheses:

(2×4)+(2×0.65)= (2\times4)+(2\times0.65)=

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

8+1.3=9.3 8+1.3=9.3

We obtain the following exercise:

9.3×6.3= 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.

9.3×6.3=58.59 9.3\\\times6.3\\=58.59

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

58.59x 58.59x

Answer

58.59x 58.59x

Exercise #2

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