Examples with solutions for Associative Property: By multiplication only

Exercise #1

7×5×2= 7\times5\times2=

Video Solution

Step-by-Step Solution

According to the rules of the order of operations, you can use the substitution property and start the exercise from right to left to comfortably calculate:

5×2=10 5\times2=10

7×10=70 7\times10=70

Answer

70

Exercise #2

3×5×4= 3\times5\times4=

Video Solution

Step-by-Step Solution

According to the order of operations, we must solve the exercise from left to right.

But, this can leave us with awkward or complicated numbers to calculate.

Since the entire exercise is a multiplication, you can use the associative property to reorganize the exercise:

3*5*4=

We will start by calculating the second exercise, so we will mark it with parentheses:

3*(5*4)=

3*(20)=

Now, we can easily solve the rest of the exercise:

3*20=60

Answer

60

Exercise #3

12×5×6= 12\times5\times6=

Video Solution

Step-by-Step Solution

According to the rules of the order of operations, we solve the exercise from left to right:

12×5=60 12\times5=60

60×6=360 60\times6=360

Answer

360

Exercise #4

35×6×2= 35\times6\times2=

Video Solution

Step-by-Step Solution

According to the rules of the order of operations, you can use the substitution property and organize the exercise in a more convenient way to calculate:

35×2×6= 35\times2\times6=

We solve the exercise from left to right:

35×2=70 35\times2=70

70×2=140 70\times2=140

Answer

420

Exercise #5

Solve the following problem:

11x×5×6= 11x\times5\times6=

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 itself, for example in this case: 11×x 11\times x
Therefore, we can apply the distributive property to separate the variable, and come back to it later.
Proceed to solve the exercise from right to left since it's simpler this way.

5×6=30 5\times6=30

We obtain the following:

11x×30= 11x\times30=

We'll put aside the x and add it at the end of the exercise.

By solving the exercise in an organized way we simplify the solution process.

It's important to maintain the correct order when solving the problem, meaning first multiply the ones of the first number by the ones of the second number,
then the tens of the first number by the ones of the second number, and so on.

30×11=330 30\\\times11\\=330

Don't forget to add the variable at the end. The answer is as follows:

330x 330x

Answer

330x 330x

Exercise #6

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 #7

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

Exercise #8

Solve the following problem:

356×556×13x= 3\frac{5}{6}\times5\frac{5}{6}\times\frac{1}{3}x=

Video Solution

Step-by-Step Solution

First, let's convert all mixed fractions to simple fractions:

3×6+56×5×6+56×13x= \frac{3\times6+5}{6}\times\frac{5\times6+5}{6}\times\frac{1}{3}x=

Let's solve the exercises with the eight fractions:

18+56×30+56×13x= \frac{18+5}{6}\times\frac{30+5}{6}\times\frac{1}{3}x=

236×356×13x= \frac{23}{6}\times\frac{35}{6}\times\frac{1}{3}x=

Since the exercise only involves multiplication, we'll combine all the numerators and denominators:

23×356×6×3x=805108x \frac{23\times35}{6\times6\times3}x=\frac{805}{108}x

Answer

805108x \frac{805}{108}x