Associative Property: More than two fractions

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:

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

First we will break down each of the factors in the exercise into a whole number and its remainder:

$8+0.5+5+0.2+8+0.4=$

Now we'll combine only the whole numbers:

$8+5+8=13+8=21$

Then we'll calculate the remainder:

$0.5+0.2+0.4=0.7+0.4=1.1$

Finally, we are left with the following:

$21+1.1=22.1$

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

We will first calculate the addition exercise in the vertical column, since it contains two numbers after the decimal point:

$0.85+7.61=8.46$

Now we will get the exercise:

$8.46+2.3=$

Let's remember that:

$2.3=2.30$

We will calculate in the vertical column and get:

$10.76$

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:

$457.856$

Note that the right-hand side of the addition exercise between the fractions gives a result of a whole number, so we'll start with that:

$6\frac{2}{3}+\frac{1}{3}=7$

Giving us:

$7\frac{5}{6}+7=14\frac{5}{6}$

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

Let's note that in the first addition exercise, we have an addition between two halves that will give us a whole number, so:

$\frac{1}{2}+3\frac{1}{2}=4$

Now we will get the exercise:

$4+4\frac{2}{4}=$

Let's note that we can simplify the mixed fraction:

$\frac{2}{4}=\frac{1}{2}$

Now the exercise we get is:

$4+4\frac{1}{2}=8\frac{1}{2}$

According to the rules of the order of operations in arithmetic, we solve the exercise from left to right.

Let's note that:

$\frac{1}{3}+\frac{2}{3}=\frac{3}{3}=1$

We should obtain the following exercise:

$1+2\frac{3}{4}=3\frac{3}{4}$

Let's solve the exercise from left to right.

We will combine the left expression in the following way:

$\frac{6+8}{7}x=\frac{14}{7}x=2x$

Now we get:

$2x+3\frac{2}{3}x=5\frac{2}{3}x$

The first step is factorising each of the terms in the exercise into a whole number and its remainder:

$10x+0.1x+5x+0.2x+2x+0.4x=$

Now we'll combine only the whole numbers:

$10x+5x+2x=15x+2x=17x$

Next, we will calculate the remainder:

$0.1x+0.2x+0.4x=0.3x+0.4x=0.7x$

Finally, we are left with the following:

$17x+0.7x=17.7x$

First, let's convert the mixed fraction to an improper fraction as follows:

$\frac{1}{5}\times\frac{7}{8}\times\frac{3\times2+2}{3}=$

Let's solve the equation in the numerator:

$\frac{1}{5}\times\frac{7}{8}\times\frac{6+2}{3}=$

$\frac{1}{5}\times\frac{7}{8}\times\frac{8}{3}=$

Since the only operation in the equation is multiplication, we'll combine everything into one equation:

$\frac{1\times7\times8}{5\times8\times3}=$

Let's simplify the 8 in the numerator and denominator of the fraction:

$\frac{1\times7}{5\times3}=$

Let's solve the equations in the numerator and denominator and we get:

$\frac{7}{15}$

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

$0.2x+8.6x=8.8x$

We'll break down 8.8 into a smaller addition exercise that will be easier for us to calculate:

$8x+0.8x+0.65x=$

Now we'll use the commutative property since the exercise only involves addition.

Let's focus on the leftmost addition exercise, remembering that:

$0.8=0.80$$$

We'll calculate the following exercise:

$0.80x+0.65x=1.45x$

And finally, we'll get the exercise:

$8x+1.45x=9.45x$

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:

$24.336 x$

Let's begin by combining the simple fractions into a single multiplication exercise:

$\frac{3\times2}{4\times3}\times2\frac{1}{4}x=$

Let's now proceed to solve the exercise in the numerator and denominator:

$\frac{6}{12}\times2\frac{1}{4}x=$

Finally we'll simplify the simple fraction in order to obtain the following:

$\frac{1}{2}\times2\frac{1}{4}x=1\frac{1}{8}x$

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

$\frac{3\times6+5}{6}\times\frac{5\times6+5}{6}\times\frac{1}{3}x=$

Let's solve the exercises with the eight fractions:

$\frac{18+5}{6}\times\frac{30+5}{6}\times\frac{1}{3}x=$

$\frac{23}{6}\times\frac{35}{6}\times\frac{1}{3}x=$

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

$\frac{23\times35}{6\times6\times3}x=\frac{805}{108}x$

First, we'll convert the mixed fractions to simple fractions as follows:

$\frac{2}{3}\times\frac{7\times3+2}{3}\times\frac{3\times2+1}{2}=$

Let's solve the exercises in the fraction multiplier:

$\frac{2}{3}\times\frac{21+2}{3}\times\frac{6+1}{2}=$

$\frac{2}{3}\times\frac{23}{3}\times\frac{7}{2}=$

Since the only operation in the exercise is multiplication, we'll combine everything into one exercise and get:

$\frac{2\times23\times7}{3\times3\times2}=\frac{46\times7}{9\times2}=\frac{322}{18}$

First, let's find a common denominator for 4, 8, and 6: it's 24.

Now, we'll multiply each fraction by the appropriate number to get:

$\frac{5\times4}{6\times4}x+\frac{7\times3}{8\times3}x+\frac{2\times6}{4\times6}x=$

Let's solve the multiplication exercises in the numerator and denominator:

$\frac{20}{24}x+\frac{21}{24}x+\frac{12}{24}x=$

We'll connect all the numerators:

$\frac{20+21+12}{24}x=\frac{41+12}{24}x=\frac{53}{24}x$

Let's break down the numerator into a smaller addition exercise:

$\frac{48+5}{24}=\frac{48}{24}+\frac{5}{24}=2+\frac{5}{24}=2\frac{5}{24}x$

First, let's convert the mixed fraction to a simple fraction as follows:

$\frac{7}{8}\times\frac{8\times2+7}{8}\times\frac{1}{4}=$

Let's solve the exercise in the numerator:

$\frac{7}{8}\times\frac{16+7}{8}\times\frac{1}{4}=$

$\frac{7}{8}\times\frac{23}{8}\times\frac{1}{4}=$

Since the only operation in the exercise is multiplication, we'll combine everything into one exercise:

$\frac{7\times23\times1}{8\times8\times4}=$

Let's solve the exercises in the numerator and denominator:

$\frac{7\times23}{64\times4}=\frac{161}{256}$