Associative Property: More than two fractions

We will break down each of the factors in the exercise into a whole number and its remainder.

We get:

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

Now we'll combine only the whole numbers:

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

Now we'll calculate the remainder:

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

And now we'll get the exercise:

$21+1.1=22.1$

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, 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:

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

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

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

Now we get:

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

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:

$\frac{7}{15}$

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:

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

We will factor each of the terms in the exercise into a whole number and its remainder.

We get:

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

Now we'll combine only the whole numbers:

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

Now we'll calculate the remainder:

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

And now we'll get the exercise:

$17x+0.7x=17.7x$

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:

$8x+1.45x=9.45x$

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:

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

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 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, 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:

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