Associative Property: Using fractions

$1+2\times3-7:4=$

According to the rules of the order of arithmetic operations, we must first enclose both the multiplication and division exercises inside of parentheses:

$1+(2\times3)-(7:4)=$

We then solve the exercises within the parentheses:

$2\times3=6$

$7:4=\frac{7}{4}$

We obtain the following:

$1+6-\frac{7}{4}=$

We continue by solving the exercise from left to right:

$1+6=7$

$7-\frac{7}{4}=$

Lastly we break down the numerator of the fraction with a sum exercise as seen below:

$7-(\frac{4+3}{4})$

$7-(\frac{4}{4}+\frac{3}{4})$

$7-(1+\frac{3}{4})$

$7-1\frac{3}{4}=5\frac{1}{4}$

$5\frac{1}{4}$

$3+\frac{3}{3}\times\frac{2}{3}-2=$

According to the rules of the order of arithmetic operations, we first place the multiplication exercise inside of parentheses:

$3+(\frac{3}{3}\times\frac{2}{3})-2=$

We then solve the exercise in the parentheses, combining the multiplication into a single exercise:

$(\frac{3}{3}\times\frac{2}{3})=\frac{3\times2}{3\times3}=\frac{6}{9}=\frac{2}{3}$

We obtain the following exercise:

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

Lastly we solve the exercise from left to right:

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

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

$1\frac{2}{3}$

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

According to the rules of the order of arithmetic operations, we must first place the two multiplication exercises inside of the parentheses:

$(\frac{1}{4}\times\frac{1}{3})+(4\times\frac{3}{4})=$

We then focus on the left parenthesis and combine the multiplication exercise:

$(\frac{1}{4}\times\frac{1}{3})=\frac{1\times1}{4\times3}=\frac{1}{12}$

Next we focus on the right parenthesis and we again combine the multiplication exercise:

$(4\times\frac{3}{4})=\frac{4\times3}{4}=\frac{12}{4}=3$

Finally we obtain the following exercise:

$\frac{1}{12}+3=3\frac{1}{12}$

$3\frac{1}{12}$

$-5+3+4=$

This exercise can be solved in order, but to make it easier, the associative property can be used

$-5+(3+4)=$

$-5+7=$

$7-5=2$

$2$

$\frac{3}{4}\times\frac{2}{3}\times2\frac{1}{4}x=$

First, we'll combine the simple fractions into a single multiplication exercise:

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

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

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

We'll simplify the simple fraction and get:

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

$1\frac{1}{8}x$

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

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:

$\frac{7}{15}$

$\frac{7}{15}$

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

We move the fraction to the beginning of the exercise and will place the rest of the exercise in parentheses to make solving the equation easier:

$\frac{a}{4}+(2-2)=$

$\frac{a}{4}+0=\frac{a}{4}$

$\frac{9}{4}$

$\frac{2}{3}\times7\frac{2}{3}\times3\frac{1}{2}=$

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:

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

$17\frac{8}{9}$

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

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:

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

$2\frac{5}{24}x$

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

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:

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

$\frac{161}{256}$

$3\frac{5}{6}\times5\frac{5}{6}\times\frac{1}{3}x=$

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:

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

$\frac{805}{108}x$

$4.1\cdot1.6\cdot3.2+4.7=\text{?}$

We begin by converting the decimal numbers into mixed fractions:

$4\frac{1}{10}\times1\frac{6}{10}\times3\frac{2}{10}+4\frac{7}{10}=$

We then convert the mixed fractions into simple fractions:

$\frac{41}{10}\times\frac{16}{10}\times\frac{32}{10}+\frac{47}{10}=$

We solve the exercise from left to right:

$\frac{41\times16}{10\times10}=\frac{656}{100}$

This results in the following exercise:

$\frac{656}{100}\times\frac{32}{10}+\frac{47}{10}=$

We solve the multiplication exercise:

$\frac{656\times32}{100\times10}=\frac{20,992}{1,000}$

Now we get the exercise:

$\frac{20,992}{1,000}+\frac{47}{10}=$

We then multiply the fraction on the right so that its denominator is also 1000:

$\frac{47\times100}{10\times100}=\frac{4,700}{1,000}$

We obtain the exercise:

$\frac{20,992}{1,000}+\frac{4,700}{1,000}=\frac{20,992+4,700}{1,000}=\frac{25,692}{1,000}$

Lastly we convert the simple fraction into a decimal number:

$\frac{25,692}{1,000}=25.692$

25.692

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

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:

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

$14\frac{5}{6}$

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

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:

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

$8\frac{1}{2}$

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

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

Let's note that:

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

Now we'll get the exercise:

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

$3\frac{3}{4}$

$\frac{6}{7}x+\frac{8}{7}x+3\frac{2}{3}x=$

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:

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

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

$4\frac{2}{3}+5\frac{2}{3}+6\frac{1}{3}=\text{?}$

$16\frac{2}{3}$

$\frac{2}{3}\times\frac{1}{4}+\frac{1}{6}\times\frac{5}{2}=$

$\frac{7}{12}$

$\frac{4}{9}\times\frac{1.5}{2}+\frac{3}{4}\times\frac{3}{3}=$

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

$\frac{4}{7}\cdot\frac{3}{2}\cdot\frac{7}{4}=\text{?}$

$\frac{3}{2}$