All Operations in the Order of Operations: Using fractions

$(85+5):10=$

According to the order of operations rules, we must first solve the expression within the parentheses:

$85+5=90$

We should obtain the following expression:

$90:10=9$

9

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

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:

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

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

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

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

$5\frac{1}{4}$

$0.5-0.1:0.2=$

According to the order of operations in arithmetic, multiplication and division take precedence over addition and subtraction.

We'll start with the division operation and write the fractions as decimal fractions, then as simple fractions:

$0.1:0.2=\frac{0.1}{0.2}=\frac{1}{2}$

In the next step, we'll write the decimal fraction 0.5 as a simple fraction:

$0.5=\frac{1}{2}$

Now let's solve the problem

$\frac{1}{2}-\frac{1}{2}=0$

0

$11:2+4\frac{1}{2}=$

According to the order of operations rules, we first enter the division problem into parentheses:

$(11:2)+4\frac{1}{2}=$

Let's solve the problem inside the parentheses:

$11:2=\frac{11}{2}=5\frac{1}{2}$

Now we get the expression:

$5\frac{1}{2}+4\frac{1}{2}=10$

10

$\frac{12+8}{5}=$

First, we'll solve the numerator of the fraction according to the order of operations, from left to right:

$12+8=20$

Now we'll get the exercise:

$\frac{20}{5}=20:5=4$

4

$5-2\times\frac{1}{2}+1=$

בשלב הראשון של התרגיל יש לחשב את הכפל.

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

מכאן ניתן להמשיך לשאר פעולות החיבור והחיסור, מימין לשמאל.

$5-1+1=5$

5

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

Let's first solve the numerator of the fraction according to the order of operations, from left to right:

$5+3=8$

$8-2=6$

Now we'll get the exercise:

$\frac{6}{3}=6:3=2$

2

$7-1+\frac{1}{2}=$

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

$7-1=6$

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

6 1/2

$7+1+0.2=$

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

$7+1=8$

$8+0.2=8.2$

8.2

$11-3:4=$

According to the order of operations rules, we'll put the division operation in parentheses:

$11-(3:4)=$

Let's solve the operation inside the parentheses:

$3:4=\frac{3}{4}$

And we'll get the expression:

$11-\frac{3}{4}=10\frac{1}{4}$

$10\frac{1}{4}$

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

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:

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

$3\frac{1}{12}$

$12:(4\times2-\frac{9}{3})=$

Given that, according to the rules of the order of operations, parentheses come first, we will first solve the exercise that appears within the parentheses.

$4\times2-\frac{9}{3}=$

We solve the multiplication exercise:

$4\times2=8$

We divide the fraction (numerator by denominator)$\frac{9}{3}=3$

And now the exercise obtained within the parentheses is$8-3=5$

Finally, we divide:$12:5=\frac{12}{5}$

$\frac{12}{5}$

$\frac{1\frac{1}{2}}{6}=\text{?}$

Let's first refer to the numerator of the fraction, we'll convert it to an addition exercise of two fractions:

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

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

Now we get:

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

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

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

Let's multiply the two fractions - numerator by numerator and denominator by denominator:

$\frac{1\times3}{2\times6}=$

$\frac{3}{12}=\frac{3}{3\times4}$

Let's simplify:

$\frac{3}{3\times4}=\frac{1}{4}$

$\frac{1}{4}=0.25$

$0.25$

$20-\frac{16-10}{2}=\text{?}$

According to the order of operations, we will first solve the fraction exercise:

$\frac{16-10}{2}=\frac{6}{2}=3$

$20-3=17$

$17$

$\frac{90-15-3}{8}=$

Let's first solve the numerator of the fraction, according to the order of operations from left to right:

$90-15=75$

$75-3=72$

Now we get the exercise:

$\frac{72}{8}=72:8=9$

$9$

$\frac{20}{2+3}+6=\text{?}$

According to the order of operations, we will first solve the fraction exercise:

$\frac{20}{3+2}=\frac{20}{5}=4$

$4+6=10$

$10$

$\frac{20-5}{7+3}=$

First, let's solve the numerator of the fraction:

$20-5=15$

Now let's solve the denominator of the fraction:

$7+3=10$

We get:

$\frac{15}{10}=1\frac{5}{10}=1\frac{1}{2}$

$1\frac{1}{2}$

$\frac{0.18+0.37}{89+13-\frac{2}{1}}=$

Let's first calculate the numerator of the fraction:

$0.18+0.37=0.55$

Now let's calculate the denominator of the fraction, we'll start with the division exercise:

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

Now we get the exercise:

$89+13-2=$

Let's solve from left to right:

$89+13=102$

$102-2=100$

Now we have the exercise:

$\frac{0.55}{100}=0.55:100$

We'll move the decimal point two places to the left (according to the two zeros of 100)

And we'll get the number:

$0.0055$

0.0055

$\frac{21:\sqrt{49}+2}{8-(2+2\times3)}=$

In the numerator we solve the square root exercise:

$\sqrt{49}=7$

In the denominator we solve the exercise within parentheses:

$(2+2\times3)=$

$2+6=8$

The exercise we now have is:

$\frac{21:7+2}{8-8}=$

We solve the exercise in the numerator of fractions from left to right:

$21:7=3$

$3+2=5$

We obtain the exercise:

$\frac{5}{8-8}=\frac{5}{0}$

Since it is impossible for the denominator of the fraction to be 0, it is impossible to solve the exercise.

Cannot be solved