All Operations in the Order of Operations: Using fractions

Let's begin by solving the numerator of the fraction from left to right, according to the order of operations:

$90-15=75$

$75-3=72$

We should obtain the following exercise:

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

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

$7-1=6$

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

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

$7+1=8$

$8+0.2=8.2$

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.

$5-1+1=5$

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:

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

According to rules of the order of operations, we must first place the division operation within parentheses:

$11-(3:4)=$

We then proceed to solve the operation inside of the parentheses:

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

We should obtain the following expression:

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

Let's begin by solving the numerator of the fraction according to the order of operations, from left to right:

$5+3=8$

$8-2=6$

We should obtain the following exercise:

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

Let's begin by solving the numerator of the fraction, from left to right, according to the order of operations:

$12+8=20$

We should obtain the following exercise:

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

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

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

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:

$90:10=9$

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:

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

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

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

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

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:

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

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:$12:5=\frac{12}{5}$

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:

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

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:

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

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

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

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

$4+6=10$

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

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

$20-3=17$

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:

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

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

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:

$0.0055$

We start by solving the exercise in the numerator and then solve the exercise in the denominator.

We know that multiplication and division operations come before addition and subtraction operations, so first we will divide 15:3 and then multiply the result by 2:

$15:3=5$

$12-5\times2=12-10=2$

The result of the numerator is 2 and now we will solve the exercise that appears in the denominator.

It is known that according to the rules of the order of operations, the exercise that appears between parentheses goes first, so we first solve the exercise$2+3=5$

$$Now, we solve the division exercise:$10:5=2$

The result we get in the denominator is 2.

Finally, divide the numerator by the denominator:

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