All Operations in the Order of Operations: Using fractions

According to the order of operations, we first place the multiplication operation inside parenthesis:

$(7\times1)+\frac{1}{2}=$

Then, we perform this operation:

$7\times1=7$

Finally, we are left with the answer:

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

According to the order of operations, we will solve the exercise from left to right since it only contains multiplication and division operations:

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

$2\times1=2$

According to the order of operations, since the exercise only involves addition operations, we will solve the problem from left to right:

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

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

In the first stage of the exercise, you need to calculate the multiplication.

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

From here you can continue with the rest of the addition and subtraction operations, from right to left.

$5-1+1=5$

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

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

$0.5+0.5=1$

$1-0=1$

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:

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

To solve the equation $\frac{25+25}{10}=$, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). In this problem, we will tackle the following steps:

• Parentheses: Solve any operations inside the parentheses first. Here, we have a simple addition $25 + 25$.
• So, $25 + 25 = 50$.
• Next, we address the division, which comes after addition:
• Compute the division of the result by 10: $\frac{50}{10}$.
• The result is $5$.

Thus, the value of $\frac{25+25}{10}$ is $5$.

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:

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

To solve the expression $\frac{0.5 + 2}{5}$, we must follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here, we need to focus on the addition within the fraction, and then the division that forms the fraction.

Let's break down the steps:

• Start with the expression inside the numerator: $0.5 + 2$.
• Perform the addition: $0.5 + 2 = 2.5$.
• The expression now becomes: $\frac{2.5}{5}$.
• Next, perform the division: divide 2.5 by 5. To do this, consider the division operation:
• $2.5 \div 5$
• Convert 2.5 to a fraction: $\frac{5}{2}$
• Divide by 5: $\frac{5}{2} \times \frac{1}{5}$ (since dividing by a number is the same as multiplying by its reciprocal).
• This becomes: $\frac{5 \times 1}{2 \times 5} = \frac{5}{10}$
• Simplify the fraction $\frac{5}{10}$ to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (5), resulting in: $\frac{1}{2}$.

Therefore, the value of the expression $\frac{0.5+2}{5}$ is $\frac{1}{2}$, as given.

To solve the expression $\frac{18}{18+36}$, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here we have only addition and division.

First, we perform the operation inside the parentheses, which is addition in this case:

• Add the numbers in the denominator: $18 + 36 = 54$.

Now, we substitute back into the fraction:$\frac{18}{54}$.

Next, simplify the fraction:

• We look for the greatest common divisor (GCD) of 18 and 54. The GCD is 18.

• Divide both the numerator and the denominator by the GCD:

  • $\frac{18}{18} = 1$

  • $\frac{54}{18} = 3$

Thus, the simplified fraction is $\frac{1}{3}$.

The final answer is: $\frac{1}{3}$.

To solve the expression $\frac{9}{42+7}$, we need to follow the order of operations, commonly known by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). In this question, we focus on Parentheses and Addition.

Step-by-Step Solution:

• First, we identify the operation inside the parentheses: $42 + 7$.
• According to the order of operations, we must solve what is inside the parentheses before dealing with any division. So, we perform the addition first.
• Calculate $42 + 7$ to get $49$.
• We then substitute $49$ back into the original expression in the place of $42 + 7$.
• This gives us a simplified expression: $\frac{9}{49}$.
• Since $9$ and $49$ do not have any common factors aside from $1$, this fraction cannot be simplified further.

Therefore, the final answer is $\frac{9}{49}$.

We are given the expression $\frac{100+1}{25}$ and we need to evaluate it step by step according to the order of operations.

Step 1: Evaluate the expression inside the fraction.
We first perform the addition within the numerator:
$100 + 1 = 101$

Step 2: Divide the result by the denominator.
Now we can simplify the fraction:
$\frac{101}{25}$

Step 3: Convert the improper fraction to a mixed number.
To convert $\frac{101}{25}$ to a mixed number, we divide 101 by 25.
25 goes into 101 four times with a remainder:

• 25 times 4 equals 100
• 101 minus 100 equals 1

Therefore, $\frac{101}{25}$ is equivalent to $4 \frac{1}{25}$.

According to the rules of the order of operations, we should first solve the exercise from left to right since there are only multiplication and division operations present:

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

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

According to the order of operations, we must solve the exercise from left to right since it contains only multiplication operations:

$\frac{3}{2}\times1=\frac{3}{2}$

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

Then, we will multiply the 3 by 3 to get:

$\frac{1}{2}\times1=\frac{1}{2}$

According to the order of operations rules, we must first solve the fraction:

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

Resulting in the following expression:

$2-1=1$

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:

$7+1=8$

$8+0.2=8.2$

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:

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

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

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

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

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:

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

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:

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