Parentheses in simple Order of Operations: Using fractions

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

$7-1=6$

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

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

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.

$5-1+1=5$

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:

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

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 $5$.

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

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

Then solve the operations inside the parenthesis:

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

Now we get the expression:

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

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: $\frac{1}{3}$.

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:

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

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 $\frac{9}{42+7}$, 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 $\frac{9}{49}$.