Additional Arithmetic Rules: Exercises with 2 terms

To solve this problem, we'll follow these steps:

• Step 1: Calculate the sum inside the parentheses.
• Step 2: Subtract the result of the sum from 100.

Now, let's work through each step:
Step 1: Calculate $5 + 55$, which gives $60$.
Step 2: Perform the subtraction $100 - 60$, which equals $40$.

Therefore, the solution to the problem is $40$.

To solve the expression $10 : (10 : 5)$, we will apply the order of operations systematically.

Step 1: Evaluate the inner division $10 : 5$.
When we compute $10 : 5$, we are finding how many times 5 fits into 10. This calculation can be expressed as:
$\frac{10}{5} = 2$.

Step 2: Substitute the result from step 1 into the outer division.
Now, we substitute $10 : (10 : 5)$ with $10 : 2$. Once again, we apply division:
$\frac{10}{2} = 5$.

Therefore, the solution to the expression $10 : (10 : 5)$ is $5$.

First we need to apply the following formula:

$a:(b\times c)=a:b:c$

Therefore, we get:

$15:2:5=$

Now, let's rewrite the exercise as a fraction:

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

Then we'll convert it to a multiplication of two fractions:

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

Finally, we multiply numerator by numerator and denominator by denominator, leaving us with:

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

To solve the expression $18 \div (6 \times 3)$, we need to follow the order of operations, which specifies that multiplication should be performed before division. Therefore, we proceed as follows:

• Step 1: Calculate the operation inside the parentheses: $(6 \times 3)$.
  We multiply $6$ by $3$ to get $18$.
• Step 2: Replace the multiplication expression in the original division: $18 \div 18$.
• Step 3: Perform the division: $18 \div 18 = 1$.

Thus, the result of the expression $18 \div (6 \times 3)$ is $\mathbf{1}$.

To solve the problem $19 - (5 + 11)$, we will follow these steps:

• Step 1: Evaluate the expression inside the parentheses. This means we need to calculate $5 + 11$.
• Step 2: Once the sum inside the parentheses is found, subtract this sum from 19.

Let's work through each step:

Step 1: Calculate $5 + 11$ which equals 16.

Step 2: Substitute 16 in place of $5 + 11$ in the original expression. You have $19 - 16$.

Now, solve $19 - 16$, which equals 3.

Therefore, the solution to the problem is $3$.

To solve the expression $2 - (1 + 1)$, follow these steps:

• First, evaluate the expression inside the parentheses: $1 + 1$.
• This gives $2$.
• Now replace the parentheses with this result, transforming the expression to $2 - 2$.
• The result of $2 - 2$ is $0$.

Therefore, the solution to the expression is $0$.

We will use the formula:

$a:(b:c)=a:b\times c$

Therefore, we will get:

$21:30\times10=$

Let's write the division exercise as a fraction:

$\frac{21}{30}=\frac{7}{10}$

Now let's multiply by 10:

$\frac{7}{10}\times\frac{10}{1}=$

We'll reduce the 10 and get:

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

To solve this problem, we'll follow these steps:

• Step 1: Evaluate the inner expression $6 - 13$
• Step 2: Substitute the result from Step 1 into $21 - \text{result from Step 1}$

Now, let's work through each step:

Step 1: Calculate $6 - 13$. In this calculation, we subtract 13 from 6. The result is $-7$, because when subtracting a larger number from a smaller one, the result is negative.

Step 2: Substitute $-7$ into the outer expression $21 - (-7)$. Since subtracting a negative is equivalent to adding the positive opposite, this simplifies to $21 + 7$.

Now, compute $21 + 7$, which equals 28.

Therefore, the solution to the problem is $28$.

To solve the problem $26 - (11 - 2)$, we'll proceed as follows:

Step 1: Evaluate the expression inside the parentheses:

• $11 - 2 = 9$

Step 2: Subtract this result from 26:

• $26 - 9 = 17$

Therefore, the solution to the problem is $17$.

To solve this problem, we'll follow these steps:

• Step 1: Compute the product $5 \times 6$.
• Step 2: Perform the division operation $300 \div 30$.

Now, let's work through each step:

Step 1: Calculate $5 \times 6$.

$5 \times 6 = 30$

Step 2: Divide 300 by the result from Step 1.

$300 \div 30 = 10$

Therefore, the solution to the problem is $\boxed{10}$.

This matches the choice: 10.

To solve this problem, we'll follow these steps:

• Step 1: Calculate $2000 \div 25$.
• Step 2: Calculate $500 \div (\text{result from Step 1})$.

Let's work through each step:

Step 1: Calculate $2000 \div 25$.

$2000 \div 25$ can be calculated as follows:

Divide 2000 by 25:

$2000 \div 25 = 80$

Step 2: Use the result from Step 1 to perform the division with 500.

Now, calculate $500 \div 80$.

$500 \div 80 = \frac{500}{80} = \frac{25}{4} = 6.25$

Finally, $6.25$ can be expressed as a mixed number:

$6\frac{1}{4}$

Therefore, the solution to the problem is $6\frac{1}{4}$.

To solve this problem, we'll follow these steps:

• Step 1: Evaluate the inner division $360 : 60$.
• Step 2: Use the result from Step 1 to evaluate the outer division $66 : \text{(result from Step 1)}$.

Now, let's work through each step:

Step 1: Evaluate $360 : 60$. This means $\frac{360}{60}$. Dividing, we have:

$\frac{360}{60} = 6$.

Step 2: Use the result from Step 1 to evaluate $66 : 6$. This means $\frac{66}{6}$. Dividing, we get:

$\frac{66}{6} = 11$.

Therefore, the solution to the problem is $11$.

To solve this problem, we'll follow these steps:

• Step 1: Calculate the product of $14$ and $5$.
• Step 2: Use this product to divide $70$.
• Step 3: Compare the calculated result with the given choices.

Now, let's work through each step:
Step 1: First, calculate the product of $14$ and $5$. Using basic multiplication:
$14 \times 5 = 70$ Step 2: Divide $70$ by the product, which is also $70$:
$70 \div 70 = 1$

Therefore, the solution to the problem is $1$. This matches choice 1 from the provided options.

To solve this problem, we will follow these steps to evaluate the expression $87 - (7 + 0)$.

Step 1: Start by evaluating the expression inside the bracket:

$7 + 0 = 7$

Step 2: Substitute the value back into the original expression:

$87 - 7$

Step 3: Perform the subtraction:

$87 - 7 = 80$

Therefore, the solution to the problem is $80$.

To solve this problem, we'll follow these steps:

• Step 1: Perform the inner division operation.
• Step 2: Use the result of Step 1 in the outer division operation.

Now, let's work through each step:

Step 1: Calculate $33:10$.
This operation is equivalent to dividing 33 by 10, which gives us:
$\frac{33}{10} = 3.3$.

Step 2: Use the result from Step 1 to perform the division $99:3.3$.
This operation now becomes:
$\frac{99}{3.3} = 30$.

Therefore, the solution to the problem is $30$.

To solve this problem, we'll follow these steps:

• Step 1: Convert $100\frac{1}{4}$ to an improper fraction.
• Step 2: Calculate the product $\frac{1}{4} \times 5$.
• Step 3: Perform the division of the improper fraction by the product from step 2.
• Step 4: Convert the result to a mixed number if needed.

Now, let's work through each step:
Step 1: The mixed number $100\frac{1}{4}$ converts to an improper fraction as follows:
$100\frac{1}{4} = \frac{100 \times 4 + 1}{4} = \frac{401}{4}$.
Step 2: The product of the fraction and integer is $\frac{1}{4} \times 5 = \frac{5}{4}$.
Step 3: We perform the division $\frac{401}{4} : \frac{5}{4}$. In fraction terms, this is:
$\frac{401}{4} \times \frac{4}{5} = \frac{401 \times 4}{4 \times 5} = \frac{401}{5}$.
Step 4: Convert $\frac{401}{5}$ to a mixed number:
Perform the division $401 \div 5$; quotient is 80 and remainder is 1.
Thus, $\frac{401}{5} = 80\frac{1}{5}$.

Therefore, the solution to the problem is $80\frac{1}{5}$.

To solve the problem $10 \div (5 \times \frac{1}{2})$, we'll follow these steps:

• Step 1: Evaluate the expression inside the parentheses. Multiply $5$ by $\frac{1}{2}$.
• Step 2: Use the result from Step 1 for division with $10$.

Now, let's work through each step:

Step 1: Calculate the multiplication inside the parentheses:
$5 \times \frac{1}{2} = \frac{5}{2} = 2.5$.

Step 2: Divide $10$ by the result from Step 1:
$10 \div 2.5 = 4$.

Hence, the solution to the given expression is $4$.

To solve this problem, we’ll follow these steps:

• Step 1: Evaluate the expression inside the parentheses.
• Step 2: Subtract the result from 10.

Now, let's work through each step:
Step 1: Inside the parentheses, we have $\frac{4}{2} + \frac{3}{2}$. First, simplify $\frac{4}{2}$ to 2 and $\frac{3}{2}$ remains as $\frac{3}{2}$.
The sum is $2 + \frac{3}{2} = \frac{4}{2} + \frac{3}{2} = \frac{7}{2}$.
Step 2: Now, subtract $\frac{7}{2}$ from 10.
Express 10 as a fraction: $\frac{20}{2} - \frac{7}{2} = \frac{13}{2}$.
Convert the fraction back to a mixed number: $\frac{13}{2} = 6\frac{1}{2}$.

Therefore, the solution to the problem is $6\frac{1}{2}$.

To solve the problem, follow these steps:

• Step 1: Simplify $0.5 : 0.25$.
• Step 2: Square the result of step 1.
• Step 3: Divide 112 by the result of step 2.

Let's perform each step:
Step 1: Calculate $0.5 : 0.25$.
To find this, divide 0.5 by 0.25. Since dividing by a fraction is the same as multiplying by its reciprocal,
we have: $0.5 \div 0.25 = 0.5 \times 4 = 2$.
Step 2: Now, square this result:
$(2)^2 = 4$.
Step 3: Finally, divide 112 by this square:
$\frac{112}{4} = 28$.

Thus, the solution to the problem is $28$.

To solve this problem, we must first evaluate the nested division expression $15:(15:\frac{1}{2})$.

Let's start by handling the innermost division $15:\frac{1}{2}$. Division by a fraction is equivalent to multiplication by its reciprocal. Therefore:

• The reciprocal of $\frac{1}{2}$ is $2$.
• Hence, $15:\frac{1}{2} = 15 \times 2 = 30$.

Now, we use the result of this inner division, $30$, as the divisor for the outer expression $15:30$.

• Perform the division $15:30$, which simplifies to $\frac{15}{30}$.
• Simplify the fraction $\frac{15}{30}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 15.
• This gives us $\frac{15 \div 15}{30 \div 15} = \frac{1}{2}$.

Therefore, the solution to the problem is $\frac{1}{2}$.