Additional Arithmetic Rules: Exercises with 2 terms

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.

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 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 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: 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 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 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 $0$.

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 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: 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 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 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: 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: 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 $30$.

We will solve the expression $2 - \left(\frac{1}{1} + \frac{1}{2}\right)$ step by step:

• Step 1: Calculate the expression inside the parentheses first.

We have $\frac{1}{1} + \frac{1}{2}$.

• The simplest way to add fractions is to find a common denominator. The denominators here are 1 and 2, so the least common denominator is 2.

Convert $\frac{1}{1}$ to $\frac{2}{2}$ for easy addition:

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

Now add $\frac{2}{2} + \frac{1}{2}$:

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

• Step 2: Subtract this result from 2.

Write 2 as a fraction with a denominator of 2 to facilitate subtraction:

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

Now perform the subtraction:

$\frac{4}{2} - \frac{3}{2} = \frac{1}{2}$

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

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 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 given expression $220 : (15 \times 8)$, follow these steps:

• Step 1: Calculate the multiplication inside the parentheses: $15 \times 8$.

• Step 2: Divide 220 by the result obtained from Step 1.

Let us perform the calculations:

Step 1: Calculate the multiplication.
$15 \times 8 = 120$.

Step 2: Divide 220 by 120.
So, $220 \div 120 = \frac{220}{120}$.

To simplify $\frac{220}{120}$:

Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 20.

The division yields:
$\frac{220}{120} = \frac{11 \times 20}{6 \times 20} = \frac{11}{6}$.

This fraction $\frac{11}{6}$ can be expressed as a mixed number by dividing 11 by 6:

- 11 divided by 6 equals 1 with a remainder of 5, so:

$1\frac{5}{6}$.

Thus, the solution to the problem is $1 \frac{5}{6}$.

To solve this mathematical problem, let's follow a structured approach:

Step 1: Convert the Mixed Number to an Improper Fraction

The first part of the problem is to convert $20\frac{1}{2}$ into an improper fraction. To do this, follow the standard conversion method:

• Multiply the denominator of the fractional part by the integer part. Here, $2 \times 20 = 40$.
• Add the numerator of the fractional part. So, $40 + 1 = 41$.
• This results in the improper fraction $\frac{41}{2}$.

Step 2: Perform the Multiplication

Next, we need to multiply the improper fraction $\frac{41}{2}$ by 4. Treat 4 as a fraction $\frac{4}{1}$, and multiply:

• Numerator: $41 \times 4 = 164$.
• Denominator: $2 \times 1 = 2$.
• The result of the multiplication is $\frac{164}{2}$.

Next, simplify the fraction $\frac{164}{2}$ to find the product:

• $\frac{164}{2} = 82$.

Step 3: Perform the Division

Finally, divide 492 by the result from step 2:

• $492 \div 82 = 6$.

Thus, the final result of the given expression $492: (20\frac{1}{2} \times 4)$ is $\boxed{6}$.