Additional Arithmetic Rules Practice Problems & Solutions

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 $10 : (10 : 5)$, 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 $5$.

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 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 $3$.