Division of Whole Numbers with Multiplication in Parentheses

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

Another way to solve this exercise is to apply the order of operations, that is:

$24:\left(6\times2\right)=$

We will start by solving the expression in parentheses using the order of operations and we will get:

$24:12=2$

If you are interested in this article you may also be interested in the following articles:

• Subtraction of whole numbers with parentheses where there are additions
• Subtraction of whole numbers with parentheses in which there are subtractions
• Division of integers with parentheses in which there is division

For a wide range of math articles visit the Tutorelablog.

Task:

$87:(12\times(35:(2\times12)))=$

Solution:

We first tackle the innermost parentheses and break down the expression to make the calculation easier.

$87:(12\times(35:(2\times10+2\times2)))=$

We solve the exercise in the innermost parentheses.

$87:(12\times(35:(20+4)))=$

$87:(12\times(35:24))=$

We break down the $35$ into $2$ numbers to make the calculation easier.

$87:(12\times(24+11):24))=$

We solve accordingly.

$87:(12\times(1+\frac{11}{24}))=$

$87:(12+\frac{12\times11}{24})$

We reduce the fraction by $2$ and continue solving accordingly.

$87:(12+\frac{11}{2})=$

We convert the simple fraction into a decimal number.

$87:\left(12+5.5\right)=$

We solve accordingly.

$87:17.5=$

We can multiply the expression by $2$ to make the calculation easier.

$174:35=$

We break down the $174$ into $2$ numbers to make the calculation easier.

$\left(175-1\right):35=$

We convert the exercise into a simple fraction.

$\frac{175}{35}-\frac{1}{35}=$

$5-\frac{1}{35}=$

$4\frac{34}{35}$

Answer:

$4\frac{34}{35}$

Task:

$13:(9\times(4:(18\times5)))=$

Solution:

We deal with the innermost parentheses first.

$13:(9\times(\frac{4}{18\times5}))=$

We continue solving the exercise.

$=13:\left(9\cdot\left(\frac{4}{18\cdot5}\right)\right)=13:\frac{9\cdot4}{18\cdot5}$

$=\frac{13\cdot5}{2}=\frac{10\cdot5+3\cdot5}{2}=\frac{50+15}{2}$

$=25+7.5=32.5$

Answer:

$32.5$

Task:

$7:(8\times(10:(3\times12)))=$

Solution:

We convert the inner parentheses into a multiplication expression.

$7:\frac{8\times10}{3\times12}=$

$\frac{21\cdot3}{20}$

$\frac{63}{20}=\frac{60+3}{20}=3+\frac{3}{20}$

We multiply the last fraction by $5$ so that it represents a decimal fraction.

$3+\frac{15}{100}$

Answer:

$3.15$

Task:

$35:(2\times7)=$

Solution:

We convert $35$ into a multiplication expression to make the calculation easier.

$(5\times7):(2\times7)=$

Let's reduce by the $7$

$5:2=$

We break down the $5$ into an addition expression to make the calculation easier.

$\left(4+1\right):2=$

We convert the exercise into simple fractions.

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

We solve accordingly.

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

Answer:

$2\frac{1}{2}$

Task:

$60:(10\times2)=$

Solution

We convert $60$ into a multiplication expression and divide the exercise between parentheses (we create a simple fraction).

$\frac{6\times10}{2\times10}=$

Simplify the $10$ and solve.

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

Answer:

$3$

The parentheses are a grouping sign. As the name implies, they helps us to group operations where certain mathematical operations need to be performed. These parentheses indicate that the operations must be performed from the inside out, that is, first we must solve the operations that are inside the parentheses, in this case the multiplication, and then use that number in our division operation.

The operations in an expression have an order that we must solve by. The order of operations has a useful acronym (PEMDAS):

1. Parentheses
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction.

While it is true that we can just use the order of operations to solve this type of problem, we can also remove the parentheses with the following formula:

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

In order to eliminate the parentheses in a division expression with multiplication inthe parentheses, we can use the formula mentioned above or use the order of operations, let's see some examples:

Task:

$90:\left(5\times9\right)=$

We can eliminate the parentheses with the formula that we already know:

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

And the result will be as follows:

$90:5:9=$

We proceed to solve the first division.

$90:5:9=18:9$

Finally, we perform the division.

$18:9=2$

Answer:

$2$

Now we will solve the same example, but by using the order of operations.

$90:\left(5\times9\right)=$

In this case, we start by solving the operation that is inside the parentheses, that is, the multiplication of $5\times9$

$90:\left(5\times9\right)=90:45$

Next, we perform the division.

$90:45=2$

Notice that we got the same result with both methods.

Task:

$240:\left(10\times\left(20:\left(5\times4\right)\right)\right)=$

Here we are going to split the exercise into two parts, since it presents the same form twice. Then we can proceed to solve it by using the formula. We'll start with the following parentheses:

$20:\left(5\times4\right)=20:5:4$

$20:5:4=4:4=1$

Since $20:\left(5\times4\right)=1$ we can substitute this result in the first operation giving us the following:

$240:\left(10\times\left(20:\left(5\times4\right)\right)\right)=240:\left(10\times1\right)=$

Again, we can use the formula or order of operations.

In $240:\left(10\times1\right)=$, we will use the formula.

$240:\left(10\times1\right)=240:10:1=$

$24:1=24$

Result

$24$