## In general, this operation can be expressed by the following formula

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

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:

$24:12=2$

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## Exercises for dividing whole numbers with multiplication in parentheses

### Exercise 1

**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:**

$4\frac{34}{35}$

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### Exercise 2

**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:**

$32.5$

### Exercise 3

**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:**

$3.15$

Do you know what the answer is?

### Exercise 4

**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:**

$2\frac{1}{2}$

### Exercise 5

**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:**

$3$

## Review questions

### What is the division of whole numbers with multiplication in parentheses?

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.

### What is the order of operations?

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

**P**arentheses**E**xponents**M**ultiplication and **D**ivision**A**ddition and **S**ubtraction.

Do you think you will be able to solve it?

### What is the formula for expressing the division of numbers with multiplication in parentheses?

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:

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

### How to eliminate parentheses in a division expression with multiplication in parentheses?

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:

#### Example 1

**Task:**

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

##### Solution 1

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:**

$2$

##### Solution 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.

#### Example 2

**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**

$24$

## examples with solutions for division of whole numbers with multiplication in parentheses

### Exercise #1

### Video Solution

### Step-by-Step Solution

According to the order of operations, we first solve the exercise within parentheses:

$2\times2=4$

Now we divide:

$12:4=3$

### Answer

### Exercise #2

### Video Solution

### Step-by-Step Solution

According to the order of operations, we first solve the exercise within parentheses:

$4+2=6$

Now we solve the rest of the exercise:

$7-6=1$

### Answer

### Exercise #3

### Video Solution

### Step-by-Step Solution

According to the order of operations, we first solve the exercise within parentheses:

$2+1=3$

Now we solve the rest of the exercise:

$8-3=5$

### Answer

### Exercise #4

### Video Solution

### Step-by-Step Solution

According to the order of operations, we first solve the exercise within parentheses:

$7+4=11$

Now we subtract:

$13-11=2$

### Answer

### Exercise #5

### Video Solution

### Step-by-Step Solution

According to the order of operations, first we solve the exercise within parentheses:

$18+20=38$

Now, the exercise obtained is:

$38-38=0$

### Answer