# Additional arithmetic rules - Examples, Exercises and Solutions

## More arithmetic rules: subtraction of a sum, subtraction of a difference, division by product, and division by quotient

In this article, we will dive into the world of essential arithmetic rules that are fundamental for tackling a wide variety of mathematical exercises. Mastering these rules will provide you with a solid foundation and allow you to solve problems with greater confidence and precision. From basic operations like addition and subtraction to more advanced concepts like the division of products and quotients, we will explore each of these rules in detail. Are you ready to deepen your mathematical skills?
Let's get started!

## Practice Additional arithmetic rules

### Exercise #1

$60:(10\times2)=$

### Step-by-Step Solution

We write the exercise in fraction form:

$\frac{60}{10\times2}=$

Let's separate the numerator into a multiplication exercise:

$\frac{10\times6}{10\times2}=$

We simplify the 10 in the numerator and denominator, obtaining:

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

$3$

### Exercise #2

$12:(2\times2)=$

### Step-by-Step Solution

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

$2\times2=4$

Now we divide:

$12:4=3$

$3$

### Exercise #3

$7-(4+2)=$

### 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:

$7-6=1$

$1$

### Exercise #4

$8-(2+1)=$

### 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:

$8-3=5$

$5$

### Exercise #5

$13-(7+4)=$

### Step-by-Step Solution

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

$7+4=11$

Now we subtract:

$13-11=2$

$2$

### Exercise #1

$38-(18+20)=$

### 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:

$38-38=0$

$0$

### Exercise #2

$28-(4+9)=$

### Step-by-Step Solution

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

$4+9=13$

Now we obtain the exercise:

$28-13=15$

$15$

### Exercise #3

$55-(8+21)=$

### Step-by-Step Solution

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

$8+21=29$

Now we obtain the exercise:

$55-29=26$

$26$

### Exercise #4

$37-(4-7)=$

### Step-by-Step Solution

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

$4-7=-3$

Now we obtain:

$37-(-3)=$

Remember that the product of a negative and a negative results in a positive, therefore:

$-(-3)=+3$

Now we obtain:

$37+3=40$

$40$

### Exercise #5

$80-(4-12)=$

### Step-by-Step Solution

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

$4-12=-8$

Now we obtain the exercise:

$80-(-8)=$

Remember that the product of plus and plus gives us a positive:

$-(-8)=+8$

Now we obtain:

$80+8=88$

$88$

### Exercise #1

$100-(30-21)=$

### Step-by-Step Solution

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

$30-21=9$

Now we obtain:

$100-9=91$

$91$

### Exercise #2

$22-(28-3)=$

### Step-by-Step Solution

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

$28-3=25$

Now we obtain the exercise:

$22-25=-3$

$-3$

### Exercise #3

$60:(5\times3)=$

### Step-by-Step Solution

We write the exercise in fraction form:

$\frac{60}{5\times3}$

We break down 60 into a multiplication exercise:

$\frac{20\times3}{5\times3}=$

We simplify the 3s and obtain:

$\frac{20}{5}$

We break down the 5 into a multiplication exercise:

$\frac{5\times4}{5}=$

We simplify the 5 and obtain:

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

$4$

### Exercise #4

$35:(2\times7)=$

### Step-by-Step Solution

We write the exercise in fraction form:

$\frac{35}{2\times7}=$

We separate the numerator into a multiplication exercise:

$\frac{7\times5}{2\times7}=$

We simplify the 7 in the numerator and denominator, obtaining:

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

$2\frac{1}{2}$

### Exercise #5

$9:(3\times2)=$

### Step-by-Step Solution

We rewrite the expression as a fraction:

$\frac{9}{3\times2}=$

We rewrite the numerator as a multiplication expression:

$\frac{3\times3}{3\times2}=$

We simplify the 3 in the numerator and denominator, obtaining:

$\frac{3}{2}=1\frac{1}{2}=1.5$

$1.5$