Additional Arithmetic Rules - Examples, Exercises and Solutions

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:

$\frac{7}{1}=7$

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:

$\frac{15}{10}=1\frac{5}{10}=1\frac{1}{2}$

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:

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

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

$2\times2=4$

Now we divide:

$12:4=3$

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

$4+2=6$

Now we solve the rest of the exercise:

$7-6=1$

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

$2+1=3$

Now we solve the rest of the exercise:

$8-3=5$

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

$7+4=11$

Now we subtract:

$13-11=2$

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

$18+20=38$

Now, the exercise obtained is:

$38-38=0$

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

$4+9=13$

Now we obtain the exercise:

$28-13=15$

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

$8+21=29$

Now we obtain the exercise:

$55-29=26$

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:

$37+3=40$

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:

$80+8=88$

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

$30-21=9$

Now we obtain:

$100-9=91$

According to the order of operations rules, we first solve the expression inside of the parentheses:

$15-10=5$

We obtain the following expression:

$66-5=61$

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

$28-3=25$

Now we obtain the exercise:

$22-25=-3$