Additional Arithmetic Rules: Number of terms

First, let's write the multiplication exercise in the inner parentheses as a fraction:

$30/(3:\frac{13}{2})=$

Now let's flip the fraction to create a multiplication exercise:

$30/(3\times\frac{2}{13})=$

Let's add 13 to the fraction's numerator in a multiplication exercise:

$30/(\frac{3\times2}{13})=$

Now let's flip the fraction to create a multiplication exercise:

$30\times\frac{13}{3\times2}=$

Let's add 30 to the fraction's numerator in a multiplication exercise:

$\frac{30\times13}{3\times2}=$

Let's break down the 30 into a smaller multiplication exercise:

$\frac{10\times3\times13}{3\times2}=$

Let's reduce between the 3 in the numerator and denominator:

$\frac{10\times13}{2}=$

Let's break down the 10 into a smaller multiplication exercise:

$\frac{5\times2\times13}{2}=$

Let's reduce between the 2 in the numerator and denominator to get:

$5\times13=65$

First, we rewrite the multiplication exercise inside parentheses as a fraction:

$15/(4:\frac{2}{8})=$

Now we invert the fraction to create a multiplication exercise:

$15/(4\times\frac{8}{2})=$

We add the 4 to the numerator of the fraction in the multiplication exercise:

$15/(\frac{4\times8}{2})=$

Now we invert the fraction to create a multiplication exercise:

$15\times\frac{2}{4\times8}=$

We add the 15 to the numerator of the fraction in the multiplication exercise:

$\frac{15\times2}{4\times8}=$

We separate the 4 into a smaller multiplication exercise:

$\frac{15\times2}{2\times2\times8}=$

We simplify the 2 in the numerator and denominator:

$\frac{15}{2\times8}=\frac{15}{16}$

First, we rewrite the multiplication exercise within the inner parentheses as a fraction:

$75:(8:\frac{4}{15})=$

Now we invert the fraction to create a multiplication exercise:

$75:(8\times\frac{15}{4})=$

We add the 8 to the numerator of the fraction in the multiplication exercise:

$75:\frac{8\times15}{4}=$

Now we invert the fraction to create a multiplication exercise:

$75\times\frac{4}{8\times15}=$

We add the 75 to the numerator of the fraction in the multiplication exercise:

$\frac{75\times4}{8\times15}=$

We break down the 75 and the 8 into smaller multiplication exercises:

$\frac{15\times5\times4}{4\times2\times15}=$

We simplify the 4 and the 15 in the numerator and denominator:

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

First, we rewrite the multiplication exercise inside parentheses as a fraction:

$3:(4:\frac{5}{12})=$

Now we invert the fraction to create a multiplication exercise:

$3:(4\times\frac{12}{5})=$

We add the 4 to the numerator of the fraction in the multiplication exercise:

$3:\frac{4\times12}{5}=$

Now we invert the fraction to create a multiplication exercise:

$3\times\frac{5}{4\times12}=$

We add the 3 to the numerator of the fraction in the multiplication exercise:

$\frac{3\times5}{4\times12}=$

We break down the 12 into a smaller multiplication exercise:

$\frac{3\times5}{4\times3\times4}=$

We simplify the 3 in the numerator and denominator:

$\frac{5}{4\times4}=\frac{5}{16}$

Let's begin by remembering the order of arithmetic operations: calculation of the operation within parentheses, multiplication and division (from left to right), addition and subtraction (from left to right)

We must also underline that when there are parentheses within parentheses, we should start with the innermost first.

$7-(10-(4-3))=$
In this exercise, there are only subtraction operations and parentheses within parentheses.

Therefore, we will first perform the operation of the inner parentheses. After which we will be able to remove the inner parentheses and will be left with only one pair of parentheses.

$7-(10-(1))=7-(10-1)=$

When we perform an operation of ("addition and subtraction") with directed numbers, we enclose the directed number inside of parentheses.

Parentheses can be omitted, but when omitting the parentheses, remember that (-=+-)

$7-(9)=7-9=-2$

Reminder: addition and subtraction of directed numbers

In this case, we remember that when we have two numbers with different signs, it is important to determine which number is greater in terms of absolute value (absolute - the distance from zero). The larger number will determine the sign of the result and we will perform a subtraction exercise.

Therefore, the correct answer is option c: (-2)

Let's recall the order of arithmetic operations: calculate what's in parentheses, multiplication and division (from left to right), addition and subtraction (from left to right)

We emphasize that when there are parentheses within parentheses, we start with the innermost ones first.

$43-(35-(24-18))=$

In this exercise, there are only subtraction operations and parentheses within parentheses.

Therefore, we will first perform the operation in the inner parentheses, and after calculating we can remove the inner parentheses and be left with only one set of parentheses.

$43-(35-(24-18))= 43-(35-(6))$

$43-(35-(6))=43-(35-6)$
Now we will perform the operation in the remaining parentheses and after calculating we will remove the parentheses

$43-(35-6) = 43-(29)$

$43-(29) = 43-29 = 14$

Therefore the answer is option a - (14)

Let's look at the expression in parentheses and write it as a fraction:

$(8\times(10:(3\times12)))=8\times\frac{10}{3\times12}$

Now we'll get the expression:

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

Let's address the parentheses and combine the 8 with the multiplication in the numerator:

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

Let's break down the 8 and 12 into smaller multiplication problems:

$7:(\frac{4\times2\times10}{3\times4\times3})=$

Let's reduce between the 4 in the numerator and denominator and get:

$7:(\frac{2\times10}{3\times3})=$

Let's solve the multiplication problems in the parentheses and get:

$7:(\frac{20}{9})=$

Let's switch between the numerator and denominator so we can turn the expression into multiplication and add the 7 to the fraction's numerator:

$7\times\frac{9}{20}=\frac{7\times9}{20}=\frac{63}{20}$

Let's separate the fraction's numerator into an addition problem:

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

Now let's separate it into an addition of fractions:

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

Let's multiply the fraction by 5:

$3+\frac{3\times5}{20\times5}=3+\frac{15}{100}$

And we'll get the expression:

$3+0.15=3.15$

We rewrite the innermost parentheses in fraction form:

$10/(7:\frac{9}{2})=$

We convert the parentheses into a multiplication exercise through inverting the fraction:

$10/(7\times\frac{2}{9})=$

We add the 7 to the numerator for the multiplication exercise:

$10/(\frac{7\times2}{9})=10:\frac{7\times2}{9}$

We convert the exercise into a multiplication by inverting the fraction:

$10\times\frac{9}{7\times2}=$

We add the 10 to the numerator for the multiplication exercise:

$\frac{10\times9}{7\times2}=$

We break down the 10 into a simpler multiplication exercise:

$\frac{5\times2\times9}{7\times2}=$

We simplify the 2 in the numerator and denominator:

$\frac{5\times9}{7}=\frac{45}{7}$

We convert the fraction's numerator into a sum exercise:

$\frac{42+3}{7}=\frac{42}{7}+\frac{3}{7}=6+\frac{3}{7}=6\frac{3}{7}$

First, we rewrite down the multiplication exercise within the inner parentheses as a fraction:$25:(3:\frac{10}{35})=$

Now we invert the fraction to create a multiplication exercise:

$25:(3\times\frac{35}{10})=$

We add the 3 to the numerator of the fraction in the multiplication exercise:

$25:\frac{3\times35}{10}=$

Now we invert the fraction to create a multiplication exercise:

$25\times\frac{10}{3\times35}=$

We add the 25 to the numerator of the fraction in the multiplication exercise:

$\frac{25\times10}{3\times35}=$

We separate the 10 and 35 into smaller multiplication exercises:

$\frac{25\times5\times2}{3\times7\times5}=$

We simplify the 5 in the numerator and denominator:

$\frac{25\times2}{3\times7}=\frac{50}{21}$

We separate the numerator of the fraction into a sum exercise:

$\frac{42+8}{21}=$

We separate into sum exercises among fractions:

$\frac{42+8}{21}=\frac{42}{21}+\frac{8}{21}=2+\frac{8}{21}=2\frac{8}{21}$

First, we rewrite the multiplication exercise inside parentheses as a fraction:

$\frac{2}{7}:(\frac{3}{5}:\frac{7}{8})=$

Now we invert the fraction to create a multiplication exercise:

$\frac{2}{7}:(\frac{3}{5}\times\frac{8}{7})=\frac{2}{7}:(\frac{3\times8}{5\times7})$

Now we invert the fraction to create a multiplication exercise:

$\frac{2}{7}\times\frac{5\times7}{3\times8}=\frac{2\times5\times7}{7\times3\times8}$

We simplify the 7 in the numerator and denominator:

$\frac{2\times5}{3\times8}=$

We break down the 8 into a shorter multiplication exercise:

$\frac{2\times5}{3\times2\times4}=$

We simplify the 2 in the numerator and denominator:

$\frac{5}{3\times4}=\frac{5}{12}$

First, we rewrite the multiplication exercise inside parentheses as a fraction:

$10:(2:\frac{15}{7})=$

Now we invert the fraction to create a multiplication exercise:

$10:(2\times\frac{7}{15})=$

We add the 2 to the numerator of the fraction in the multiplication exercise:

$10:\frac{2\times7}{15}=$

Now we invert the fraction to create a multiplication exercise:

$10\times\frac{15}{2\times7}=$

We add the 10 to the numerator of the fraction in the multiplication exercise:

$\frac{10\times15}{2\times7}=$

We break down the 10 into a smaller multiplication exercise.

$\frac{5\times2\times15}{2\times7}=$

We simplify the 2 in the numerator and denominator:

$\frac{5\times15}{7}=\frac{75}{7}$

We separate the fraction into a sum exercise between fractions:

$\frac{70+5}{7}=\frac{70}{7}+\frac{5}{7}=10+\frac{5}{7}=10\frac{5}{7}$

First, let's write the multiplication exercise in the inner parentheses as a fraction:

$38:(6:\frac{2}{6})=$

Now let's flip the fraction to create a multiplication exercise:

$38:(6\times\frac{6}{2})=$

Let's add the 6 to the fraction's numerator to create a multiplication exercise:

$38:\frac{6\times6}{2}=$

Let's flip the fraction to create a multiplication exercise:

$38\times\frac{2}{6\times6}=$

Let's add the 38 to the fraction's numerator to create a multiplication exercise:

$\frac{38\times2}{6\times6}=$

Let's break down the 38 and the two 6's in the denominator into smaller multiplication exercises:

$\frac{19\times2\times2}{2\times3\times2\times3}=$

Let's reduce the 2 in both numerator and denominator:

$\frac{19}{3\times3}=\frac{19}{9}$

Let's separate the fraction into an addition exercise between fractions:

$\frac{18+1}{9}=\frac{18}{9}+\frac{1}{9}=2+\frac{1}{9}=2\frac{1}{9}$

First, we rewrite the multiplication exercise in the innermost parentheses as a fraction:

$49:(7:(\frac{4}{3}\times\frac{1}{7}))=$

We multiply the fractions and combine them since it is just a multiplication operation:

$49:(7:\frac{4\times1}{3\times7})=$

Now we invert the fraction to create a multiplication exercise:

$49:(7\times\frac{3\times7}{4\times1})=$

We add the 7 to the numerator of the fraction in the multiplication exercise:

$49:\frac{7\times3\times7}{4\times1}=$

We invert the fraction to create a multiplication exercise:

$49\times\frac{4\times1}{7\times3\times7}=$

We add the 49 to the numerator of the fraction in the multiplication exercise:

$\frac{49\times4\times1}{7\times3\times7}=$

We break down the 49 into a smaller multiplication exercise:

$\frac{7\times7\times4\times1}{7\times3\times7}=$

We simplify the 7 in the numerator and denominator:

$\frac{4\times1}{3}=\frac{4}{3}=1\frac{1}{3}$

Let's begin by remembering the order of arithmetic operations: calculation of the operation within parentheses, multiplication and division (from left to right), addition and subtraction (from left to right)

We must also underline that when there are parentheses within parentheses, we should start with the innermost first.

$17-(3-(-7-4))=$

In this exercise, there are only subtraction operations and parentheses within parentheses.

Therefore, we will first perform the operation of the inner parentheses. After which we will be able to remove the inner parentheses and will be left with only one pair of parentheses.

Adding and subtracting directed numbers is based on several key principles. In this case, we will remember that when we have two directed numbers with the same sign (plus or minus), the result will also have the same sign, which will actually be the result of an addition exercise.

$17-(3-(-7-4))= 17-(3-(-11))$
Keep in mind

What happens when there is a sequence of two signs present in the exercise (these are usually separated by parentheses) Let's highlight several different cases:

When a sequence with two plus signs appears, the result will also be a plus.

When a sequence with two minus signs appears, the result will also be a plus.

When a sequence with minus and plus signs or plus and minus signs appears, the result will be minus.

$17-(3-(-11))=17-(3+11)=$
Now we will perform the operation of the remaining parentheses and after the calculation, we will remove the parentheses.

$17-(14)=17-14=3$

Therefore, the correct answer is option b: (3)

Let's begin by remembering the order of arithmetic operations: calculation of the operation within parentheses, multiplication and division (from left to right), addition and subtraction (from left to right)

We must also underline that when there are parentheses within parentheses, we should start with the innermost first.

$25-(34-(20-8))=$

In this exercise, there are only subtraction operations and parentheses within parentheses.

Therefore, we will first perform the operation of the inner parentheses. After which we will be able to remove the inner parentheses and will be left with only one pair of parentheses.

$25-(34-(20-8))=25-(34-(12))$
Keep in mind

What happens when there is a sequence of two signs present in the exercise (these are usually separated by parentheses) Let's highlight several different cases:

When a sequence with two plus signs appears, the result will also be a plus.

When a sequence with two minus signs appears, the result will also be a plus.

When a sequence with minus and plus signs or plus and minus signs appears, the result will be minus.

$25-(34-(12))=25-(34-12)$
Now we will perform the operation of the remaining parentheses and after the calculation, we will remove the parentheses.

$25-(34-12)=25-(22)$

$25-(22)=25-22=3$

Therefore, the correct answer is option c: (3)

Let's begin by remembering the order of arithmetic operations: calculation of the operation within parentheses, multiplication and division (from left to right), addition and subtraction (from left to right)

We must also underline that when there are parentheses within parentheses, we should start with the innermost first.

$13-(10-((-4)-(-10))) =$

Let's begin by remembering the order of arithmetic operations: calculation of the operation within parentheses, multiplication and division (from left to right), addition and subtraction (from left to right)

We must also underline that when there are parentheses within parentheses, we should start with the innermost first.

Keep in mind

What happens when there is a sequence of two signs present in the exercise (these are usually separated by parentheses) Let's highlight several different cases:

When a sequence with two plus signs appears, the result will also be a plus.

When a sequence with two minus signs appears, the result will also be a plus.

When a sequence with minus and plus signs or plus and minus signs appears, the result will be minus.

$13-(10-((-4)-(-10))) = 13-(10-((-4)+10))$

Reminder: addition and subtraction of directed numbers

When we have two numbers with different signs, it is important to determine which number is greater in terms of absolute value (absolute - the distance from zero). The larger number will determine the sign of the result and we will perform a subtraction exercise.

Now we will perform the operation of the remaining parentheses and after the calculation, we will remove the parentheses.

$13-(4) = 13-4 = 9$

Therefore, the correct answer is c: (9)

Let's begin by remembering the order of arithmetic operations: calculation of the operation within parentheses, multiplication and division (from left to right), addition and subtraction (from left to right)

We must also underline that when there are parentheses within parentheses, we should start with the innermost first.

$74-(78-(10-13)=$

In this exercise, there are only subtraction operations and parentheses within parentheses.

Therefore, we will first perform the operation of the inner parentheses. After which we will be able to remove the inner parentheses and will be left with only one pair of parentheses.

$74-(78-(10-13)= 74-(78-(-3))$

Keep in mind

What happens when there is a sequence of two signs present in the exercise (these are usually separated by parentheses) Let's highlight several different cases:

When a sequence with two plus signs appears, the result will also be a plus.

When a sequence with two minus signs appears, the result will also be a plus.

When a sequence with minus and plus signs or plus and minus signs appears, the result will be minus.

$74-(78-(-3)) =74-(78+3)$
Now we will perform the operation of the remaining parentheses and after the calculation we will remove the parentheses entirely.

$74-(78+3)=74-(81)$$74-(81)=74-81=-7$

Therefore, the answer is option b: (-7)

Let's begin by remembering the order of arithmetic operations: calculation of the operation within parentheses, multiplication and division (from left to right), addition and subtraction (from left to right)

We must also underline that when there are parentheses within parentheses, we should start with the innermost first.

$10-(12-(4-12))=$

In this exercise, there are only subtraction operations and parentheses within parentheses.

Therefore, we will first perform the operation of the inner parentheses. After which we will be able to remove the inner parentheses and will be left with only one pair of parentheses.

$10-(12-(4-12))=10-(12-(-8))$

Keep in mind

What happens when there is a sequence of two signs present in the exercise (these are usually separated by parentheses) Let's highlight several different cases:

When a sequence with two plus signs appears, the result will also be a plus.

When a sequence with two minus signs appears, the result will also be a plus.

When a sequence with minus and plus signs or plus and minus signs appears, the result will be minus.

$10-(12-(-8)) = 10-(12+8)$

Now we will perform the operation of the remaining parentheses and after the calculation, we will remove the parentheses.

$10-(12+8)=10-(20)$$10-\left(20\right)=10-20=-10$

Therefore, the correct answer is option a: (-10)

Let's recall the order of operations: calculating what's in parentheses, multiplication and division (from left to right), addition and subtraction (from left to right)

We emphasize that when there are parentheses within parentheses, we start with the innermost ones first.

$84-(77-(93-81))=$

In this exercise, there are only subtraction operations and parentheses within parentheses.

Therefore, we will first perform the operation in the inner parentheses, and after calculating we can remove the inner parentheses and are left with only one set of parentheses.

$84-(77-(93-81)) = 84-(77-(12))$

$84-(77-(12))=84-(77-12)$
Now we will perform the operation in the remaining parentheses and after calculating we will remove the parentheses

$84-(77-12) = 84-(65)$

$84-(65) = 84-65 = 19$

Therefore the answer is option A - (19)

Let's first address the expression in parentheses and convert it to a fraction:

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

Now we'll get the expression:

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

We'll add the 9 to the numerator of the fraction in the multiplication expression, and we'll separate the 18 into a smaller multiplication expression:

$13:(\frac{9\times4}{2\times9\times5})=$

Let's reduce the 9 in both numerator and denominator:

$13:(\frac{4}{2\times5})=$

Let's factor the numerator into a multiplication expression:

$13:(\frac{2\times2}{2\times5})=$

Let's reduce the 2 in both numerator and denominator:

$13:(\frac{2}{5})=$

We'll write the fraction in inverse form so we can convert the expression to a multiplication expression:

$13\times\frac{5}{2}=\frac{13\times5}{2}=\frac{65}{2}$

Let's factor the numerator into an addition expression:

$\frac{65}{2}=\frac{60+5}{2}$

Let's separate it into an addition of fractions:

$\frac{60}{2}+\frac{5}{2}=30+2.5=32.5$