Multiplication and Division of Signed Mumbers: Using fractions

Let's convert the mixed fraction to an improper fraction:

$1\frac{5}{6}=\frac{11}{6}$

Now let's write the exercise:

$7\times\frac{11}{6}=\frac{7}{1}\times\frac{11}{6}=$

We'll multiply numerator by numerator and denominator by denominator:

$\frac{7\times11}{1\times6}=\frac{77}{6}$

Let's convert the improper fraction to a mixed fraction:

$\frac{77}{6}=12\frac{5}{6}$

Let's write the expression in the form of a simple fraction:

$\frac{-\frac{72}{3}}{0}$

Since it is not possible to divide a number by 0, the expression is invalid.

Let's convert 4 to a simple fraction:

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

Now the exercise we received is:

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

Let's convert the division exercise to a multiplication exercise, and don't forget to switch the numerator and denominator in the second fraction:

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

We'll combine it into one multiplication exercise and solve:

$\frac{1\times1}{2\times4}=\frac{1}{8}$

Let's first convert 2 and seven-sevenths into a simple fraction:

$2\frac{1}{7}=2+\frac{1}{7}=2\times\frac{7}{7}+\frac{1}{7}=\frac{2\times7}{7}+\frac{1}{7}=\frac{14}{7}+\frac{1}{7}=\frac{14+1}{7}=\frac{15}{7}$

Now the exercise we have is:

$\frac{15}{7}:\frac{1}{4}=$

next we convert the division exercise into a multiplication exercise, remembering to switch the numerator and denominator in the second fraction:

$\frac{15}{7}\times\frac{4}{1}=$

Let's now combine into one multiplication exercise:

$\frac{15\times4}{7\times1}=\frac{60}{7}$

Next, we factor 60 into an addition exercise:

$\frac{56+4}{7}=$

Then let's separate the exercise into addition between fractions:

$\frac{56}{7}+\frac{4}{7}=$

Finally, we solve the first fraction exercise to get our answer:

$8+\frac{4}{7}=8\frac{4}{7}$

Let's convert 9 and a quarter to a simple fraction:

$9\frac{1}{4}=9+\frac{1}{4}=\frac{9\times4}{4}+\frac{1}{4}=\frac{36}{4}+\frac{1}{4}=\frac{36+1}{4}=\frac{37}{4}$

Now the exercise we got is:

$\frac{37}{4}:\frac{24}{7}=$

Let's convert the division exercise to a multiplication exercise, and don't forget to switch the numerator and denominator in the second fraction:

$\frac{37}{4}\times\frac{7}{24}=$

Let's combine it into one multiplication exercise:

$\frac{37\times7}{24\times4}=\frac{259}{96}$

Let's note that we are dividing a positive number by a negative number, and therefore the result will necessarily be a negative number:

$+:-=-$

Let's remember the rule:

$\frac{x}{1}=x$

In other words, any number divided by 1 will be equal to itself.

Therefore:

$\frac{850}{-1}=-850$

Note that we are dividing a negative number by a positive number, and therefore the result must be a negative number:

$-:+=-$

We will write the exercise in the following way:

$\frac{-7\frac{1}{2}}{1}=$

Let's remember the rule:

$\frac{x}{1}=x$

In other words, any number divided by 1 will be equal to itself.

Therefore, the answer is:

$-7\frac{1}{2}$

Let's recall the rule:

$(-x)\times(-x)=+x$

Therefore, the sign of the exercise result will be positive:

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

To solve the problem $\frac{60}{-120}$, follow these steps:

• Step 1: Find the greatest common divisor (GCD) of 60 and 120. The GCD is 60.
• Step 2: Simplify the fraction by dividing both the numerator and the denominator by their GCD:

$\frac{60}{-120} = \frac{60 \div 60}{-120 \div 60} = \frac{1}{-2}$

• Step 3: When dividing a positive number by a negative number, the result is negative. Thus, $\frac{1}{-2}$ simplifies to $-\frac{1}{2}$.

Thus, the solution to the problem is $\boxed{-\frac{1}{2}}$.

Note that we are dividing a negative number by a positive number, and therefore the result will necessarily be a negative number:

$-:+=-$

Let's remember the rule:

$\frac{x}{1}=x$

In other words, any number divided by 1 will be equal to itself.

Therefore:

$\frac{-50}{1}=-50$

First let's write the expression in the form of a simple fraction:

$\frac{-\frac{4}{7}}{0}$

Since it is not possible to divide a number by 0, the expression is invalid.

Since we are dividing two positive numbers, the result must be a positive number:

$+:+=+$

First, we'll convert each mixed fraction into an improper fraction as follows:

$3\frac{3}{13}=\frac{3\times13+3}{13}=\frac{39+3}{13}=\frac{42}{13}$

$1\frac{12}{13}=\frac{1\times13+12}{13}=\frac{13+12}{13}=\frac{25}{13}$

Now we have:

$\frac{42}{13}:\frac{25}{13}$

We'll convert the division problem into multiplication, remembering to switch the numerator and denominator:

$\frac{42}{13}\times\frac{13}{25}=$

We'll simplify the 13 to get:

$\frac{42}{25}=$

Now we'll factor 42 into an addition problem:

$\frac{25+17}{25}=\frac{25}{25}+\frac{17}{25}=$

Finally, we will solve accordingly to get:

$1+\frac{17}{25}=1\frac{17}{25}$

Since we are dividing two positive numbers, the result must be a positive number:

$+:+=+$

First, let's convert each mixed fraction to an improper fraction as follows:

$9=\frac{9}{1}$

$45\frac{7}{15}=\frac{45\times15+7}{15}=$

Let's solve the multiplication in the numerator:

$45\\\times15\\675$

We should obtain the following:

$\frac{675+7}{15}=\frac{682}{15}$

Now our division problem between the fractions looks like this:

$\frac{682}{15}:\frac{9}{1}=$

Let's convert the division to multiplication, and don't forget to switch between numerator and denominator:

$\frac{682}{15}\times\frac{1}{9}=$

Let's combine everything into one problem:

$\frac{682\times1}{15\times9}=$

Let's solve the problem in the numerator:

$15\\\times9\\135$

And the result is:

$\frac{682}{135}$