Division and Fraction Bars (Vinculum)

When we study the order of mathematical operations we come across the terms division bar and fraction bar, but what do they mean and why are they so special?

First of all, we must remember that the fraction bar—or vinculum—is exactly the same as a division. $10:2$ is the same as ${\ {10 \over 2}}$ and ${\ {10/ 2}}$ .

Two things to remember:

You cannot divide by $0$ . To prove this, let's look at the following example: ${\ {3:0=}}$ .
To solve this, we must be able to do the following: ${\ {0 \cdot ?=3}}$ . However, since there is no number that can be multiplied by $0$ to give the result $3$ , there is also therefore no number that can be divided by $0$ .
When we have a fraction bar, it is as if there are parentheses in the numerator. We solve the numerator first and then continue with the exercise. For example:

${\ {{10-2 \over 2}= {8 \over 2} = 4}}$

Detailed explanation

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Test yourself on special cases (0 and 1, inverse, fraction line)!

$12+3\times0=$

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If you liked this article, you may also be interested in the following:

Fractions

How to reduce fractions?

Division of powers of equal base

The Distributive Property in the Case of Divisions

Division of integers between parentheses in which there is a multiplication

Division of integers between parentheses in which there is a division

In the Tutorela blog, you can find a wide variety of helpful mathematics articles!

Exerces with Divisions and Fraction lines

Write the following expressions with fraction bars and solve them:

$(17-7):(55-20)=\frac{10}{35}$

$(9+7):(24+7)=\frac{16}{31}$

$(6+1):(X\times7)=\frac{7}{7X}$

$(2:6):(49:7)=\frac{\frac{1}{3}}{7}$

$(8\times X):(22-8)=\frac{8X}{14}$

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Test your knowledge

Question 1

$$ 2+0:3= $$

Question 2

$$ 19+1-0= $$

Question 3

$$ 9-0+0.5= $$

Solve the following exercises that include parentheses:

$\ {{20-5} \over {7+3}}=$
$\ 18:3=$
$\ 11-3:4=$
$\ (85+5):10=$
$\ 11:2+4{1 \over 2}=$
$\ 0.5-0.1:0.2=$
$\ {18 \over {18+36}}=$
$\ {{0.18+0.37} \over {99+13-{2 \over 1}}}=$

Division and Fraction Bar Exercises

Exercise 1

Task:

Solve the following equation:

$[(3-2+4)^2-2^2]:\frac{(\sqrt{9}\cdot7)}{3}=$

Solution:

In the first step, we solve the brackets starting with the addition and subtraction operations inside the inner parentheses, followed by the powers.

$[5^2-4]:\frac{(\sqrt{9}\cdot7)}{3}=$

In the second step, we solve the root in the additional parenthesis in the fraction.

$[5^2-4]:\frac{(3\cdot7)}{3}=$

Continue to solve according to the order of operations.

$[25-4]:\frac{21}{3}=$

$21:7=3$

Answer:

$3$

Do you know what the answer is?

Question 1

$\frac{1}{2}+0+\frac{1}{2}=$

Question 2

$$ 0+0.2+0.6= $$

Question 3

$$ 12+1+0= $$

Exercise 2

Task:

Solve the following equation:

$\frac{(44-3\cdot0)}{11}:4-\frac{3\cdot4+5}{17}=$

Solution:

First we solve the parentheses in the first fraction. After that, we solve the equation in the second fraction using the order of arithmetic operations.

$\frac{44}{11}:4-\frac{12+5}{17}=$

We continue solving:

$4:4-\frac{17}{17}=$

$1-1=0$

Answer:

$0$

Exercise 3

Question:

Solve the following equation:

$\frac{7+8-3}{2}:3+4=$

Solution:

We start solving the equation according to the order of operations.

$\frac{12}{2}:3+4=$

$6:3+4=$

$2+4=6$

Answer:

$6$

Check your understanding

Question 1

$$ 0:7+1= $$

Question 2

$\frac{25+25}{10}=$

Question 3

Solve the following exercise:

$$ 2+0:3= $$

Exercise 4

Question:

Solve the following equation:

$\frac{36-(4\cdot5)}{8}-3\cdot2=$

Solution:

We begin by solving the parentheses that appear in the fraction.

$\frac{36-20}{8}-3\cdot2=$

Then we continue solving according to the order of the operations.

$\frac{16}{8}-6=$

$2-6=-4$

Answer:

$-4$

Exercise 5

Question:

Calculate the correct answer.

$\frac{25+3-2}{13}+5\cdot4=$

Solution:

We solve the equation according to the order of the operations.

$\frac{26}{13}+5\cdot4=$

We then perform the division operation of the fraction before the multiplication.

$2+20=22$

Answer:

$22$

Do you think you will be able to solve it?

Question 1

Solve the following exercise:

$12+3\cdot0=$

Question 2

$8\times(5\times1)=$

Question 3

$7\times1+\frac{1}{2}=$

Examples with solutions for Division and Fraction Bars (Vinculum)

Exercise #1

Solve the following exercise:

$12+3\cdot0=$

Step-by-Step Solution

According to the order of operations, we first multiply and then add:

$12+(3\cdot0)=$

$3\times0=0$

$12+0=12$

Answer

$12$

Exercise #2

Solve the following exercise:

$2+0:3=$

Step-by-Step Solution

According to the order of operations rules, we first divide and then add:

$2+(0:3)=$

$0:3=0$

$2+0=2$

Answer

$2$

Exercise #3

$\frac{25+25}{10}=$

Video Solution

Step-by-Step Solution

Let's begin by multiplying the numerator:

$25+25=50$

We obtain the following fraction:

$\frac{50}{10}$

Finally let's reduce the numerator and denominator by 10 and we are left with the following result:

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

Answer

$5$

Exercise #4

$0:7+1=$

Video Solution

Step-by-Step Solution

According to the order of operations rules, we first divide and then add:

$0:7=0$

$0+1=1$

Answer

$1$

Exercise #5

$12+1+0=$

Video Solution

Step-by-Step Solution

According to the order of operations rules, since the exercise only involves addition operations, we will solve the problem from left to right:

$12+1=13$

$13+0=13$

Answer

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