Division and Fraction Bars (Vinculum)

πŸ†Practice special cases (0 and 1, inverse, fraction line)

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 barβ€”or vinculumβ€”is exactly the same as a division. 10:2 10:2 is the same as Β 102{\ {10 \over 2}} and Β 10/2{\ {10/ 2}}.

Two things to remember:

  • You cannot divide by 00. To prove this, let's look at the following example: Β 3:0={\ {3:0=}}.
    To solve this, we must be able to do the following: Β 0β‹…?=3{\ {0 \cdot ?=3}}. However, since there is no number that can be multiplied by 00 to give the result 33, there is also therefore no number that can be divided by 00.
  • 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:

Β 10βˆ’22=82=4{\ {{10-2 \over 2}= {8 \over 2} = 4}}


Start practice

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

einstein

Solve the following exercise:

\( 12+3\cdot0= \)

Practice more now

Exerces with Divisions and Fraction lines

Write the following expressions with fraction bars and solve them:

(17βˆ’7):(55βˆ’20)=1035 (17-7):(55-20)=\frac{10}{35}

(9+7):(24+7)=1631 (9+7):(24+7)=\frac{16}{31}

(6+1):(XΓ—7)=77X (6+1):(X\times7)=\frac{7}{7X}

(2:6):(49:7)=137 (2:6):(49:7)=\frac{\frac{1}{3}}{7}

(8Γ—X):(22βˆ’8)=8X14 (8\times X):(22-8)=\frac{8X}{14}


Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Test your knowledge

Solve the following exercises that include parentheses:

  • Β 20βˆ’57+3=\ {{20-5} \over {7+3}}=
  • Β 18:3=\ 18:3=
  • Β 11βˆ’3:4=\ 11-3:4=
  • Β (85+5):10=\ (85+5):10=
  • Β 11:2+412=\ 11:2+4{1 \over 2}=
  • Β 0.5βˆ’0.1:0.2=\ 0.5-0.1:0.2=
  • Β 1818+36=\ {18 \over {18+36}}=
  • Β 0.18+0.3799+13βˆ’21=\ {{0.18+0.37} \over {99+13-{2 \over 1}}}=

Division and Fraction Bar Exercises

Exercise 1

Task:

Solve the following equation:

[(3βˆ’2+4)2βˆ’22]:(9β‹…7)3= [(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.

[52βˆ’4]:(9β‹…7)3= [5^2-4]:\frac{(\sqrt{9}\cdot7)}{3}=

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

[52βˆ’4]:(3β‹…7)3= [5^2-4]:\frac{(3\cdot7)}{3}=

Continue to solve according to the order of operations.

[25βˆ’4]:213= [25-4]:\frac{21}{3}=

21:7=3 21:7=3

Answer:

3 3


Do you know what the answer is?

Exercise 2

Task:

Solve the following equation:

(44βˆ’3β‹…0)11:4βˆ’3β‹…4+517= \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.

4411:4βˆ’12+517= \frac{44}{11}:4-\frac{12+5}{17}=

We continue solving:

4:4βˆ’1717= 4:4-\frac{17}{17}=

1βˆ’1=0 1-1=0

Answer:

0 0


Exercise 3

Question:

Solve the following equation:

7+8βˆ’32:3+4= \frac{7+8-3}{2}:3+4=

Solution:

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

122:3+4= \frac{12}{2}:3+4=

6:3+4= 6:3+4=

2+4=6 2+4=6

Answer:

6 6


Check your understanding

Exercise 4

Question:

Solve the following equation:

36βˆ’(4β‹…5)8βˆ’3β‹…2= \frac{36-(4\cdot5)}{8}-3\cdot2=

Solution:

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

36βˆ’208βˆ’3β‹…2= \frac{36-20}{8}-3\cdot2=

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

168βˆ’6= \frac{16}{8}-6=

2βˆ’6=βˆ’4 2-6=-4

Answer:

βˆ’4 -4


Exercise 5

Question:

Calculate the correct answer.

25+3βˆ’213+5β‹…4= \frac{25+3-2}{13}+5\cdot4=

Solution:

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

2613+5β‹…4= \frac{26}{13}+5\cdot4=

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

2+20=22 2+20=22

Answer:

22 22


Do you think you will be able to solve it?

Examples with solutions for Division and Fraction Bars (Vinculum)

Exercise #1

Solve the following exercise:

12+3β‹…0= 12+3\cdot0=

Step-by-Step Solution

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

12+(3β‹…0)= 12+(3\cdot0)=

3Γ—0=0 3\times0=0

12+0=12 12+0=12

Answer

12 12

Exercise #2

Solve the following exercise:

2+0:3= 2+0:3=

Step-by-Step Solution

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

2+(0:3)= 2+(0:3)=

0:3=0 0:3=0

2+0=2 2+0=2

Answer

2 2

Exercise #3

0+0.2+0.6= 0+0.2+0.6=

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:

0+0.2=0.2 0+0.2=0.2

0.2+0.6=0.8 0.2+0.6=0.8

Answer

0.8

Exercise #4

0:7+1= 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 0:7=0

0+1=1 0+1=1

Answer

1 1

Exercise #5

12+1+0= 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 12+1=13

13+0=13 13+0=13

Answer

13

Start practice