First of all, we must remember that the fraction barβor vinculumβis exactly the same as a division.10:2 is the same as Β 210β and Β 10/2.
Two things to remember:
You cannot divide by 0. To prove this, let's look at the following example: Β 3:0=. To solve this, we must be able to do the following: Β 0β ?=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:
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Exerces with Divisions and Fraction lines
Write the following expressions with fraction bars and solve them:
(17β7):(55β20)=3510β
(9+7):(24+7)=3116β
(6+1):(XΓ7)=7X7β
(2:6):(49:7)=731ββ
(8ΓX):(22β8)=148Xβ
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Test your knowledge
Question 1
Solve the following exercise:
\( 2+0:3= \)
Incorrect
Correct Answer:
\( 2 \)
Question 2
\( \frac{25+25}{10}= \)
Incorrect
Correct Answer:
\( 5 \)
Question 3
\( 0:7+1= \)
Incorrect
Correct Answer:
\( 1 \)
Solve the following exercises that include parentheses:
Β 7+320β5β=
Β 18:3=
Β 11β3:4=
Β (85+5):10=
Β 11:2+421β=
Β 0.5β0.1:0.2=
Β 18+3618β=
Β 99+13β12β0.18+0.37β=
Division and Fraction Bar Exercises
Exercise 1
Task:
Solve the following equation:
[(3β2+4)2β22]:3(9ββ 7)β=
Solution:
In the first step, we solve the brackets starting with the addition and subtraction operations inside the inner parentheses, followed by the powers.
[52β4]:3(9ββ 7)β=
In the second step, we solve the root in the additional parenthesis in the fraction.
[52β4]:3(3β 7)β=
Continue to solve according to the order of operations.
[25β4]:321β=
21:7=3
Answer:
3
Do you know what the answer is?
Question 1
\( 12+1+0= \) ?
Incorrect
Correct Answer:
13
Question 2
\( 0+0.2+0.6= \) ?
Incorrect
Correct Answer:
0.8
Question 3
\( \frac{1}{2}+0+\frac{1}{2}= \) ?
Incorrect
Correct Answer:
\( 1 \)
Exercise 2
Task:
Solve the following equation:
11(44β3β 0)β:4β173β 4+5β=
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.
1144β:4β1712+5β=
We continue solving:
4:4β1717β=
1β1=0
Answer:
0
Exercise 3
Question:
Solve the following equation:
27+8β3β:3+4=
Solution:
We start solving the equation according to the order of operations.
212β:3+4=
6:3+4=
2+4=6
Answer:
6
Check your understanding
Question 1
Solve the following exercise:
\( 9-0+0.5= \)
Incorrect
Correct Answer:
9.5
Question 2
Solve the following exercise:
\( 19+1-0= \)
Incorrect
Correct Answer:
\( 20 \)
Question 3
\( 2+0:3= \)
Incorrect
Correct Answer:
\( 2 \)
Exercise 4
Question:
Solve the following equation:
836β(4β 5)ββ3β 2=
Solution:
We begin by solving the parentheses that appear in the fraction.
836β20ββ3β 2=
Then we continue solving according to the order of the operations.
816ββ6=
2β6=β4
Answer:
β4
Exercise 5
Question:
Calculate the correct answer.
1325+3β2β+5β 4=
Solution:
We solve the equation according to the order of the operations.
1326β+5β 4=
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
\( 12+3\times0= \)
Incorrect
Correct Answer:
12
Question 2
\( 8\times(5\times1)= \)
Incorrect
Correct Answer:
40
Question 3
\( 7\times1+\frac{1}{2}=\text{ ?} \)
Incorrect
Correct Answer:
\( 7\frac{1}{2} \)
Examples with solutions for Division and Fraction Bars (Vinculum)
Exercise #1
12+3Γ0=
Video Solution
Step-by-Step Solution
According to the order of operations, we first multiply and then add:
3Γ0=0
12+0=12
Answer
12
Exercise #2
2+0:3=
Video Solution
Step-by-Step Solution
According to the order of operations rules, we first divide and then add:
0:3=0
2+0=2
Answer
2
Exercise #3
Solve the following exercise:
19+1β0=
Video Solution
Step-by-Step Solution
According to the order of operations rules, since the exercise only involves addition and subtraction operations, we will solve the problem from left to right:
19+1=20
20β0=20
Answer
20
Exercise #4
Solve the following exercise:
9β0+0.5=
Video Solution
Step-by-Step Solution
According to the order of operations rules, since the exercise only involves addition and subtraction, we will solve the problem from left to right:
9β0=9
9+0.5=9.5
Answer
9.5
Exercise #5
21β+0+21β= ?
Video Solution
Step-by-Step Solution
According to the order of operations, since the exercise only involves addition operations, we will solve the problem from left to right: