Exerces with Divisions and Fraction lines Write the following expressions with fraction bars and solve them: ( 17 − 7 ) : ( 55 − 20 ) = 10 35 (17-7):(55-20)=\frac{10}{35} ( 17 − 7 ) : ( 55 − 20 ) = 35 10
( 9 + 7 ) : ( 24 + 7 ) = 16 31 (9+7):(24+7)=\frac{16}{31} ( 9 + 7 ) : ( 24 + 7 ) = 31 16
( 6 + 1 ) : ( X × 7 ) = 7 7 X (6+1):(X\times7)=\frac{7}{7X} ( 6 + 1 ) : ( X × 7 ) = 7 X 7
( 2 : 6 ) : ( 49 : 7 ) = 1 3 7 (2:6):(49:7)=\frac{\frac{1}{3}}{7} ( 2 : 6 ) : ( 49 : 7 ) = 7 3 1
( 8 × X ) : ( 22 − 8 ) = 8 X 14 (8\times X):(22-8)=\frac{8X}{14} ( 8 × X ) : ( 22 − 8 ) = 14 8 X
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Solve the following exercises that include parentheses: 20 − 5 7 + 3 = \ {{20-5} \over {7+3}}= 7 + 3 20 − 5 = 18 : 3 = \ 18:3= 18 : 3 = 11 − 3 : 4 = \ 11-3:4= 11 − 3 : 4 = ( 85 + 5 ) : 10 = \ (85+5):10= ( 85 + 5 ) : 10 = 11 : 2 + 4 1 2 = \ 11:2+4{1 \over 2}= 11 : 2 + 4 2 1 = 0.5 − 0.1 : 0.2 = \ 0.5-0.1:0.2= 0.5 − 0.1 : 0.2 = 18 18 + 36 = \ {18 \over {18+36}}= 18 + 36 18 = 0.18 + 0.37 99 + 13 − 2 1 = \ {{0.18+0.37} \over {99+13-{2 \over 1}}}= 99 + 13 − 1 2 0.18 + 0.37 =
Division and Fraction Bar Exercises Exercise 1 Task:
Solve the following equation:
[ ( 3 − 2 + 4 ) 2 − 2 2 ] : ( 9 ⋅ 7 ) 3 = [(3-2+4)^2-2^2]:\frac{(\sqrt{9}\cdot7)}{3}= [( 3 − 2 + 4 ) 2 − 2 2 ] : 3 ( 9 ⋅ 7 ) =
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 ] : ( 9 ⋅ 7 ) 3 = [5^2-4]:\frac{(\sqrt{9}\cdot7)}{3}= [ 5 2 − 4 ] : 3 ( 9 ⋅ 7 ) =
In the second step, we solve the root in the additional parenthesis in the fraction.
[ 5 2 − 4 ] : ( 3 ⋅ 7 ) 3 = [5^2-4]:\frac{(3\cdot7)}{3}= [ 5 2 − 4 ] : 3 ( 3 ⋅ 7 ) =
Continue to solve according to the order of operations.
[ 25 − 4 ] : 21 3 = [25-4]:\frac{21}{3}= [ 25 − 4 ] : 3 21 =
21 : 7 = 3 21:7=3 21 : 7 = 3
Answer:
3 3 3
Do you know what the answer is?
Exercise 2 Task:
Solve the following equation:
( 44 − 3 ⋅ 0 ) 11 : 4 − 3 ⋅ 4 + 5 17 = \frac{(44-3\cdot0)}{11}:4-\frac{3\cdot4+5}{17}= 11 ( 44 − 3 ⋅ 0 ) : 4 − 17 3 ⋅ 4 + 5 =
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.
44 11 : 4 − 12 + 5 17 = \frac{44}{11}:4-\frac{12+5}{17}= 11 44 : 4 − 17 12 + 5 =
We continue solving:
4 : 4 − 17 17 = 4:4-\frac{17}{17}= 4 : 4 − 17 17 =
1 − 1 = 0 1-1=0 1 − 1 = 0
Answer:
0 0 0
Exercise 3 Question:
Solve the following equation:
7 + 8 − 3 2 : 3 + 4 = \frac{7+8-3}{2}:3+4= 2 7 + 8 − 3 : 3 + 4 =
Solution:
We start solving the equation according to the order of operations.
12 2 : 3 + 4 = \frac{12}{2}:3+4= 2 12 : 3 + 4 =
6 : 3 + 4 = 6:3+4= 6 : 3 + 4 =
2 + 4 = 6 2+4=6 2 + 4 = 6
Answer:
6 6 6
Exercise 4 Question:
Solve the following equation:
36 − ( 4 ⋅ 5 ) 8 − 3 ⋅ 2 = \frac{36-(4\cdot5)}{8}-3\cdot2= 8 36 − ( 4 ⋅ 5 ) − 3 ⋅ 2 =
Solution:
We begin by solving the parentheses that appear in the fraction.
36 − 20 8 − 3 ⋅ 2 = \frac{36-20}{8}-3\cdot2= 8 36 − 20 − 3 ⋅ 2 =
Then we continue solving according to the order of the operations.
16 8 − 6 = \frac{16}{8}-6= 8 16 − 6 =
2 − 6 = − 4 2-6=-4 2 − 6 = − 4
Answer:
− 4 -4 − 4
Exercise 5 Question:
Calculate the correct answer.
25 + 3 − 2 13 + 5 ⋅ 4 = \frac{25+3-2}{13}+5\cdot4= 13 25 + 3 − 2 + 5 ⋅ 4 =
Solution:
We solve the equation according to the order of the operations.
26 13 + 5 ⋅ 4 = \frac{26}{13}+5\cdot4= 13 26 + 5 ⋅ 4 =
We then perform the division operation of the fraction before the multiplication.
2 + 20 = 22 2+20=22 2 + 20 = 22
Answer:
22 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 + 3 ⋅ 0 = 12+3\cdot0= 12 + 3 ⋅ 0 =
Step-by-Step Solution According to the order of operations, we first multiply and then add:
12 + ( 3 ⋅ 0 ) = 12+(3\cdot0)= 12 + ( 3 ⋅ 0 ) =
3 × 0 = 0 3\times0=0 3 × 0 = 0
12 + 0 = 12 12+0=12 12 + 0 = 12
Answer Exercise #2 Solve the following exercise:2 + 0 : 3 = 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)= 2 + ( 0 : 3 ) =
0 : 3 = 0 0:3=0 0 : 3 = 0
2 + 0 = 2 2+0=2 2 + 0 = 2
Answer Exercise #3 0 + 0.2 + 0.6 = 0+0.2+0.6= 0 + 0.2 + 0.6 =
Video Solution Step-by-Step Solution According to the order of operations, the exercise is solved from left to right as it contains only an addition operation:
0 + 0.2 = 0.2 0+0.2=0.2 0 + 0.2 = 0.2
0.2 + 0.6 = 0.8 0.2+0.6=0.8 0.2 + 0.6 = 0.8
Answer Exercise #4 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 : 7 = 0
0 + 1 = 1 0+1=1 0 + 1 = 1
Answer Exercise #5 12 + 1 + 0 = 12+1+0= 12 + 1 + 0 =
Video Solution Step-by-Step Solution According to the order of operations, the exercise is solved from left to right as it only involves an addition operation:
12 + 1 = 13 12+1=13 12 + 1 = 13
13 + 0 = 13 13+0=13 13 + 0 = 13
Answer 
