अपने छोटे भाई को, जो जरा जरा सी बात पर दुखी हो जाता है। जीवन के सत्य ( सुख-दुख को समान भाव से लेना) से परिचित करते हुए एक पत्र लिखिए
Answers
Answer:
Given:
\tt4\frac{1}{3} - 3 \frac{11}{12} + 5\frac{1}{6}4
3
1
−3
12
11
+5
6
1
To Find:
The value of the expression after evaluation
Solution:
How To Solve?
⇢ So, here we have been given few mixed fractions which form an expression and It is said that we have to evaluate the expression given respectively! Now, we can start the process by converting the mixed fractions to improper fractions or by Subtracting their whole part and simplifying the rest proper fractions!
★Expression:
\longrightarrow \tt 4 \frac{1}{3} - 3 \frac{11}{12} + 5 \frac{1}{6}⟶4
3
1
−3
12
11
+5
6
1
★Evaluation:
\begin{gathered} \longrightarrow \tt \: 4 \frac{1}{3} - 3 \frac{11}{12} + 5 \frac{1}{6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: 4 - 3 + 5 + ( \frac{1}{3} - \frac{11}{12} + \frac{1}{6} ) \\ \\ \\ \longrightarrow \tt \: 6 + ( \frac{4}{12} - \frac{11}{12} + \frac{2}{12} ) \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: 6 + ( \frac{4 + 2 - 11}{12} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: 6 + (\frac{6 - 11}{12} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: 6 \frac{ - 5}{12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: 5 (\frac{12}{12} - \frac{5}{12} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \pink{ \boxed{\tt{ \: 5 \frac{7}{12} }} \star} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered}
⟶4
3
1
−3
12
11
+5
6
1
⟶4−3+5+(
3
1
−
12
11
+
6
1
)
⟶6+(
12
4
−
12
11
+
12
2
)
⟶6+(
12
4+2−11
)
⟶6+(
12
6−11
)
⟶6
12
−5
⟶5(
12
12
−
12
5
)
⟶
5
12
7
⋆
Hence the answer is 5 + 7/12
[Method 2]
[converting them into improper fractions]
How do u convert into improper fractions?
⇢ When a mixed fraction is in the from \tt a\frac {b}{c}a
c
b
We simply multiply c and a then then add the product to the number b
So, the fraction obtained are :
\begin{gathered}\purple{ \rightarrow} \tt \frac{13}{3} \\ \\ \purple{ \rightarrow} \tt \: \frac{47}{12} \\ \\ \purple{ \rightarrow} \tt\frac{62}{12} \end{gathered}
→
3
13
→
12
47
→
12
62
Now let's Simplify the expression:
\longrightarrow \tt \: \frac{13}{3} - \frac{47}{12} + \frac{31}{6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:⟶
3
13
−
12
47
+
6
31
Let's take the least Common multiple :
\begin{gathered}\begin{gathered}\:\:\:\:\:\:\:\:\:\:\:\begin{gathered} \begin{array}{c|c} \underline{\sf{3}}& {\sf{ \underline{ \red{3,12,6} \: \: \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\ \underline{\sf{2}}&{\sf{ \underline{1,4 ,2 \: \: \: \: \: }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\\underline{\sf{2}}&{\sf{ \underline{1 ,2,1\: \: \: \: \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\ \sf{} & \sf{1,1,1 \: \: \: \: \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{array}\end{gathered}\end{gathered}\end{gathered}
3
2
2
3,12,6
1,4,2
1,2,1
1,1,1
\begin{gathered} \tt \: l.c.m = { \pink{ \boxed{3}}} \times{ \pink{ \boxed{2}}} \times { \pink{ \boxed{2}}} \\ \\ \tt \: l.c.m ={ \purple{ \boxed{12}} \star} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered}
l.c.m=
3
×
2
×
2
l.c.m=
12
⋆
Let's Simplify the rest now :
\begin{gathered} \longrightarrow \tt \: \frac{13 \times 4}{3 \times 4} - \frac{47 \times 1}{12 \times 1} + \frac{31 \times 5}{6 \times 2} \\ \\ \\ \longrightarrow \tt \: \frac{52}{12} - \frac{47}{12} + \frac{62}{12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: \frac{52 - 47 + 62}{12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \blue{ \boxed{ \tt {\: \frac{67}{12} }} \star} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered}
⟶
3×4
13×4
−
12×1
47×1
+
6×2
31×5
⟶
12
52
−
12
47
+
12
62
⟶
12
52−47+62
⟶
12
67
$^~%+)55{>&)33/
⋆
Hence:
The evaluated form of expression = \tt 5 \frac{7}{12} or \frac{67}{12}5
12
7
or
12
67
yuoto9298t95