Question

$\red{\boxed{\mathfrak\colorbox{grey}{Question}}}$
[Urgent]
$4\frac{1}{3} - 3 \frac{11}{12} + 5 \frac{1}{6}$
​

Answer 1

Given:

• $\tt4\frac{1}{3} - 3 \frac{11}{12} + 5\frac{1}{6}$

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:

$\longrightarrow \tt 4 \frac{1}{3} - 3 \frac{11}{12} + 5 \frac{1}{6}$

★Evaluation:

$\longrightarrow \tt \: 4 \frac{1}{3} - 3 \frac{11}{12} + 5 \frac{1}{6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: 4 - 3 + 5 + ( \frac{1}{3} - \frac{11}{12} + \frac{1}{6} ) \\ \\ \\ \longrightarrow \tt \: 6 + ( \frac{4}{12} - \frac{11}{12} + \frac{2}{12} ) \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: 6 + ( \frac{4 + 2 - 11}{12} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: 6 + (\frac{6 - 11}{12} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: 6 \frac{ - 5}{12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: 5 (\frac{12}{12} - \frac{5}{12} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \pink{ \boxed{\tt{ \: 5 \frac{7}{12} }} \star} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• 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 $\tt a\frac {b}{c}$

We simply multiply c and a then then add the product to the number b

So, the fraction obtained are :

$\purple{ \rightarrow} \tt \frac{13}{3} \\ \\ \purple{ \rightarrow} \tt \: \frac{47}{12} \\ \\ \purple{ \rightarrow} \tt\frac{62}{12}$

Now let's Simplify the expression:

$\longrightarrow \tt \: \frac{13}{3} - \frac{47}{12} + \frac{31}{6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Let's take the least Common multiple :

$\begin{gathered}\:\:\:\:\:\:\:\:\:\:\:\begin{gathered} \begin{array}{c|c} \underline{\sf{3}}& {\sf{ \underline{ \red{3,12,6} \: \: \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\ \underline{\sf{2}}&{\sf{ \underline{1,4 ,2 \: \: \: \: \: }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\\underline{\sf{2}}&{\sf{ \underline{1 ,2,1\: \: \: \: \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\ \sf{} & \sf{1,1,1 \: \: \: \: \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{array}\end{gathered}\end{gathered}$

$\tt \: l.c.m = { \pink{ \boxed{3}}} \times{ \pink{ \boxed{2}}} \times { \pink{ \boxed{2}}} \\ \\ \tt \: l.c.m ={ \purple{ \boxed{12}} \star} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Let's Simplify the rest now :

$\longrightarrow \tt \: \frac{13 \times 4}{3 \times 4} - \frac{47 \times 1}{12 \times 1} + \frac{31 \times 5}{6 \times 2} \\ \\ \\ \longrightarrow \tt \: \frac{52}{12} - \frac{47}{12} + \frac{62}{12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: \frac{52 - 47 + 62}{12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \blue{ \boxed{ \tt {\: \frac{67}{12} }} \star} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence:

• The evaluated form of expression = $\tt 5 \frac{7}{12} or \frac{67}{12}$

Answer 2

$\huge{\bf{\green{\mathfrak{Question:-}}}}$

• $\sf 4\dfrac{1}{3} \:-\: 3 \dfrac{11}{12}\: + \:5 \dfrac{1}{6}$

$\huge {\bf{\orange{\mathfrak{Answer:-}}}}$

• $\textsf{The given fractions are in mixed form.}$

• $\textsf{Converting them to improper fractions,}$

• $\sf \dfrac{13}{3} \: - \: \dfrac{47}{12} \: + \: \dfrac{31}{6}$

• $\textsf{Taking LCM,}$

• $\sf \dfrac{13}{3} \: * \: \dfrac{4}{4} \: - \: \dfrac{47}{12} \: * \: \dfrac{1}{1} \: + \: \dfrac{31}{6} \: * \: \dfrac{2}{2}$

• $\sf \dfrac{52}{12} \: - \: \dfrac{47}{12} \: + \: \dfrac{62}{12}$

• $\sf \dfrac{52 \: - \: 47 \: + \: 62}{12}$

• $\sf \dfrac{5 \: + \: 62}{12}$

• $\boxed{\sf \dfrac{67}{12}}$

$\huge{\bf{\red{\mathfrak{Conclusion:-}}}}$

• $\boxed{\therefore{\sf 4\dfrac{1}{3} \:-\: 3 \dfrac{11}{12}\: + \:5 \dfrac{1}{6} \: = \: \dfrac{67}{12} \: = \: 5 \dfrac{7}{12}}}$

$\huge{\bf{\purple{\mathfrak{Extra \: Information:-}}}}$

• $\textsf{\underline{\underline{Fraction :-}}}$

• A fraction is in the form of $\sf \dfrac{p}{q}$ where p and q belongs to Z (Integers) and q is not equal to 0.

• $\textsf{\underline{\underline{There are 3 types of fractions :-}}}$

• $\textsf{\underline{\underline{Proper Fraction :-}}}$

• In a proper fraction, numerator is lesser than denominator.

• Ex:- $\sf \dfrac{1}{2} \: , \: \dfrac{13}{19} \: , \: etc.$

• $\textsf{\underline{\underline{Improper Fraction :-}}}$

• In a improper fraction, numerator is greater or equal to denominator.

• Ex:- $\sf \dfrac{4}{4} \: , \: \dfrac{45}{19} \: , \: etc.$

• $\textsf{\underline{\underline{Mixed Fraction :-}}}$

• Mixed fraction is a combination of a whole number and a fraction.

• Ex:- $\sf 12\dfrac{1}{4} \: , \: 9\dfrac{5}{19} \: , \: etc.$