Solve the equation:
$ 18 \frac{12}{19}+23 \frac{18}{19}-15 \frac{14}{19} $

Given: $ 18 \frac{12}{19}+23 \frac{18}{19}-15 \frac{14}{19} $

To do: Solve the expression

Solution:

To solve this problem we should know to convert mixed fraction into improper fraction.

You can do it using the formula

Improper fraction = $\frac{Whole\ number \times Denominator + Numerator}{Denominator}$ 

Consider$18\frac{12}{19}$$18 \frac{12}{19}$

Here Whole number = 18, Denominator = 19, Numerator = 12. 

Substitute in the above formula $18\frac{12}{19}=\frac{18\times19+12}{7}$

$18 \frac{12}{19}=\frac{(18 \times 19)+12}{7}$

So we solve the question with the following steps:

$18\frac{12}{19}+23\frac{18}{19}-15\frac{14}{19}$

$\begin{array}{l}18\frac{12}{19}+23\frac{18}{19}-15\frac{14}{19}\\ \\ \\ =\frac{18\times 19+12}{19}+\frac{23\times 19+18}{19}-\frac{(15\times 19+14)}{19}\\ \\ =\frac{18\times 19+12+23\times 19+18-15\times 19-14}{19}\\ \\ =\frac{(18+23-15)\times 19+12+18-14}{19}\\ \\ =\frac{26\times 19+16}{19}\\ \\ =\frac{510}{19}\end{array}$

$$$\begin{array}{l}$ 18\frac{12}{19} \ +\ 23\frac{18}{19} \ -\ 15\frac{14}{19}\ \ \ =\ \frac{18\times 19\ +12}{19} \ +\ \frac{23\times 19\ +18}{19} \ -\ \frac{( 15\times 19\ +14)}{19}\ \ =\ \frac{18\times 19\ +12\ +\ 23\times 19\ +18\ -15\times 19\ -\ 14\ }{19}\ \ =\ \frac{( 18+23-15) \times 19\ +12+18\ -14}{19}\ \ =\ \frac{26\times 19\ +\ 16}{19}\ \ =\frac{510}{19} \end{array}

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Updated on: 10-Oct-2022

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