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Verified Answer :

Answer:

\(3\frac{7}{8}\)

Step-by-step explanation:

The given expression is \(3\frac{1}{4} - (\frac{-5}{8})\)

We need to simplify the fractions.

Let's convert the mixed number \(3\frac{1}{4}\) to improper fraction.

\(3\frac{1}{4} = \frac{4.3 +1}{4} = \frac{12 + 1}{4} = \frac{13}{4}\)

So, \(\frac{13}{4} -(\frac{-5}{8} )\)

= \(\frac{13}{4} +(\frac{5}{8} )\)

Now we have to find the least common divisor (LCD) of 4 and 8. So that we can simplify the fractions.

The LCD of 4 and 8 is 8.

So make the denominators as 8.

= \(\frac{13(2)}{4(2)} + \frac{5}{8}\)

= \(\frac{26}{8} + \frac{5}{8}\)

Now the denominators became the same. Now we can simplify the numerator and keep the denominator as it is.

=  \(\frac{26 + 5}{8}\)

=  \(\frac{31}{8}\)

Now we can convert this improper fraction to mixed number

= \(3\frac{7}{8}\)

To solve the expression we will first convert the improper fraction to a Proper fraction.

The expression is equivalent to \(3\dfrac{7}{8}\).

What is a Fraction?

A fraction is a way to describe a part of a whole. such as the fraction \(\dfrac{1}{4}\)

can be described as 0.25.

What is a Mixed Fraction?

A mixed fraction is a fraction that contains a whole number and a fraction whose denominator is greater than the numerator.

Given to us

  • \(3\dfrac{1}{4} - (\dfrac{-5}{8} )\)

 \(3\dfrac{1}{4} - (\dfrac{-5}{8} )\)

Solving the mixed fraction,

\(=3\dfrac{1}{4} - (\dfrac{-5}{8} )\\\\=\dfrac{(3\times 4)+1}{4} - (\dfrac{-5}{8} )\\\\=\dfrac{13}{4} - (\dfrac{-5}{8} )\)

Taking the LCM of the denominator,

\(=\dfrac{(13\times 2)}{(4\times 2)} + \dfrac{5}{8}\)

\(=\dfrac{26}{8} + \dfrac{5}{8}\\\\=\dfrac{26+5}{8}\\\\=\dfrac{31}{8}\\\)

Converting it to a mixed fraction,

\(=3\dfrac{7}{8}\)

Hence, the expression is equivalent to \(3\dfrac{7}{8}\).

Learn more about Mixed fractions:

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