Answer:
[tex]3\frac{7}{8}[/tex]
Step-by-step explanation:
The given expression is [tex]3\frac{1}{4} - (\frac{-5}{8})[/tex]
We need to simplify the fractions.
Let's convert the mixed number [tex]3\frac{1}{4}[/tex] to improper fraction.
[tex]3\frac{1}{4} = \frac{4.3 +1}{4} = \frac{12 + 1}{4} = \frac{13}{4}[/tex]
So, [tex]\frac{13}{4} -(\frac{-5}{8} )[/tex]
= [tex]\frac{13}{4} +(\frac{5}{8} )[/tex]
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.
= [tex]\frac{13(2)}{4(2)} + \frac{5}{8}[/tex]
= [tex]\frac{26}{8} + \frac{5}{8}[/tex]
Now the denominators became the same. Now we can simplify the numerator and keep the denominator as it is.
= [tex]\frac{26 + 5}{8}[/tex]
= [tex]\frac{31}{8}[/tex]
Now we can convert this improper fraction to mixed number
= [tex]3\frac{7}{8}[/tex]
To solve the expression we will first convert the improper fraction to a Proper fraction.
The expression is equivalent to [tex]3\dfrac{7}{8}[/tex].
A fraction is a way to describe a part of a whole. such as the fraction [tex]\dfrac{1}{4}[/tex]
can be described as 0.25.
A mixed fraction is a fraction that contains a whole number and a fraction whose denominator is greater than the numerator.
Given to us
[tex]3\dfrac{1}{4} - (\dfrac{-5}{8} )[/tex]
Solving the mixed fraction,
[tex]=3\dfrac{1}{4} - (\dfrac{-5}{8} )\\\\=\dfrac{(3\times 4)+1}{4} - (\dfrac{-5}{8} )\\\\=\dfrac{13}{4} - (\dfrac{-5}{8} )[/tex]
Taking the LCM of the denominator,
[tex]=\dfrac{(13\times 2)}{(4\times 2)} + \dfrac{5}{8}[/tex]
[tex]=\dfrac{26}{8} + \dfrac{5}{8}\\\\=\dfrac{26+5}{8}\\\\=\dfrac{31}{8}\\[/tex]
Converting it to a mixed fraction,
[tex]=3\dfrac{7}{8}[/tex]
Hence, the expression is equivalent to [tex]3\dfrac{7}{8}[/tex].
Learn more about Mixed fractions:
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