Question

Reduce to a single fraction: $2\frac{5}{8}-2\frac{1}{6}+4\frac{3}{4}$

Answer 1

Step 1: Converting the mixed fractions into improper fractions.
$Mixedfraction=\frac{Integralpart\times Denominator+Numerator}{Denominator}$

We will use the above formula to convert the mixed fraction into improper fraction.
$2\frac{5}{8}-2\frac{1}{6}+4\frac{3}{4}$
$=\frac{2\times 8+5}{8}-\frac{2\times 6+1}{6}+\frac{4\times 4+3}{4}$
$=\frac{16+5}{8}-\frac{12+1}{6}+\frac{16+3}{4}$
$=\frac{21}{8}-\frac{13}{6}+\frac{19}{4}$

Step 2: Simplifying the expression by converting into like fractions.

To simplify the given expression first we have to convert the fractions into like fractions.

LCM of the denominators of the fractions is
LCM (8, 6, 4) = $2\times 2\times 2\times 3=24$

Now, we will make the denominator of each fraction equal to LCM and simplify as follows:

$\frac{21}{8}-\frac{13}{6}+\frac{19}{4}=\frac{21\times 3}{8\times 3}-\frac{13\times 4}{6\times 4}+\frac{19\times 6}{4\times 6}$
$=\frac{63}{24}-\frac{52}{24}+\frac{114}{24}$
$=\frac{63-52+114}{24}=\frac{125}{24}$.


Therefore, the reduced form of the given expression is $\frac{125}{24}\text{or}5\frac{5}{24}$.