Question

What should be subtracted from $8\frac{3}{4}$ to get $2\frac{2}{3}$ ?

Answer 1

Step 1: Converting the given statement into mathematical expression.
Let the number that should be subtracted from $8\frac{3}{4}$ be x to get $2\frac{2}{3}$
⇒ $8\frac{3}{4}$ − 𝑥 = $2\frac{2}{3}$
Step 2: Convert the mixed fractions into improper fractions
Now, we have:
$8\frac{3}{4}$−𝑥=$2\frac{2}{3}$

𝑀𝑖𝑥𝑒𝑑 𝐹𝑟𝑎𝑐𝑡𝑖𝑜n
=$\frac{(Integralpart\times Denominator+Numerator)}{Denominator}$

We will use the above formula to convert the mixed fraction into improper fraction
$\frac{8\times 4+3}{4}$ - 𝑥 = $\frac{2\times 3+2}{3}$
⇒$\frac{32+3}{4}$ - 𝑥 =$\frac{6+2}{3}$
⇒$\frac{35}{4}$ - 𝑥 =$\frac{8}{3}$
⇒$x=\frac{35}{4}-\frac{8}{3}$
Step 3: Convert the fractions into like fractions and find the value of x
$x=\frac{35\times 3}{4\times 3}-\frac{8\times 4}{3\times 4}$
[LCM of (3,4=12]
$=\frac{105}{12}-\frac{32}{12}$
$=\frac{105-32}{12}$
$=\frac{73}{12}=6\frac{1}{12}$

Hence, $\frac{73}{12}or6\frac{1}{12}$ should be subtracted from $8\frac{3}{4}$ to get $2\frac{2}{3}$.