Question

Can i get some help :

Answer 1

Answer:

b = $\frac{7}{12}$

Step-by-step explanation:

b + $\frac{2}{3}$ = 1 $\frac{1}{4}$ ← change to an improper fraction

b + $\frac{2}{3}$ = $\frac{5}{4}$

Multiply through by 12 ( the LCM of 3 and 4 ) to clear the fractions

12b + 8 = 15 ( subtract 8 from both sides )

12b = 7 ( divide both sides by 12 )

b = $\frac{7}{12}$

Answer 2

Answer:

The value of b is 7/12.

Step-by-step explanation:

Question :

Solve for b.

${\implies{\sf{b + \dfrac{2}{3} = 1 \dfrac{1}{4}}}}$

Enter your answer as a fraction in simplest form in the box.

$\implies{\sf{b = \square}}$

$\begin{gathered}\end{gathered}$

Solution :

${\implies{\sf{b + \dfrac{2}{3} = 1 \dfrac{1}{4}}}}$

Converting the mixed fractions into improper fraction.

${\implies{\sf{b + \dfrac{2}{3} = \dfrac{(1 \times 4) + 1}{4}}}}$

${\implies{\sf{b + \dfrac{2}{3} = \dfrac{(4)+ 1}{4}}}}$

${\implies{\sf{b + \dfrac{2}{3} = \dfrac{4+ 1}{4}}}}$

${\implies{\sf{b + \dfrac{2}{3} = \dfrac{5}{4}}}}$

Now, transporting LHS to RHS.

${\implies{\sf{b= \dfrac{5}{4} - \dfrac{2}{3}}}}$

Taking LCM of denominators and subtracting.

${\implies{\sf{b= \dfrac{(5 \times 3) - (2 \times 4)}{12}}}}$

${\implies{\sf{b= \dfrac{(15) - (8)}{12}}}}$

${\implies{\sf{b= \dfrac{15 - 8}{12}}}}$

${\implies{\sf{b= \dfrac{7}{12}}}}$

${\star{\red{\underline{\boxed{\sf{b= \dfrac{7}{12}}}}}}}$

Hence, the value of b is 7/12.

$\begin{gathered}\end{gathered}$

Verification :

${\implies{\sf{b + \dfrac{2}{3} = 1 \dfrac{1}{4}}}}$

Substituting the value of (b=7/12)

${\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = 1 \dfrac{1}{4}}}}$

Converting mixed fractions into improper fraction

${\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = \dfrac{(1 \times 4) + 1}{4}}}}$

${\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = \dfrac{(4) + 1}{4}}}}$

${\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = \dfrac{4 + 1}{4}}}}$

${\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = \dfrac{5}{4}}}}$

Taking LCM of denominators in LHS and adding.

${\implies{\sf{ \dfrac{(7 \times 1) + (2 \times 4)}{12} = \dfrac{5}{4}}}}$

${\implies{\sf{ \dfrac{(7) + (8)}{12} = \dfrac{5}{4}}}}$

${\implies{\sf{ \dfrac{7 + 8}{12} = \dfrac{5}{4}}}}$

${\implies{\sf{ \dfrac{15}{12} = \dfrac{5}{4}}}}$

Cutting the fraction to simplest form.

${\implies{\sf{ \cancel{\dfrac{15}{12}} = \dfrac{5}{4}}}}$

${\implies{\sf{ \dfrac{5}{4}= \dfrac{5}{4}}}}$

${\star{\red{\underline{\boxed{\sf{LHS = RHS}}}}}}$

Hence Verified!

$\underline{\rule{220pt}{3.5pt}}$