Question

1. \\(\frac{2}{7} = \frac{b + 1}{56}\\)

Explanation:

Step1: Cross - multiply the equation

Given the equation $\frac{2}{7}=\frac{b + 1}{56}$, cross - multiplying (which is based on the property that if $\frac{a}{c}=\frac{d}{e}$, then $a\times e=c\times d$) gives us $2\times56 = 7\times(b + 1)$.
Calculating the left - hand side: $2\times56=112$. So the equation becomes $112=7\times(b + 1)$.

Step2: Solve for \(b + 1\)

Divide both sides of the equation $112 = 7\times(b + 1)$ by 7. We know that to isolate $(b + 1)$, we use the inverse operation of multiplication (which is division). So $\frac{112}{7}=b + 1$.
Since $\frac{112}{7}=16$, the equation simplifies to $16=b + 1$.

Step3: Solve for \(b\)

Subtract 1 from both sides of the equation $16=b + 1$ to isolate $b$. Using the inverse operation of addition (subtraction), we get $b=16 - 1$.
Calculating $16-1 = 15$.

Answer:

\(b = 15\)