Bobbie Comstock

2021-12-29

To solve: $\frac{3}{8}+\frac{b}{3}=\frac{5}{12}$

usumbiix

Step 1
Myltiply by 2 on both sides,
$24\left(\frac{3}{8}+\frac{b}{3}\right)=\frac{5}{12}×24$
By distributive property,
$24\left(\frac{3}{8}+\frac{b}{3}\right)=24\frac{3}{8}+\frac{b}{3}24$
$24\left(\frac{3}{8}+\frac{b}{3}\right)=3×3+b×8$
$24\left(\frac{3}{8}+\frac{b}{3}\right)=9+8b$
$\frac{5}{12}×24=5×2$
$\frac{5}{12}×24=10$
The value of $\frac{5}{12}×24$ is 10
Replace $24\left(\frac{3}{8}+\frac{b}{3}\right)$ with $9+8b$
Replace $\frac{5}{12}×24$ with 10
$9+8b=10$
Subtract 9 on both sides,
$9+8b-9=10-9$
$8b+0=1$
$8b=1$
Divide by 8 on both sides,
$\frac{8b}{8}=\frac{1}{8}$
So, the value of b is $\frac{1}{8}$

Esther Phillips

Step 1
Given: $\frac{3}{8}+\frac{b}{3}=\frac{5}{12}$
Subtract $\frac{3}{8}$ from both sides
$\frac{3}{8}+\frac{b}{3}-\frac{3}{8}=\frac{5}{12}-\frac{3}{8}$
Simplify
$\frac{3}{8}+\frac{b}{3}-\frac{3}{8}$
$\frac{3}{8}-\frac{3}{8}=0$
$=\frac{b}{3}$
Simplify
$\frac{5}{12}-\frac{3}{8}$
Least Common Multiplier of
Adjust Fractions based on the LCm
$=\frac{10}{24}-\frac{9}{24}$
Since the denominators are equal, combine the fractions:
$\frac{a}{c}±\frac{b}{c}=\frac{a±b}{c}$
$=\frac{10-9}{24}$
Subtract the numbers: $10-9=1$
$\frac{b}{3}=\frac{1}{24}$
Multiply both sides by 3
$\frac{3b}{3}=\frac{1×3}{24}$
Simplify
$b=\frac{1}{8}$

karton

Step 1
Group all constants on the right side of the equation
$\frac{3}{8}+\frac{b}{3}=\frac{5}{12}$
Subtract $\frac{3}{8}$ from both sides:
$\frac{3}{8}+\frac{b}{3}-\frac{3}{8}=\frac{5}{12}-\frac{3}{8}$
Group like terms:
$\frac{b}{3}+\frac{3}{8}+\frac{-3}{8}=\frac{5}{12}-\frac{3}{8}$
Combine the fractions:
$\frac{b}{3}+\frac{3-3}{8}=\frac{5}{12}-\frac{3}{8}$
Combine the numerators:
$\frac{b}{3}+0=\frac{5}{12}-\frac{3}{8}$
Simplify the aritmetic:
$\frac{b}{3}=\frac{5}{12}-\frac{3}{8}$
Find the lowest common denominator:
$\frac{b}{3}=\frac{5×2}{12×2}+\frac{-3×3}{8×3}$
Multiply the denominators:
$\frac{b}{3}=\frac{5×2}{24}+\frac{-3×3}{24}$
Multiply the numerators:
$\frac{b}{3}=\frac{10}{24}+\frac{-9}{24}$
Combine the fractions:
$\frac{b}{3}=\frac{10-9}{24}$
Combine the numerators:
$\frac{b}{3}=\frac{1}{24}$
Step 2
Isolate the b
$\frac{b}{3}=\frac{1}{24}$
Multiply to both sides by 3:
$\frac{b}{3}×3=\frac{1}{24}×3$
Group like terms:
$\frac{1}{3}×3×b=\frac{1}{24}×3$
Simplify the fraction:
$b=\frac{1}{24}×3$
Multiply the fractions:
$b=\frac{1×3}{24}$
Find the greatest common factor of the numerator and denominator:
$b=\frac{1×3}{8×3}$
Factor out and cancel the greatest common factor:
$b=\frac{1}{8}$

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