Solve for b in 3b = 7/6: Linear Equation with Fractions

Q: How do I divide a fraction by a whole number?

When dividing $ \frac{7}{6} ÷ 3 $, imagine it as $ \frac{\frac{7}{6}}{3} $. To simplify, multiply the denominator of the top fraction by the bottom number: $ \frac{7}{6×3} = \frac{7}{18} $.

Q: Should I convert mixed numbers in the answer choices to improper fractions?

Yes! Convert $ 4\frac{1}{3} $ to $ \frac{13}{3} $ and compare. This makes it much easier to see which answer matches your solution of $ \frac{7}{18} $.

Q: What if I get confused with all the fractions?

Take it step by step! Write each step clearly: (1) Start with $ 3b = \frac{7}{6} $, (2) Divide both sides by 3, (3) Get $ b = \frac{7}{18} $. Don't rush!

Q: How can I check if 7/18 is in simplest form?

Find the greatest common factor (GCF) of 7 and 18. Since 7 is prime and doesn't divide 18, the GCF is 1. Therefore, $ \frac{7}{18} $ is already simplified!

Linear Equations with Fraction Division

$3b=\frac{7}{6}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown B

00:06 We'll divide by the unknown's coefficient to isolate unknown B

00:17 Every number is essentially divided by 1

00:23 Division by a fraction is essentially multiplication by its reciprocal

00:33 We'll make sure to multiply numerator by numerator and denominator by denominator

00:46 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$3b=\frac{7}{6}$

Step-by-step solution

To solve the equation $3b = \frac{7}{6}$ for the variable $b$ , we will perform the following steps:

Step 1: Identify the equation. The given equation is $3b = \frac{7}{6}$ .
Step 2: Isolate the variable. Divide both sides by 3 to solve for $b$ .

When we divide both sides of the equation by 3, we obtain:

b = \frac{\frac{7}{6}}{3}

Step 3: Simplify the expression. Dividing a fraction by an integer is equivalent to multiplying the denominator of the fraction by that integer:

b = \frac{7}{6 \times 3}

The denominator becomes:

b = \frac{7}{18}

Thus, the solution to the equation is $b = \frac{7}{18}$ .

This matches the correct answer choice among the given options.

Therefore, the value of $b$ is $b = \frac{7}{18}$ .

Final Answer

$b=\frac{7}{18}$

Key Points to Remember

Essential concepts to master this topic

Rule: To isolate variable, divide both sides by coefficient
Technique: Dividing by whole number means multiplying denominator: $\frac{7}{6} ÷ 3 = \frac{7}{6×3} = \frac{7}{18}$
Check: Substitute back: $3 × \frac{7}{18} = \frac{21}{18} = \frac{7}{6}$ ✓

Common Mistakes

Avoid these frequent errors

Converting fraction to decimal too early
Don't convert $\frac{7}{6}$ to 1.167 then divide by 3 = 0.389 (messy decimal)! This creates rounding errors and loses exact precision. Always keep fractions as fractions and divide by multiplying the denominator.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why don't I multiply both sides by 1/3 instead of dividing by 3?

You can do either! Dividing by 3 is the same as multiplying by $\frac{1}{3}$ . Most students find division easier to understand conceptually.

How do I divide a fraction by a whole number?

When dividing $\frac{7}{6} ÷ 3$ , imagine it as $\frac{\frac{7}{6}}{3}$ . To simplify, multiply the denominator of the top fraction by the bottom number: $\frac{7}{6×3} = \frac{7}{18}$ .

Should I convert mixed numbers in the answer choices to improper fractions?

Yes! Convert $4\frac{1}{3}$ to $\frac{13}{3}$ and compare. This makes it much easier to see which answer matches your solution of $\frac{7}{18}$ .

What if I get confused with all the fractions?

Take it step by step! Write each step clearly: (1) Start with $3b = \frac{7}{6}$ , (2) Divide both sides by 3, (3) Get $b = \frac{7}{18}$ . Don't rush!

How can I check if 7/18 is in simplest form?

Find the greatest common factor (GCF) of 7 and 18. Since 7 is prime and doesn't divide 18, the GCF is 1. Therefore, $\frac{7}{18}$ is already simplified!

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