Solve the Equation: b - 3⅘ = -8⅗ with Mixed Numbers

Q: Why do I need to convert mixed numbers to improper fractions?

Converting makes the math much easier! Working with improper fractions like $ \frac{19}{5} $ is simpler than juggling whole numbers and fractions separately.

Q: What about negative mixed numbers like -8³⁄₅?

The negative sign applies to the entire mixed number. Convert normally, then make the result negative: $ -8\frac{3}{5} = -\frac{43}{5} $.

Q: How do I check if my answer is correct?

Substitute your answer back into the original equation: $ -4\frac{4}{5} - 3\frac{4}{5} $ should equal $ -8\frac{3}{5} $. If it does, you're right!

Linear Equations with Mixed Number Operations

$b-3\frac{4}{5}=-8\frac{3}{5}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve the problem step by step.

00:10 First, we need to isolate the unknown variable, B, and calculate its value.

00:29 Next, let's convert the mixed number into a fraction.

00:35 After that, use long subtraction to complete the calculation.

00:52 And that's how we find the solution to this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$b-3\frac{4}{5}=-8\frac{3}{5}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert mixed numbers to improper fractions
Step 2: Isolate the variable $b$ by applying algebraic operations
Step 3: Simplify the result to find the value of $b$

Now, let's work through each step:

Step 1: Convert the mixed numbers to improper fractions.
$3\frac{4}{5} = \frac{15}{5} + \frac{4}{5} = \frac{19}{5}$
$-8\frac{3}{5} = -\left(\frac{40}{5} + \frac{3}{5}\right) = -\frac{43}{5}$

Step 2: Add $\frac{19}{5}$ to both sides of the equation to isolate $b$ .

$b - \frac{19}{5} = -\frac{43}{5}$

Add $\frac{19}{5}$ to both sides:
$b - \frac{19}{5} + \frac{19}{5} = -\frac{43}{5} + \frac{19}{5}$
This simplifies to:
$b = \frac{-43+19}{5} = \frac{-24}{5} = -4\frac{4}{5}$

Therefore, the solution to the problem is $b = -4\frac{4}{5}$ .

Final Answer

$b=-4\frac{4}{5}$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Transform mixed numbers to improper fractions first
Technique: Convert $3\frac{4}{5} = \frac{19}{5}$ by multiplying and adding
Check: Substitute $b = -4\frac{4}{5}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Working with mixed numbers directly without converting
Don't try to add/subtract mixed numbers like $3\frac{4}{5} + 8\frac{3}{5}$ without converting = messy fractions and wrong answers! Mixed numbers make arithmetic operations confusing and error-prone. Always convert to improper fractions first, then perform operations.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Why do I need to convert mixed numbers to improper fractions?

Converting makes the math much easier! Working with improper fractions like $\frac{19}{5}$ is simpler than juggling whole numbers and fractions separately.

How do I convert a mixed number like 3⁴⁄₅?

Multiply the whole number by the denominator, then add the numerator: 3 × 5 + 4 = 19. So $3\frac{4}{5} = \frac{19}{5}$ .

What about negative mixed numbers like -8³⁄₅?

The negative sign applies to the entire mixed number. Convert normally, then make the result negative: $-8\frac{3}{5} = -\frac{43}{5}$ .

Do I need to convert my final answer back to a mixed number?

Check what format the answer choices use! If they show mixed numbers like $-4\frac{4}{5}$ , convert your improper fraction $-\frac{24}{5}$ back to match.

How do I check if my answer is correct?

Substitute your answer back into the original equation: $-4\frac{4}{5} - 3\frac{4}{5}$ should equal $-8\frac{3}{5}$ . If it does, you're right!

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