Solve: Adding (-1/5) and (-3 4/5) Negative Fractions

Q: Why do I need to convert the mixed number to an improper fraction?

Converting $ 3\frac{4}{5} $ to $ \frac{19}{5} $ makes addition easier! When both fractions have the same denominator, you just add the numerators: $ -1 + (-19) = -20 $.

Q: How do I convert a mixed number to an improper fraction?

Use this formula: multiply whole number × denominator, then add numerator. For $ 3\frac{4}{5} $: $ (3 × 5) + 4 = 15 + 4 = 19 $, so it becomes $ \frac{19}{5} $.

Q: What if the denominators are different?

When denominators are different, find the LCD (Least Common Denominator) first. Convert both fractions to equivalent fractions with the same denominator, then add the numerators.

Q: Can I add the whole numbers and fractions separately?

With negative mixed numbers, it's safer to convert to improper fractions first. This prevents sign errors and makes the calculation cleaner.

Q: How do I know if my final answer should be simplified?

Always check if your answer can be simplified! $ -\frac{20}{5} $ simplifies to $ -4 $ because 20 ÷ 5 = 4. Look for common factors in the numerator and denominator.

Negative Fraction Addition with Mixed Numbers

Solve the following problem:

$(-\frac{1}{5})+(-3\frac{4}{5})=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Find the point on the axis

00:07 Positive times negative is always negative, therefore subtract

00:10 To subtract, move in the left (negative) direction on the axis

00:17 Calculate

00:19 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

Solve the following problem:

$(-\frac{1}{5})+(-3\frac{4}{5})=$

Step-by-step solution

Let's mark minus $\frac{1}{5}$ on the number line and move $3\frac{4}{5}$ steps to the left, meaning our result will be a negative number:

Let's remember the rule:

$+(-x)=-x$

Now let's write the exercise in the appropriate form and solve it:

$-\frac{1}{5}-3\frac{4}{5}=-4$

Final Answer

$-4$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Adding two negative numbers always gives a negative result
Convert: Change $3\frac{4}{5}$ to $\frac{19}{5}$ before adding fractions
Check: $-\frac{1}{5} + (-\frac{19}{5}) = -\frac{20}{5} = -4$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting that adding two negatives stays negative
Don't think $(-\frac{1}{5}) + (-3\frac{4}{5})$ becomes positive = wrong sign on answer! Many students forget that negative + negative = negative. Always remember that when both numbers are negative, your sum must also be negative.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

Why do I need to convert the mixed number to an improper fraction?

Converting $3\frac{4}{5}$ to $\frac{19}{5}$ makes addition easier! When both fractions have the same denominator, you just add the numerators: $-1 + (-19) = -20$ .

How do I convert a mixed number to an improper fraction?

Use this formula: multiply whole number × denominator, then add numerator. For $3\frac{4}{5}$ : $(3 × 5) + 4 = 15 + 4 = 19$ , so it becomes $\frac{19}{5}$ .

What if the denominators are different?

When denominators are different, find the LCD (Least Common Denominator) first. Convert both fractions to equivalent fractions with the same denominator, then add the numerators.

Can I add the whole numbers and fractions separately?

With negative mixed numbers, it's safer to convert to improper fractions first. This prevents sign errors and makes the calculation cleaner.

How do I know if my final answer should be simplified?

Always check if your answer can be simplified! $-\frac{20}{5}$ simplifies to $-4$ because 20 ÷ 5 = 4. Look for common factors in the numerator and denominator.

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