Solve Mixed Number Equation: 2⅕ + (-30/50) with Negative Fractions

Q: Why does minus negative equal plus?

Think of it like directions: if you're told "don't go backward", that means go forward! Mathematically, $ -(-x) = +x $ because two negatives cancel out.

Q: Should I reduce fractions before or after adding?

It's easier to reduce fractions first! In this problem, $ \frac{30}{50} = \frac{3}{5} $ when you divide both parts by 10, making the addition much simpler.

Q: How do I add a mixed number and a fraction?

You have two options: convert the mixed number to improper fraction OR add the fraction to the fractional part. For $ 2\frac{1}{5} + \frac{3}{5} $, add: $ \frac{1}{5} + \frac{3}{5} = \frac{4}{5} $, then combine with the 2.

Q: What if the denominators are different?

You'd need to find a common denominator first. But in this problem, both fractions end up with denominator 5, so you can add directly: $ \frac{1}{5} + \frac{3}{5} = \frac{4}{5} $.

Q: How can I check my answer is right?

Convert everything to the same form and verify! $ 2\frac{4}{5} = \frac{14}{5} $ and $ 2\frac{1}{5} + \frac{3}{5} = \frac{11}{5} + \frac{3}{5} = \frac{14}{5} $ ✓

Mixed Numbers with Double Negative Signs

$(+2\frac{1}{5})-(-\frac{30}{50})=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Negative times negative is always positive

00:06 Let's reduce to 10

00:09 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

$(+2\frac{1}{5})-(-\frac{30}{50})=$

Step-by-step solution

Let's remember the rule:

$-(-x)=+x$

Now let's write the exercise in the following way:

$2\frac{1}{5}+\frac{30}{50}=$

We'll reduce the fraction $\frac{30}{50}$ by 10

$2\frac{1}{5}+\frac{3}{5}=2\frac{4}{5}$

Final Answer

$2\frac{4}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Double negative becomes positive: -(-x) = +x
Technique: Simplify fractions first: 30/50 = 3/5 by dividing by 10
Check: Convert to improper fractions: 11/5 + 3/5 = 14/5 = 2⁴⁄₅ ✓

Common Mistakes

Avoid these frequent errors

Treating double negative as subtraction
Don't solve 2¹⁄₅ - 30/50 = 1³⁄₅! This ignores the double negative rule and gives the wrong answer. The double negative -(-30/50) becomes +30/50, so you're actually adding. Always change -(-x) to +x first.

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 does minus negative equal plus?

Think of it like directions: if you're told "don't go backward", that means go forward! Mathematically, $-(-x) = +x$ because two negatives cancel out.

Should I reduce fractions before or after adding?

It's easier to reduce fractions first! In this problem, $\frac{30}{50} = \frac{3}{5}$ when you divide both parts by 10, making the addition much simpler.

How do I add a mixed number and a fraction?

You have two options: convert the mixed number to improper fraction OR add the fraction to the fractional part. For $2\frac{1}{5} + \frac{3}{5}$ , add: $\frac{1}{5} + \frac{3}{5} = \frac{4}{5}$ , then combine with the 2.

What if the denominators are different?

You'd need to find a common denominator first. But in this problem, both fractions end up with denominator 5, so you can add directly: $\frac{1}{5} + \frac{3}{5} = \frac{4}{5}$ .

How can I check my answer is right?

Convert everything to the same form and verify! $2\frac{4}{5} = \frac{14}{5}$ and $2\frac{1}{5} + \frac{3}{5} = \frac{11}{5} + \frac{3}{5} = \frac{14}{5}$ ✓

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