Solve the Fraction Addition: 1/5 + 7/10 Step by Step

Q: Why can't I just add the tops and bottoms separately?

Because fractions represent parts of different wholes! Adding $ \frac{1}{5} $ (fifths) to $ \frac{7}{10} $ (tenths) is like adding apples to oranges. You need the same denominator to combine them properly.

Q: What if both fractions need to be converted?

Convert both fractions to have the common denominator! For example, with $ \frac{2}{3} + \frac{1}{4} $, convert both to twelfths: $ \frac{8}{12} + \frac{3}{12} = \frac{11}{12} $.

Q: Do I need to simplify my final answer?

Always check if you can simplify! In this problem, $ \frac{9}{10} $ is already in lowest terms since 9 and 10 share no common factors besides 1.

Q: What's the quickest way to check if my answer is right?

Convert your answer to a decimal and check: $ \frac{1}{5} = 0.2 $ and $ \frac{7}{10} = 0.7 $, so 0.2 + 0.7 = 0.9 = $ \frac{9}{10} $ ✓

Fraction Addition with Common Denominators

Solve the following exercise:

$\frac{1}{5}+\frac{7}{10}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply the fraction by 2 to find a common denominator

00:09 Remember to multiply both numerator and denominator

00:17 Calculate the multiplications

00:22 Add under common denominator

00:26 Calculate the numerator

00:30 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 exercise:

$\frac{1}{5}+\frac{7}{10}=\text{?}$

Step-by-step solution

To solve the problem of adding the fractions $\frac{1}{5}$ and $\frac{7}{10}$ , we follow these steps:

Step 1: Identify the least common multiple (LCM) of the denominators 5 and 10, which is 10.
Step 2: Convert $\frac{1}{5}$ to a fraction with a denominator of 10. To do this, multiply both the numerator and denominator by 2: $\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}$
Step 3: Observe that $\frac{7}{10}$ already has the common denominator of 10.
Step 4: Add the two fractions with a common denominator: $\frac{2}{10} + \frac{7}{10} = \frac{2 + 7}{10} = \frac{9}{10}$

The sum of $\frac{1}{5}$ and $\frac{7}{10}$ is thus $\mathbf{\frac{9}{10}}$ .

Final Answer

$\frac{9}{10}$

Key Points to Remember

Essential concepts to master this topic

Common Denominator Rule: Find LCM of denominators before adding fractions
Conversion Technique: Transform $\frac{1}{5}$ to $\frac{2}{10}$ by multiplying by $\frac{2}{2}$
Verification Check: Convert answer back: $\frac{9}{10} = \frac{2}{10} + \frac{7}{10}$ ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{5} + \frac{7}{10}$ as $\frac{1+7}{5+10} = \frac{8}{15}$ ! This completely ignores fraction rules and gives wrong answers. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

$\frac{3}{4}:\frac{5}{6}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just add the tops and bottoms separately?

Because fractions represent parts of different wholes! Adding $\frac{1}{5}$ (fifths) to $\frac{7}{10}$ (tenths) is like adding apples to oranges. You need the same denominator to combine them properly.

How do I find the least common multiple of 5 and 10?

List the multiples: 5 → 5, 10, 15, 20... and 10 → 10, 20, 30... The smallest number that appears in both lists is 10. Since 10 is already a multiple of 5, the LCM is 10!

What if both fractions need to be converted?

Convert both fractions to have the common denominator! For example, with $\frac{2}{3} + \frac{1}{4}$ , convert both to twelfths: $\frac{8}{12} + \frac{3}{12} = \frac{11}{12}$ .

Do I need to simplify my final answer?

Always check if you can simplify! In this problem, $\frac{9}{10}$ is already in lowest terms since 9 and 10 share no common factors besides 1.

What's the quickest way to check if my answer is right?

Convert your answer to a decimal and check: $\frac{1}{5} = 0.2$ and $\frac{7}{10} = 0.7$ , so 0.2 + 0.7 = 0.9 = $\frac{9}{10}$ ✓

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Solve the Fraction Addition: 1/5 + 7/10 Step by Step

Fraction Addition with Common Denominators

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I just add the tops and bottoms separately?

How do I find the least common multiple of 5 and 10?

What if both fractions need to be converted?

Do I need to simplify my final answer?

What's the quickest way to check if my answer is right?

🌟 Unlock Your Math Potential

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