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

Q: Why can't I just add 1/5 + 7/10 directly?

You can only add fractions when they have the same denominator. Think of it like adding apples and oranges - you need to convert them to the same unit first!

Q: How do I find the least common denominator of 5 and 10?

Since 10 is a multiple of 5 (10 = 5 × 2), the LCD is simply 10. For other denominators, list multiples of each until you find the smallest common one.

Q: Do I always multiply by 2 to convert fifths to tenths?

Yes! Since $ \frac{1}{5} $ needs denominator 10, multiply both top and bottom by 2: $ \frac{1 \times 2}{5 \times 2} = \frac{2}{10} $.

Q: Should I simplify 9/10 to lowest terms?

$ \frac{9}{10} $ is already in lowest terms because 9 and 10 share no common factors other than 1. The answer is complete as is!

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

00:05 Alright, let's solve this together.

00:08 We need to find the smallest common denominator.

00:12 So, we'll multiply by two to make a common denominator of ten.

00:17 Remember to multiply both the numerator and the denominator. This part is important!

00:23 Let's calculate those multiplications now.

00:27 Next, add under the common denominator.

00:31 Now, calculate the numerator.

00:35 And that's how we find 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 this problem, we'll follow these steps:

Step 1: Identify the least common denominator of the fractions.
Step 2: Convert each fraction to have this common denominator.
Step 3: Add the converted fractions.

Now, let's work through each step:
Step 1: The least common denominator of 5 and 10 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: Add the converted fraction $\frac{2}{10}$ to $\frac{7}{10}$ :
$\frac{2}{10} + \frac{7}{10} = \frac{2 + 7}{10} = \frac{9}{10}$

Therefore, the solution to the problem is $\frac{9}{10}$ .

Final Answer

$\frac{9}{10}$

Key Points to Remember

Essential concepts to master this topic

LCD Rule: Find least common denominator before adding fractions
Technique: Convert $\frac{1}{5}$ to $\frac{2}{10}$ by multiplying by 2
Check: Add numerators only: 2 + 7 = 9, keep denominator 10 ✓

Common Mistakes

Avoid these frequent errors

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

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why can't I just add 1/5 + 7/10 directly?

You can only add fractions when they have the same denominator. Think of it like adding apples and oranges - you need to convert them to the same unit first!

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

Since 10 is a multiple of 5 (10 = 5 × 2), the LCD is simply 10. For other denominators, list multiples of each until you find the smallest common one.

Do I always multiply by 2 to convert fifths to tenths?

Yes! Since $\frac{1}{5}$ needs denominator 10, multiply both top and bottom by 2: $\frac{1 \times 2}{5 \times 2} = \frac{2}{10}$ .

Should I simplify 9/10 to lowest terms?

$\frac{9}{10}$ is already in lowest terms because 9 and 10 share no common factors other than 1. The answer is complete as is!

What if my answer looks different from the choices?

Double-check your work! Make sure you found the correct LCD and converted fractions properly. Also verify that equivalent fractions like $\frac{18}{20}$ match simplified forms.

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