What is 2/49 plus 2/10? (Answer: 59/245)

Exact Answer

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Problem: What is 2/49 plus 2/10?
Formula / Expression: 2/49 + 2/10
Final Answer: 59/245
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 49 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 49 × 10 = 490.
Working: LCD(49, 10) = 490

Step 2: Convert to Equivalent Fractions with Common Denominator 490
Multiply the numerator and denominator of 2/49 by 10, and multiply the numerator and denominator of 2/10 by 49 so both fractions share the common base 490.
Working: 2 × 10/49 × 10 = 20/490 and 2 × 49/10 × 49 = 98/490

Step 3: Add the Numerators
Now add the numerators (20 + 98 = 118) and keep the common denominator 490 unchanged.
Working: 20 + 98/490 = 118/490

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 118 and 490, which is 2. Divide both the numerator and denominator by 2.
Working: 118 ÷ 2/490 ÷ 2 = 59/245

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 245 produces a repeating decimal (approximately 0.240816, or 24.0816%).
Working: 59 ÷ 245 = 0.240816 (24.0816%)

Key Values:
- Simplified Fraction: 59/245
- Mixed Number Form: 59/245
- Decimal Value: 0.240816
- Percentage: 24.0816%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-49-plus-2-10/
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2/49 + 2/10 = 59/245

Simplified Fraction

59/245

Mixed Number

Proper (59/245)

Decimal Value

0.240816

Percentage

24.0816%

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Step-by-Step Solution: 2/49 + 2/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 49 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 49 × 10 = 490.

LCD(49, 10) = 490

Step 2

Convert to Equivalent Fractions with Common Denominator 490

Multiply the numerator and denominator of 2/49 by 10, and multiply the numerator and denominator of 2/10 by 49 so both fractions share the common base 490.

2 × 10/49 × 10 = 20/490 and 2 × 49/10 × 49 = 98/490

Step 3

Add the Numerators

Now add the numerators (20 + 98 = 118) and keep the common denominator 490 unchanged.

20 + 98/490 = 118/490

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 118 and 490, which is 2. Divide both the numerator and denominator by 2.

118 ÷ 2/490 ÷ 2 = 59/245

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 245 produces a repeating decimal (approximately 0.240816, or 24.0816%).

59 ÷ 245 = 0.240816 (24.0816%)

Visual Representation

The diagram below illustrates 2/49 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/245`
Mixed Number Form	`59/245`
Decimal Form	`0.240816`
Percentage	`24.0816%`

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Frequently Asked Questions

What is 2/49 plus 2/10 as a fraction?

2/49 + 2/10 in simplest fraction form is 59/245.

What is 2/49 plus 2/10 as a decimal?

2/49 + 2/10 converted to a decimal is 0.240816.

What is 2/49 plus 2/10 as a percentage?

2/49 + 2/10 expressed as a percentage is 24.0816%.

Does 2/49 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.240816...) because the denominator contains prime factors other than 2 and 5.