What is 2/28 plus 2/10? (Answer: 19/70)

Exact Answer

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Problem: What is 2/28 plus 2/10?
Formula / Expression: 2/28 + 2/10
Final Answer: 19/70
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 28 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 140 (which is smaller than their product 28 × 10 = 280, keeping the calculation simpler).
Working: LCD(28, 10) = 140

Step 2: Convert to Equivalent Fractions with Common Denominator 140
Multiply the numerator and denominator of 2/28 by 5, and multiply the numerator and denominator of 2/10 by 14 so both fractions share the common base 140.
Working: 2 × 5/28 × 5 = 10/140 and 2 × 14/10 × 14 = 28/140

Step 3: Add the Numerators
Now add the numerators (10 + 28 = 38) and keep the common denominator 140 unchanged.
Working: 10 + 28/140 = 38/140

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 38 and 140, which is 2. Divide both the numerator and denominator by 2.
Working: 38 ÷ 2/140 ÷ 2 = 19/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 70 produces a repeating decimal (approximately 0.271429, or 27.1429%).
Working: 19 ÷ 70 = 0.271429 (27.1429%)

Key Values:
- Simplified Fraction: 19/70
- Mixed Number Form: 19/70
- Decimal Value: 0.271429
- Percentage: 27.1429%

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Solved with FractionsCalc:
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2/28 + 2/10 = 19/70

Simplified Fraction

19/70

Mixed Number

Proper (19/70)

Decimal Value

0.271429

Percentage

27.1429%

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Step-by-Step Solution: 2/28 + 2/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 28 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 140 (which is smaller than their product 28 × 10 = 280, keeping the calculation simpler).

LCD(28, 10) = 140

Step 2

Convert to Equivalent Fractions with Common Denominator 140

Multiply the numerator and denominator of 2/28 by 5, and multiply the numerator and denominator of 2/10 by 14 so both fractions share the common base 140.

2 × 5/28 × 5 = 10/140 and 2 × 14/10 × 14 = 28/140

Step 3

Add the Numerators

Now add the numerators (10 + 28 = 38) and keep the common denominator 140 unchanged.

10 + 28/140 = 38/140

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 38 and 140, which is 2. Divide both the numerator and denominator by 2.

38 ÷ 2/140 ÷ 2 = 19/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 70 produces a repeating decimal (approximately 0.271429, or 27.1429%).

19 ÷ 70 = 0.271429 (27.1429%)

Visual Representation

The diagram below illustrates 2/28 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/70`
Mixed Number Form	`19/70`
Decimal Form	`0.271429`
Percentage	`27.1429%`

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Frequently Asked Questions

What is 2/28 plus 2/10 as a fraction?

2/28 + 2/10 in simplest fraction form is 19/70.

What is 2/28 plus 2/10 as a decimal?

2/28 + 2/10 converted to a decimal is 0.271429.

What is 2/28 plus 2/10 as a percentage?

2/28 + 2/10 expressed as a percentage is 27.1429%.

Does 2/28 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.271429...) because the denominator contains prime factors other than 2 and 5.