What is 2/28 plus 2/5? (Answer: 33/70)

Exact Answer

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Problem: What is 2/28 plus 2/5?
Formula / Expression: 2/28 + 2/5
Final Answer: 33/70
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 28 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 28 × 5 = 140.
Working: LCD(28, 5) = 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 2/5 by 28 so both fractions share the common base 140.
Working: 2 × 5/28 × 5 = 10/140 and 2 × 28/5 × 28 = 56/140

Step 3: Add the Numerators
Now add the numerators (10 + 56 = 66) and keep the common denominator 140 unchanged.
Working: 10 + 56/140 = 66/140

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 66 and 140, which is 2. Divide both the numerator and denominator by 2.
Working: 66 ÷ 2/140 ÷ 2 = 33/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 33 by denominator 70 produces a repeating decimal (approximately 0.471429, or 47.1429%).
Working: 33 ÷ 70 = 0.471429 (47.1429%)

Key Values:
- Simplified Fraction: 33/70
- Mixed Number Form: 33/70
- Decimal Value: 0.471429
- Percentage: 47.1429%

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Solved with FractionsCalc:
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2/28 + 2/5 = 33/70

Simplified Fraction

33/70

Mixed Number

Proper (33/70)

Decimal Value

0.471429

Percentage

47.1429%

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Step-by-Step Solution: 2/28 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 28 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 28 × 5 = 140.

LCD(28, 5) = 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 2/5 by 28 so both fractions share the common base 140.

2 × 5/28 × 5 = 10/140 and 2 × 28/5 × 28 = 56/140

Step 3

Add the Numerators

Now add the numerators (10 + 56 = 66) and keep the common denominator 140 unchanged.

10 + 56/140 = 66/140

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 66 and 140, which is 2. Divide both the numerator and denominator by 2.

66 ÷ 2/140 ÷ 2 = 33/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 33 by denominator 70 produces a repeating decimal (approximately 0.471429, or 47.1429%).

33 ÷ 70 = 0.471429 (47.1429%)

Visual Representation

The diagram below illustrates 2/28 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`33/70`
Mixed Number Form	`33/70`
Decimal Form	`0.471429`
Percentage	`47.1429%`

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Frequently Asked Questions

What is 2/28 plus 2/5 as a fraction?

2/28 + 2/5 in simplest fraction form is 33/70.

What is 2/28 plus 2/5 as a decimal?

2/28 + 2/5 converted to a decimal is 0.471429.

What is 2/28 plus 2/5 as a percentage?

2/28 + 2/5 expressed as a percentage is 47.1429%.

Does 2/28 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.471429...) because the denominator contains prime factors other than 2 and 5.