What is 2/40 plus 2/14? (Answer: 27/140)

Exact Answer

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Problem: What is 2/40 plus 2/14?
Formula / Expression: 2/40 + 2/14
Final Answer: 27/140
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 14 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 280 (which is smaller than their product 40 × 14 = 560, keeping the calculation simpler).
Working: LCD(40, 14) = 280

Step 2: Convert to Equivalent Fractions with Common Denominator 280
Multiply the numerator and denominator of 2/40 by 7, and multiply the numerator and denominator of 2/14 by 20 so both fractions share the common base 280.
Working: 2 × 7/40 × 7 = 14/280 and 2 × 20/14 × 20 = 40/280

Step 3: Add the Numerators
Now add the numerators (14 + 40 = 54) and keep the common denominator 280 unchanged.
Working: 14 + 40/280 = 54/280

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 54 and 280, which is 2. Divide both the numerator and denominator by 2.
Working: 54 ÷ 2/280 ÷ 2 = 27/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 27 by denominator 140 produces a repeating decimal (approximately 0.192857, or 19.2857%).
Working: 27 ÷ 140 = 0.192857 (19.2857%)

Key Values:
- Simplified Fraction: 27/140
- Mixed Number Form: 27/140
- Decimal Value: 0.192857
- Percentage: 19.2857%

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Solved with FractionsCalc:
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2/40 + 2/14 = 27/140

Simplified Fraction

27/140

Mixed Number

Proper (27/140)

Decimal Value

0.192857

Percentage

19.2857%

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Step-by-Step Solution: 2/40 + 2/14

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 14 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 280 (which is smaller than their product 40 × 14 = 560, keeping the calculation simpler).

LCD(40, 14) = 280

Step 2

Convert to Equivalent Fractions with Common Denominator 280

Multiply the numerator and denominator of 2/40 by 7, and multiply the numerator and denominator of 2/14 by 20 so both fractions share the common base 280.

2 × 7/40 × 7 = 14/280 and 2 × 20/14 × 20 = 40/280

Step 3

Add the Numerators

Now add the numerators (14 + 40 = 54) and keep the common denominator 280 unchanged.

14 + 40/280 = 54/280

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 54 and 280, which is 2. Divide both the numerator and denominator by 2.

54 ÷ 2/280 ÷ 2 = 27/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 27 by denominator 140 produces a repeating decimal (approximately 0.192857, or 19.2857%).

27 ÷ 140 = 0.192857 (19.2857%)

Visual Representation

The diagram below illustrates 2/40 plus 2/14 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`27/140`
Mixed Number Form	`27/140`
Decimal Form	`0.192857`
Percentage	`19.2857%`

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Frequently Asked Questions

What is 2/40 plus 2/14 as a fraction?

2/40 + 2/14 in simplest fraction form is 27/140.

What is 2/40 plus 2/14 as a decimal?

2/40 + 2/14 converted to a decimal is 0.192857.

What is 2/40 plus 2/14 as a percentage?

2/40 + 2/14 expressed as a percentage is 19.2857%.

Does 2/40 plus 2/14 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.192857...) because the denominator contains prime factors other than 2 and 5.