What is 2/35 plus 2/14? (Answer: 1/5)

Exact Answer

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Problem: What is 2/35 plus 2/14?
Formula / Expression: 2/35 + 2/14
Final Answer: 1/5
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 14 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 70 (which is smaller than their product 35 × 14 = 490, keeping the calculation simpler).
Working: LCD(35, 14) = 70

Step 2: Convert to Equivalent Fractions with Common Denominator 70
Multiply the numerator and denominator of 2/35 by 2, and multiply the numerator and denominator of 2/14 by 5 so both fractions share the common base 70.
Working: 2 × 2/35 × 2 = 4/70 and 2 × 5/14 × 5 = 10/70

Step 3: Add the Numerators
Now add the numerators (4 + 10 = 14) and keep the common denominator 70 unchanged.
Working: 4 + 10/70 = 14/70

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 14 and 70, which is 14. Divide both the numerator and denominator by 14.
Working: 14 ÷ 14/70 ÷ 14 = 1/5

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 5 yields an exact terminating decimal of 0.2 (or 20%).
Working: 1 ÷ 5 = 0.2 (20%)

Key Values:
- Simplified Fraction: 1/5
- Mixed Number Form: 1/5
- Decimal Value: 0.2
- Percentage: 20%

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Solved with FractionsCalc:
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2/35 + 2/14 = 1/5

Simplified Fraction

1/5

Mixed Number

Proper (1/5)

Decimal Value

0.2

Percentage

20%

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Step-by-Step Solution: 2/35 + 2/14

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 14 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 70 (which is smaller than their product 35 × 14 = 490, keeping the calculation simpler).

LCD(35, 14) = 70

Step 2

Convert to Equivalent Fractions with Common Denominator 70

Multiply the numerator and denominator of 2/35 by 2, and multiply the numerator and denominator of 2/14 by 5 so both fractions share the common base 70.

2 × 2/35 × 2 = 4/70 and 2 × 5/14 × 5 = 10/70

Step 3

Add the Numerators

Now add the numerators (4 + 10 = 14) and keep the common denominator 70 unchanged.

4 + 10/70 = 14/70

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 14 and 70, which is 14. Divide both the numerator and denominator by 14.

14 ÷ 14/70 ÷ 14 = 1/5

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 5 yields an exact terminating decimal of 0.2 (or 20%).

1 ÷ 5 = 0.2 (20%)

Visual Representation

The diagram below illustrates 2/35 plus 2/14 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/5`
Mixed Number Form	`1/5`
Decimal Form	`0.2`
Percentage	`20%`

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Frequently Asked Questions

What is 2/35 plus 2/14 as a fraction?

2/35 + 2/14 in simplest fraction form is 1/5.

What is 2/35 plus 2/14 as a decimal?

2/35 + 2/14 converted to a decimal is 0.2.

What is 2/35 plus 2/14 as a percentage?

2/35 + 2/14 expressed as a percentage is 20%.

Does 2/35 plus 2/14 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.2) because the denominator in simplest terms contains only prime factors 2 and/or 5.