What is 2/35 plus 2/16? (Answer: 51/280)

Exact Answer

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Problem: What is 2/35 plus 2/16?
Formula / Expression: 2/35 + 2/16
Final Answer: 51/280
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 16 = 560.
Working: LCD(35, 16) = 560

Step 2: Convert to Equivalent Fractions with Common Denominator 560
Multiply the numerator and denominator of 2/35 by 16, and multiply the numerator and denominator of 2/16 by 35 so both fractions share the common base 560.
Working: 2 × 16/35 × 16 = 32/560 and 2 × 35/16 × 35 = 70/560

Step 3: Add the Numerators
Now add the numerators (32 + 70 = 102) and keep the common denominator 560 unchanged.
Working: 32 + 70/560 = 102/560

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 560, which is 2. Divide both the numerator and denominator by 2.
Working: 102 ÷ 2/560 ÷ 2 = 51/280

Step 5: Decimal & Percentage Representation
Dividing the numerator 51 by denominator 280 produces a repeating decimal (approximately 0.182143, or 18.2143%).
Working: 51 ÷ 280 = 0.182143 (18.2143%)

Key Values:
- Simplified Fraction: 51/280
- Mixed Number Form: 51/280
- Decimal Value: 0.182143
- Percentage: 18.2143%

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2/35 + 2/16 = 51/280

Simplified Fraction

51/280

Mixed Number

Proper (51/280)

Decimal Value

0.182143

Percentage

18.2143%

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Step-by-Step Solution: 2/35 + 2/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 16 = 560.

LCD(35, 16) = 560

Step 2

Convert to Equivalent Fractions with Common Denominator 560

Multiply the numerator and denominator of 2/35 by 16, and multiply the numerator and denominator of 2/16 by 35 so both fractions share the common base 560.

2 × 16/35 × 16 = 32/560 and 2 × 35/16 × 35 = 70/560

Step 3

Add the Numerators

Now add the numerators (32 + 70 = 102) and keep the common denominator 560 unchanged.

32 + 70/560 = 102/560

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 560, which is 2. Divide both the numerator and denominator by 2.

102 ÷ 2/560 ÷ 2 = 51/280

Step 5

Decimal & Percentage Representation

Dividing the numerator 51 by denominator 280 produces a repeating decimal (approximately 0.182143, or 18.2143%).

51 ÷ 280 = 0.182143 (18.2143%)

Visual Representation

The diagram below illustrates 2/35 plus 2/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`51/280`
Mixed Number Form	`51/280`
Decimal Form	`0.182143`
Percentage	`18.2143%`

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Frequently Asked Questions

What is 2/35 plus 2/16 as a fraction?

2/35 + 2/16 in simplest fraction form is 51/280.

What is 2/35 plus 2/16 as a decimal?

2/35 + 2/16 converted to a decimal is 0.182143.

What is 2/35 plus 2/16 as a percentage?

2/35 + 2/16 expressed as a percentage is 18.2143%.

Does 2/35 plus 2/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.182143...) because the denominator contains prime factors other than 2 and 5.