What is 2/35 plus 2/21? (Answer: 16/105)

Exact Answer

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Problem: What is 2/35 plus 2/21?
Formula / Expression: 2/35 + 2/21
Final Answer: 16/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).
Working: LCD(35, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 2/35 by 3, and multiply the numerator and denominator of 2/21 by 5 so both fractions share the common base 105.
Working: 2 × 3/35 × 3 = 6/105 and 2 × 5/21 × 5 = 10/105

Step 3: Add the Numerators
Now add the numerators (6 + 10 = 16) and keep the common denominator 105 unchanged.
Working: 6 + 10/105 = 16/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 16 and 105 is 1, confirming that 16/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 16/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 105 produces a repeating decimal (approximately 0.152381, or 15.2381%).
Working: 16 ÷ 105 = 0.152381 (15.2381%)

Key Values:
- Simplified Fraction: 16/105
- Mixed Number Form: 16/105
- Decimal Value: 0.152381
- Percentage: 15.2381%

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2/35 + 2/21 = 16/105

Simplified Fraction

16/105

Mixed Number

Proper (16/105)

Decimal Value

0.152381

Percentage

15.2381%

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Step-by-Step Solution: 2/35 + 2/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).

LCD(35, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 2/35 by 3, and multiply the numerator and denominator of 2/21 by 5 so both fractions share the common base 105.

2 × 3/35 × 3 = 6/105 and 2 × 5/21 × 5 = 10/105

Step 3

Add the Numerators

Now add the numerators (6 + 10 = 16) and keep the common denominator 105 unchanged.

6 + 10/105 = 16/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 16 and 105 is 1, confirming that 16/105 cannot be reduced further—it is already in its simplest irreducible form.

16/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 105 produces a repeating decimal (approximately 0.152381, or 15.2381%).

16 ÷ 105 = 0.152381 (15.2381%)

Visual Representation

The diagram below illustrates 2/35 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/105`
Mixed Number Form	`16/105`
Decimal Form	`0.152381`
Percentage	`15.2381%`

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Frequently Asked Questions

What is 2/35 plus 2/21 as a fraction?

2/35 + 2/21 in simplest fraction form is 16/105.

What is 2/35 plus 2/21 as a decimal?

2/35 + 2/21 converted to a decimal is 0.152381.

What is 2/35 plus 2/21 as a percentage?

2/35 + 2/21 expressed as a percentage is 15.2381%.

Does 2/35 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.152381...) because the denominator contains prime factors other than 2 and 5.