What is 2/21 plus 4/35? (Answer: 22/105)

Exact Answer

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Problem: What is 2/21 plus 4/35?
Formula / Expression: 2/21 + 4/35
Final Answer: 22/105
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 2/21 by 5, and multiply the numerator and denominator of 4/35 by 3 so both fractions share the common base 105.
Working: 2 × 5/21 × 5 = 10/105 and 4 × 3/35 × 3 = 12/105

Step 3: Add the Numerators
Now add the numerators (10 + 12 = 22) and keep the common denominator 105 unchanged.
Working: 10 + 12/105 = 22/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 22 and 105 is 1, confirming that 22/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 22/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 22 by denominator 105 produces a repeating decimal (approximately 0.209524, or 20.9524%).
Working: 22 ÷ 105 = 0.209524 (20.9524%)

Key Values:
- Simplified Fraction: 22/105
- Mixed Number Form: 22/105
- Decimal Value: 0.209524
- Percentage: 20.9524%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-21-plus-4-35/
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2/21 + 4/35 = 22/105

Simplified Fraction

22/105

Mixed Number

Proper (22/105)

Decimal Value

0.209524

Percentage

20.9524%

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Step-by-Step Solution: 2/21 + 4/35

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 35) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 2/21 by 5, and multiply the numerator and denominator of 4/35 by 3 so both fractions share the common base 105.

2 × 5/21 × 5 = 10/105 and 4 × 3/35 × 3 = 12/105

Step 3

Add the Numerators

Now add the numerators (10 + 12 = 22) and keep the common denominator 105 unchanged.

10 + 12/105 = 22/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 22 and 105 is 1, confirming that 22/105 cannot be reduced further—it is already in its simplest irreducible form.

22/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 22 by denominator 105 produces a repeating decimal (approximately 0.209524, or 20.9524%).

22 ÷ 105 = 0.209524 (20.9524%)

Visual Representation

The diagram below illustrates 2/21 plus 4/35 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`22/105`
Mixed Number Form	`22/105`
Decimal Form	`0.209524`
Percentage	`20.9524%`

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Frequently Asked Questions

What is 2/21 plus 4/35 as a fraction?

2/21 + 4/35 in simplest fraction form is 22/105.

What is 2/21 plus 4/35 as a decimal?

2/21 + 4/35 converted to a decimal is 0.209524.

What is 2/21 plus 4/35 as a percentage?

2/21 + 4/35 expressed as a percentage is 20.9524%.

Does 2/21 plus 4/35 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.209524...) because the denominator contains prime factors other than 2 and 5.