What is 5/21 plus 9/35? (Answer: 52/105)

Exact Answer

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Problem: What is 5/21 plus 9/35?
Formula / Expression: 5/21 + 9/35
Final Answer: 52/105
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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 5/21 by 5, and multiply the numerator and denominator of 9/35 by 3 so both fractions share the common base 105.
Working: 5 × 5/21 × 5 = 25/105 and 9 × 3/35 × 3 = 27/105

Step 3: Add the Numerators
Now add the numerators (25 + 27 = 52) and keep the common denominator 105 unchanged.
Working: 25 + 27/105 = 52/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 52 and 105 is 1, confirming that 52/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 52/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 52 by denominator 105 produces a repeating decimal (approximately 0.495238, or 49.5238%).
Working: 52 ÷ 105 = 0.495238 (49.5238%)

Key Values:
- Simplified Fraction: 52/105
- Mixed Number Form: 52/105
- Decimal Value: 0.495238
- Percentage: 49.5238%

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Solved with FractionsCalc:
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5/21 + 9/35 = 52/105

Simplified Fraction

52/105

Mixed Number

Proper (52/105)

Decimal Value

0.495238

Percentage

49.5238%

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Step-by-Step Solution: 5/21 + 9/35

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 5/21 by 5, and multiply the numerator and denominator of 9/35 by 3 so both fractions share the common base 105.

5 × 5/21 × 5 = 25/105 and 9 × 3/35 × 3 = 27/105

Step 3

Add the Numerators

Now add the numerators (25 + 27 = 52) and keep the common denominator 105 unchanged.

25 + 27/105 = 52/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 52 and 105 is 1, confirming that 52/105 cannot be reduced further—it is already in its simplest irreducible form.

52/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 52 by denominator 105 produces a repeating decimal (approximately 0.495238, or 49.5238%).

52 ÷ 105 = 0.495238 (49.5238%)

Visual Representation

The diagram below illustrates 5/21 plus 9/35 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`52/105`
Mixed Number Form	`52/105`
Decimal Form	`0.495238`
Percentage	`49.5238%`

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Frequently Asked Questions

What is 5/21 plus 9/35 as a fraction?

5/21 + 9/35 in simplest fraction form is 52/105.

What is 5/21 plus 9/35 as a decimal?

5/21 + 9/35 converted to a decimal is 0.495238.

What is 5/21 plus 9/35 as a percentage?

5/21 + 9/35 expressed as a percentage is 49.5238%.

Does 5/21 plus 9/35 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.495238...) because the denominator contains prime factors other than 2 and 5.