What is 3/35 plus 6/21? (Answer: 13/35)

Exact Answer

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Problem: What is 3/35 plus 6/21?
Formula / Expression: 3/35 + 6/21
Final Answer: 13/35
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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 3/35 by 3, and multiply the numerator and denominator of 6/21 by 5 so both fractions share the common base 105.
Working: 3 × 3/35 × 3 = 9/105 and 6 × 5/21 × 5 = 30/105

Step 3: Add the Numerators
Now add the numerators (9 + 30 = 39) and keep the common denominator 105 unchanged.
Working: 9 + 30/105 = 39/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 39 and 105, which is 3. Divide both the numerator and denominator by 3.
Working: 39 ÷ 3/105 ÷ 3 = 13/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 35 produces a repeating decimal (approximately 0.371429, or 37.1429%).
Working: 13 ÷ 35 = 0.371429 (37.1429%)

Key Values:
- Simplified Fraction: 13/35
- Mixed Number Form: 13/35
- Decimal Value: 0.371429
- Percentage: 37.1429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-35-plus-6-21/
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3/35 + 6/21 = 13/35

Simplified Fraction

13/35

Mixed Number

Proper (13/35)

Decimal Value

0.371429

Percentage

37.1429%

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Step-by-Step Solution: 3/35 + 6/21

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 3/35 by 3, and multiply the numerator and denominator of 6/21 by 5 so both fractions share the common base 105.

3 × 3/35 × 3 = 9/105 and 6 × 5/21 × 5 = 30/105

Step 3

Add the Numerators

Now add the numerators (9 + 30 = 39) and keep the common denominator 105 unchanged.

9 + 30/105 = 39/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 39 and 105, which is 3. Divide both the numerator and denominator by 3.

39 ÷ 3/105 ÷ 3 = 13/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 35 produces a repeating decimal (approximately 0.371429, or 37.1429%).

13 ÷ 35 = 0.371429 (37.1429%)

Visual Representation

The diagram below illustrates 3/35 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/35`
Mixed Number Form	`13/35`
Decimal Form	`0.371429`
Percentage	`37.1429%`

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Frequently Asked Questions

What is 3/35 plus 6/21 as a fraction?

3/35 + 6/21 in simplest fraction form is 13/35.

What is 3/35 plus 6/21 as a decimal?

3/35 + 6/21 converted to a decimal is 0.371429.

What is 3/35 plus 6/21 as a percentage?

3/35 + 6/21 expressed as a percentage is 37.1429%.

Does 3/35 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.371429...) because the denominator contains prime factors other than 2 and 5.