What is 3/30 plus 6/21? (Answer: 27/70)

Exact Answer

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Problem: What is 3/30 plus 6/21?
Formula / Expression: 3/30 + 6/21
Final Answer: 27/70
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).
Working: LCD(30, 21) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 3/30 by 7, and multiply the numerator and denominator of 6/21 by 10 so both fractions share the common base 210.
Working: 3 × 7/30 × 7 = 21/210 and 6 × 10/21 × 10 = 60/210

Step 3: Add the Numerators
Now add the numerators (21 + 60 = 81) and keep the common denominator 210 unchanged.
Working: 21 + 60/210 = 81/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 81 and 210, which is 3. Divide both the numerator and denominator by 3.
Working: 81 ÷ 3/210 ÷ 3 = 27/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 27 by denominator 70 produces a repeating decimal (approximately 0.385714, or 38.5714%).
Working: 27 ÷ 70 = 0.385714 (38.5714%)

Key Values:
- Simplified Fraction: 27/70
- Mixed Number Form: 27/70
- Decimal Value: 0.385714
- Percentage: 38.5714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-30-plus-6-21/
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3/30 + 6/21 = 27/70

Simplified Fraction

27/70

Mixed Number

Proper (27/70)

Decimal Value

0.385714

Percentage

38.5714%

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Step-by-Step Solution: 3/30 + 6/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).

LCD(30, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 3/30 by 7, and multiply the numerator and denominator of 6/21 by 10 so both fractions share the common base 210.

3 × 7/30 × 7 = 21/210 and 6 × 10/21 × 10 = 60/210

Step 3

Add the Numerators

Now add the numerators (21 + 60 = 81) and keep the common denominator 210 unchanged.

21 + 60/210 = 81/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 81 and 210, which is 3. Divide both the numerator and denominator by 3.

81 ÷ 3/210 ÷ 3 = 27/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 27 by denominator 70 produces a repeating decimal (approximately 0.385714, or 38.5714%).

27 ÷ 70 = 0.385714 (38.5714%)

Visual Representation

The diagram below illustrates 3/30 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`27/70`
Mixed Number Form	`27/70`
Decimal Form	`0.385714`
Percentage	`38.5714%`

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Frequently Asked Questions

What is 3/30 plus 6/21 as a fraction?

3/30 + 6/21 in simplest fraction form is 27/70.

What is 3/30 plus 6/21 as a decimal?

3/30 + 6/21 converted to a decimal is 0.385714.

What is 3/30 plus 6/21 as a percentage?

3/30 + 6/21 expressed as a percentage is 38.5714%.

Does 3/30 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.385714...) because the denominator contains prime factors other than 2 and 5.