What is 6/21 plus 9/30? (Answer: 41/70)

Exact Answer

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Problem: What is 6/21 plus 9/30?
Formula / Expression: 6/21 + 9/30
Final Answer: 41/70
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 6/21 by 10, and multiply the numerator and denominator of 9/30 by 7 so both fractions share the common base 210.
Working: 6 × 10/21 × 10 = 60/210 and 9 × 7/30 × 7 = 63/210

Step 3: Add the Numerators
Now add the numerators (60 + 63 = 123) and keep the common denominator 210 unchanged.
Working: 60 + 63/210 = 123/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 123 and 210, which is 3. Divide both the numerator and denominator by 3.
Working: 123 ÷ 3/210 ÷ 3 = 41/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 70 produces a repeating decimal (approximately 0.585714, or 58.5714%).
Working: 41 ÷ 70 = 0.585714 (58.5714%)

Key Values:
- Simplified Fraction: 41/70
- Mixed Number Form: 41/70
- Decimal Value: 0.585714
- Percentage: 58.5714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-21-plus-9-30/
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6/21 + 9/30 = 41/70

Simplified Fraction

41/70

Mixed Number

Proper (41/70)

Decimal Value

0.585714

Percentage

58.5714%

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Step-by-Step Solution: 6/21 + 9/30

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 30) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 6/21 by 10, and multiply the numerator and denominator of 9/30 by 7 so both fractions share the common base 210.

6 × 10/21 × 10 = 60/210 and 9 × 7/30 × 7 = 63/210

Step 3

Add the Numerators

Now add the numerators (60 + 63 = 123) and keep the common denominator 210 unchanged.

60 + 63/210 = 123/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 123 and 210, which is 3. Divide both the numerator and denominator by 3.

123 ÷ 3/210 ÷ 3 = 41/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 70 produces a repeating decimal (approximately 0.585714, or 58.5714%).

41 ÷ 70 = 0.585714 (58.5714%)

Visual Representation

The diagram below illustrates 6/21 plus 9/30 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/70`
Mixed Number Form	`41/70`
Decimal Form	`0.585714`
Percentage	`58.5714%`

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Frequently Asked Questions

What is 6/21 plus 9/30 as a fraction?

6/21 + 9/30 in simplest fraction form is 41/70.

What is 6/21 plus 9/30 as a decimal?

6/21 + 9/30 converted to a decimal is 0.585714.

What is 6/21 plus 9/30 as a percentage?

6/21 + 9/30 expressed as a percentage is 58.5714%.

Does 6/21 plus 9/30 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.585714...) because the denominator contains prime factors other than 2 and 5.