What is 7/30 plus 6/21? (Answer: 109/210)

Exact Answer

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Problem: What is 7/30 plus 6/21?
Formula / Expression: 7/30 + 6/21
Final Answer: 109/210
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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 7/30 by 7, and multiply the numerator and denominator of 6/21 by 10 so both fractions share the common base 210.
Working: 7 × 7/30 × 7 = 49/210 and 6 × 10/21 × 10 = 60/210

Step 3: Add the Numerators
Now add the numerators (49 + 60 = 109) and keep the common denominator 210 unchanged.
Working: 49 + 60/210 = 109/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 210 is 1, confirming that 109/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 210 produces a repeating decimal (approximately 0.519048, or 51.9048%).
Working: 109 ÷ 210 = 0.519048 (51.9048%)

Key Values:
- Simplified Fraction: 109/210
- Mixed Number Form: 109/210
- Decimal Value: 0.519048
- Percentage: 51.9048%

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Solved with FractionsCalc:
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7/30 + 6/21 = 109/210

Simplified Fraction

109/210

Mixed Number

Proper (109/210)

Decimal Value

0.519048

Percentage

51.9048%

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Step-by-Step Solution: 7/30 + 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 7/30 by 7, and multiply the numerator and denominator of 6/21 by 10 so both fractions share the common base 210.

7 × 7/30 × 7 = 49/210 and 6 × 10/21 × 10 = 60/210

Step 3

Add the Numerators

Now add the numerators (49 + 60 = 109) and keep the common denominator 210 unchanged.

49 + 60/210 = 109/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 210 is 1, confirming that 109/210 cannot be reduced further—it is already in its simplest irreducible form.

109/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 210 produces a repeating decimal (approximately 0.519048, or 51.9048%).

109 ÷ 210 = 0.519048 (51.9048%)

Visual Representation

The diagram below illustrates 7/30 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/210`
Mixed Number Form	`109/210`
Decimal Form	`0.519048`
Percentage	`51.9048%`

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Frequently Asked Questions

What is 7/30 plus 6/21 as a fraction?

7/30 + 6/21 in simplest fraction form is 109/210.

What is 7/30 plus 6/21 as a decimal?

7/30 + 6/21 converted to a decimal is 0.519048.

What is 7/30 plus 6/21 as a percentage?

7/30 + 6/21 expressed as a percentage is 51.9048%.

Does 7/30 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.519048...) because the denominator contains prime factors other than 2 and 5.