What is 7/30 plus 9/21? (Answer: 139/210)

Exact Answer

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Problem: What is 7/30 plus 9/21?
Formula / Expression: 7/30 + 9/21
Final Answer: 139/210
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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 9/21 by 10 so both fractions share the common base 210.
Working: 7 × 7/30 × 7 = 49/210 and 9 × 10/21 × 10 = 90/210

Step 3: Add the Numerators
Now add the numerators (49 + 90 = 139) and keep the common denominator 210 unchanged.
Working: 49 + 90/210 = 139/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 139 and 210 is 1, confirming that 139/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 139/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 139 by denominator 210 produces a repeating decimal (approximately 0.661905, or 66.1905%).
Working: 139 ÷ 210 = 0.661905 (66.1905%)

Key Values:
- Simplified Fraction: 139/210
- Mixed Number Form: 139/210
- Decimal Value: 0.661905
- Percentage: 66.1905%

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Solved with FractionsCalc:
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7/30 + 9/21 = 139/210

Simplified Fraction

139/210

Mixed Number

Proper (139/210)

Decimal Value

0.661905

Percentage

66.1905%

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Step-by-Step Solution: 7/30 + 9/21

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 9/21 by 10 so both fractions share the common base 210.

7 × 7/30 × 7 = 49/210 and 9 × 10/21 × 10 = 90/210

Step 3

Add the Numerators

Now add the numerators (49 + 90 = 139) and keep the common denominator 210 unchanged.

49 + 90/210 = 139/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 139 and 210 is 1, confirming that 139/210 cannot be reduced further—it is already in its simplest irreducible form.

139/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 139 by denominator 210 produces a repeating decimal (approximately 0.661905, or 66.1905%).

139 ÷ 210 = 0.661905 (66.1905%)

Visual Representation

The diagram below illustrates 7/30 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`139/210`
Mixed Number Form	`139/210`
Decimal Form	`0.661905`
Percentage	`66.1905%`

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Frequently Asked Questions

What is 7/30 plus 9/21 as a fraction?

7/30 + 9/21 in simplest fraction form is 139/210.

What is 7/30 plus 9/21 as a decimal?

7/30 + 9/21 converted to a decimal is 0.661905.

What is 7/30 plus 9/21 as a percentage?

7/30 + 9/21 expressed as a percentage is 66.1905%.

Does 7/30 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.661905...) because the denominator contains prime factors other than 2 and 5.