What is 9/21 plus 13/30? (Answer: 181/210)

Exact Answer

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Problem: What is 9/21 plus 13/30?
Formula / Expression: 9/21 + 13/30
Final Answer: 181/210
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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 9/21 by 10, and multiply the numerator and denominator of 13/30 by 7 so both fractions share the common base 210.
Working: 9 × 10/21 × 10 = 90/210 and 13 × 7/30 × 7 = 91/210

Step 3: Add the Numerators
Now add the numerators (90 + 91 = 181) and keep the common denominator 210 unchanged.
Working: 90 + 91/210 = 181/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 181 and 210 is 1, confirming that 181/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 181/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 181 by denominator 210 produces a repeating decimal (approximately 0.861905, or 86.1905%).
Working: 181 ÷ 210 = 0.861905 (86.1905%)

Key Values:
- Simplified Fraction: 181/210
- Mixed Number Form: 181/210
- Decimal Value: 0.861905
- Percentage: 86.1905%

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9/21 + 13/30 = 181/210

Simplified Fraction

181/210

Mixed Number

Proper (181/210)

Decimal Value

0.861905

Percentage

86.1905%

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Step-by-Step Solution: 9/21 + 13/30

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 9/21 by 10, and multiply the numerator and denominator of 13/30 by 7 so both fractions share the common base 210.

9 × 10/21 × 10 = 90/210 and 13 × 7/30 × 7 = 91/210

Step 3

Add the Numerators

Now add the numerators (90 + 91 = 181) and keep the common denominator 210 unchanged.

90 + 91/210 = 181/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 181 and 210 is 1, confirming that 181/210 cannot be reduced further—it is already in its simplest irreducible form.

181/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 181 by denominator 210 produces a repeating decimal (approximately 0.861905, or 86.1905%).

181 ÷ 210 = 0.861905 (86.1905%)

Visual Representation

The diagram below illustrates 9/21 plus 13/30 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`181/210`
Mixed Number Form	`181/210`
Decimal Form	`0.861905`
Percentage	`86.1905%`

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Frequently Asked Questions

What is 9/21 plus 13/30 as a fraction?

9/21 + 13/30 in simplest fraction form is 181/210.

What is 9/21 plus 13/30 as a decimal?

9/21 + 13/30 converted to a decimal is 0.861905.

What is 9/21 plus 13/30 as a percentage?

9/21 + 13/30 expressed as a percentage is 86.1905%.

Does 9/21 plus 13/30 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.861905...) because the denominator contains prime factors other than 2 and 5.