What is 9/30 plus 11/21? (Answer: 173/210)

Exact Answer

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Problem: What is 9/30 plus 11/21?
Formula / Expression: 9/30 + 11/21
Final Answer: 173/210
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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 9/30 by 7, and multiply the numerator and denominator of 11/21 by 10 so both fractions share the common base 210.
Working: 9 × 7/30 × 7 = 63/210 and 11 × 10/21 × 10 = 110/210

Step 3: Add the Numerators
Now add the numerators (63 + 110 = 173) and keep the common denominator 210 unchanged.
Working: 63 + 110/210 = 173/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 173 and 210 is 1, confirming that 173/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 173/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 173 by denominator 210 produces a repeating decimal (approximately 0.82381, or 82.381%).
Working: 173 ÷ 210 = 0.82381 (82.381%)

Key Values:
- Simplified Fraction: 173/210
- Mixed Number Form: 173/210
- Decimal Value: 0.82381
- Percentage: 82.381%

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Solved with FractionsCalc:
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9/30 + 11/21 = 173/210

Simplified Fraction

173/210

Mixed Number

Proper (173/210)

Decimal Value

0.82381

Percentage

82.381%

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Step-by-Step Solution: 9/30 + 11/21

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 9/30 by 7, and multiply the numerator and denominator of 11/21 by 10 so both fractions share the common base 210.

9 × 7/30 × 7 = 63/210 and 11 × 10/21 × 10 = 110/210

Step 3

Add the Numerators

Now add the numerators (63 + 110 = 173) and keep the common denominator 210 unchanged.

63 + 110/210 = 173/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 173 and 210 is 1, confirming that 173/210 cannot be reduced further—it is already in its simplest irreducible form.

173/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 173 by denominator 210 produces a repeating decimal (approximately 0.82381, or 82.381%).

173 ÷ 210 = 0.82381 (82.381%)

Visual Representation

The diagram below illustrates 9/30 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`173/210`
Mixed Number Form	`173/210`
Decimal Form	`0.82381`
Percentage	`82.381%`

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Frequently Asked Questions

What is 9/30 plus 11/21 as a fraction?

9/30 + 11/21 in simplest fraction form is 173/210.

What is 9/30 plus 11/21 as a decimal?

9/30 + 11/21 converted to a decimal is 0.82381.

What is 9/30 plus 11/21 as a percentage?

9/30 + 11/21 expressed as a percentage is 82.381%.

Does 9/30 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.82381...) because the denominator contains prime factors other than 2 and 5.