What is 1/30 plus 9/21? (Answer: 97/210)

Exact Answer

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Problem: What is 1/30 plus 9/21?
Formula / Expression: 1/30 + 9/21
Final Answer: 97/210
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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 1/30 by 7, and multiply the numerator and denominator of 9/21 by 10 so both fractions share the common base 210.
Working: 1 × 7/30 × 7 = 7/210 and 9 × 10/21 × 10 = 90/210

Step 3: Add the Numerators
Now add the numerators (7 + 90 = 97) and keep the common denominator 210 unchanged.
Working: 7 + 90/210 = 97/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 210 is 1, confirming that 97/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 97/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 210 produces a repeating decimal (approximately 0.461905, or 46.1905%).
Working: 97 ÷ 210 = 0.461905 (46.1905%)

Key Values:
- Simplified Fraction: 97/210
- Mixed Number Form: 97/210
- Decimal Value: 0.461905
- Percentage: 46.1905%

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Solved with FractionsCalc:
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1/30 + 9/21 = 97/210

Simplified Fraction

97/210

Mixed Number

Proper (97/210)

Decimal Value

0.461905

Percentage

46.1905%

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Step-by-Step Solution: 1/30 + 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 1/30 by 7, and multiply the numerator and denominator of 9/21 by 10 so both fractions share the common base 210.

1 × 7/30 × 7 = 7/210 and 9 × 10/21 × 10 = 90/210

Step 3

Add the Numerators

Now add the numerators (7 + 90 = 97) and keep the common denominator 210 unchanged.

7 + 90/210 = 97/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 97 and 210 is 1, confirming that 97/210 cannot be reduced further—it is already in its simplest irreducible form.

97/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 210 produces a repeating decimal (approximately 0.461905, or 46.1905%).

97 ÷ 210 = 0.461905 (46.1905%)

Visual Representation

The diagram below illustrates 1/30 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/210`
Mixed Number Form	`97/210`
Decimal Form	`0.461905`
Percentage	`46.1905%`

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Frequently Asked Questions

What is 1/30 plus 9/21 as a fraction?

1/30 + 9/21 in simplest fraction form is 97/210.

What is 1/30 plus 9/21 as a decimal?

1/30 + 9/21 converted to a decimal is 0.461905.

What is 1/30 plus 9/21 as a percentage?

1/30 + 9/21 expressed as a percentage is 46.1905%.

Does 1/30 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.461905...) because the denominator contains prime factors other than 2 and 5.