What is 1/30 plus 10/21? (Answer: 107/210)

Exact Answer

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Problem: What is 1/30 plus 10/21?
Formula / Expression: 1/30 + 10/21
Final Answer: 107/210
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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 10/21 by 10 so both fractions share the common base 210.
Working: 1 × 7/30 × 7 = 7/210 and 10 × 10/21 × 10 = 100/210

Step 3: Add the Numerators
Now add the numerators (7 + 100 = 107) and keep the common denominator 210 unchanged.
Working: 7 + 100/210 = 107/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 210 is 1, confirming that 107/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 107/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 210 produces a repeating decimal (approximately 0.509524, or 50.9524%).
Working: 107 ÷ 210 = 0.509524 (50.9524%)

Key Values:
- Simplified Fraction: 107/210
- Mixed Number Form: 107/210
- Decimal Value: 0.509524
- Percentage: 50.9524%

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1/30 + 10/21 = 107/210

Simplified Fraction

107/210

Mixed Number

Proper (107/210)

Decimal Value

0.509524

Percentage

50.9524%

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Step-by-Step Solution: 1/30 + 10/21

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

1 × 7/30 × 7 = 7/210 and 10 × 10/21 × 10 = 100/210

Step 3

Add the Numerators

Now add the numerators (7 + 100 = 107) and keep the common denominator 210 unchanged.

7 + 100/210 = 107/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 107 and 210 is 1, confirming that 107/210 cannot be reduced further—it is already in its simplest irreducible form.

107/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 210 produces a repeating decimal (approximately 0.509524, or 50.9524%).

107 ÷ 210 = 0.509524 (50.9524%)

Visual Representation

The diagram below illustrates 1/30 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/210`
Mixed Number Form	`107/210`
Decimal Form	`0.509524`
Percentage	`50.9524%`

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Frequently Asked Questions

What is 1/30 plus 10/21 as a fraction?

1/30 + 10/21 in simplest fraction form is 107/210.

What is 1/30 plus 10/21 as a decimal?

1/30 + 10/21 converted to a decimal is 0.509524.

What is 1/30 plus 10/21 as a percentage?

1/30 + 10/21 expressed as a percentage is 50.9524%.

Does 1/30 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.509524...) because the denominator contains prime factors other than 2 and 5.