What is 2/30 plus 10/21? (Answer: 19/35)

Exact Answer

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Problem: What is 2/30 plus 10/21?
Formula / Expression: 2/30 + 10/21
Final Answer: 19/35
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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 2/30 by 7, and multiply the numerator and denominator of 10/21 by 10 so both fractions share the common base 210.
Working: 2 × 7/30 × 7 = 14/210 and 10 × 10/21 × 10 = 100/210

Step 3: Add the Numerators
Now add the numerators (14 + 100 = 114) and keep the common denominator 210 unchanged.
Working: 14 + 100/210 = 114/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 114 and 210, which is 6. Divide both the numerator and denominator by 6.
Working: 114 ÷ 6/210 ÷ 6 = 19/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 35 produces a repeating decimal (approximately 0.542857, or 54.2857%).
Working: 19 ÷ 35 = 0.542857 (54.2857%)

Key Values:
- Simplified Fraction: 19/35
- Mixed Number Form: 19/35
- Decimal Value: 0.542857
- Percentage: 54.2857%

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Solved with FractionsCalc:
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2/30 + 10/21 = 19/35

Simplified Fraction

19/35

Mixed Number

Proper (19/35)

Decimal Value

0.542857

Percentage

54.2857%

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Step-by-Step Solution: 2/30 + 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 2/30 by 7, and multiply the numerator and denominator of 10/21 by 10 so both fractions share the common base 210.

2 × 7/30 × 7 = 14/210 and 10 × 10/21 × 10 = 100/210

Step 3

Add the Numerators

Now add the numerators (14 + 100 = 114) and keep the common denominator 210 unchanged.

14 + 100/210 = 114/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 114 and 210, which is 6. Divide both the numerator and denominator by 6.

114 ÷ 6/210 ÷ 6 = 19/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 35 produces a repeating decimal (approximately 0.542857, or 54.2857%).

19 ÷ 35 = 0.542857 (54.2857%)

Visual Representation

The diagram below illustrates 2/30 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/35`
Mixed Number Form	`19/35`
Decimal Form	`0.542857`
Percentage	`54.2857%`

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Frequently Asked Questions

What is 2/30 plus 10/21 as a fraction?

2/30 + 10/21 in simplest fraction form is 19/35.

What is 2/30 plus 10/21 as a decimal?

2/30 + 10/21 converted to a decimal is 0.542857.

What is 2/30 plus 10/21 as a percentage?

2/30 + 10/21 expressed as a percentage is 54.2857%.

Does 2/30 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.542857...) because the denominator contains prime factors other than 2 and 5.