What is 6/30 plus 10/21? (Answer: 71/105)

Exact Answer

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Problem: What is 6/30 plus 10/21?
Formula / Expression: 6/30 + 10/21
Final Answer: 71/105
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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 6/30 by 7, and multiply the numerator and denominator of 10/21 by 10 so both fractions share the common base 210.
Working: 6 × 7/30 × 7 = 42/210 and 10 × 10/21 × 10 = 100/210

Step 3: Add the Numerators
Now add the numerators (42 + 100 = 142) and keep the common denominator 210 unchanged.
Working: 42 + 100/210 = 142/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 142 and 210, which is 2. Divide both the numerator and denominator by 2.
Working: 142 ÷ 2/210 ÷ 2 = 71/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 105 produces a repeating decimal (approximately 0.67619, or 67.619%).
Working: 71 ÷ 105 = 0.67619 (67.619%)

Key Values:
- Simplified Fraction: 71/105
- Mixed Number Form: 71/105
- Decimal Value: 0.67619
- Percentage: 67.619%

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Solved with FractionsCalc:
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6/30 + 10/21 = 71/105

Simplified Fraction

71/105

Mixed Number

Proper (71/105)

Decimal Value

0.67619

Percentage

67.619%

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Step-by-Step Solution: 6/30 + 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 6/30 by 7, and multiply the numerator and denominator of 10/21 by 10 so both fractions share the common base 210.

6 × 7/30 × 7 = 42/210 and 10 × 10/21 × 10 = 100/210

Step 3

Add the Numerators

Now add the numerators (42 + 100 = 142) and keep the common denominator 210 unchanged.

42 + 100/210 = 142/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 142 and 210, which is 2. Divide both the numerator and denominator by 2.

142 ÷ 2/210 ÷ 2 = 71/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 105 produces a repeating decimal (approximately 0.67619, or 67.619%).

71 ÷ 105 = 0.67619 (67.619%)

Visual Representation

The diagram below illustrates 6/30 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/105`
Mixed Number Form	`71/105`
Decimal Form	`0.67619`
Percentage	`67.619%`

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Frequently Asked Questions

What is 6/30 plus 10/21 as a fraction?

6/30 + 10/21 in simplest fraction form is 71/105.

What is 6/30 plus 10/21 as a decimal?

6/30 + 10/21 converted to a decimal is 0.67619.

What is 6/30 plus 10/21 as a percentage?

6/30 + 10/21 expressed as a percentage is 67.619%.

Does 6/30 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.67619...) because the denominator contains prime factors other than 2 and 5.