What is 7/21 plus 10/30? (Answer: 2/3)

Exact Answer

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Problem: What is 7/21 plus 10/30?
Formula / Expression: 7/21 + 10/30
Final Answer: 2/3
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 30 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 21 × 30 = 630, keeping the calculation simpler).
Working: LCD(21, 30) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 7/21 by 10, and multiply the numerator and denominator of 10/30 by 7 so both fractions share the common base 210.
Working: 7 × 10/21 × 10 = 70/210 and 10 × 7/30 × 7 = 70/210

Step 3: Add the Numerators
Now add the numerators (70 + 70 = 140) and keep the common denominator 210 unchanged.
Working: 70 + 70/210 = 140/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 140 and 210, which is 70. Divide both the numerator and denominator by 70.
Working: 140 ÷ 70/210 ÷ 70 = 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

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Solved with FractionsCalc:
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7/21 + 10/30 = 2/3

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

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Step-by-Step Solution: 7/21 + 10/30

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 30 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 21 × 30 = 630, keeping the calculation simpler).

LCD(21, 30) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

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

7 × 10/21 × 10 = 70/210 and 10 × 7/30 × 7 = 70/210

Step 3

Add the Numerators

Now add the numerators (70 + 70 = 140) and keep the common denominator 210 unchanged.

70 + 70/210 = 140/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 140 and 210, which is 70. Divide both the numerator and denominator by 70.

140 ÷ 70/210 ÷ 70 = 2/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

The diagram below illustrates 7/21 plus 10/30 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

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Frequently Asked Questions

What is 7/21 plus 10/30 as a fraction?

7/21 + 10/30 in simplest fraction form is 2/3.

What is 7/21 plus 10/30 as a decimal?

7/21 + 10/30 converted to a decimal is 0.666667.

What is 7/21 plus 10/30 as a percentage?

7/21 + 10/30 expressed as a percentage is 66.6667%.

Does 7/21 plus 10/30 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.