What is 3/7 plus 11/21? (Answer: 20/21)

Exact Answer

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Problem: What is 3/7 plus 11/21?
Formula / Expression: 3/7 + 11/21
Final Answer: 20/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 21 is an exact multiple of 7 (7 × 3 = 21). The Least Common Denominator (LCD) is simply 21, meaning we only need to scale one fraction.
Working: LCD(7, 21) = 21

Step 2: Convert to Equivalent Fractions with Common Denominator 21
Multiply the numerator and denominator of 3/7 by 3, and multiply the numerator and denominator of 11/21 by 1 so both fractions share the common base 21.
Working: 3 × 3/7 × 3 = 9/21 and 11 × 1/21 × 1 = 11/21

Step 3: Add the Numerators
Now add the numerators (9 + 11 = 20) and keep the common denominator 21 unchanged.
Working: 9 + 11/21 = 20/21

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 20 and 21 is 1, confirming that 20/21 cannot be reduced further—it is already in its simplest irreducible form.
Working: 20/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 20 by denominator 21 produces a repeating decimal (approximately 0.952381, or 95.2381%).
Working: 20 ÷ 21 = 0.952381 (95.2381%)

Key Values:
- Simplified Fraction: 20/21
- Mixed Number Form: 20/21
- Decimal Value: 0.952381
- Percentage: 95.2381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-7-plus-11-21/
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3/7 + 11/21 = 20/21

Simplified Fraction

20/21

Mixed Number

Proper (20/21)

Decimal Value

0.952381

Percentage

95.2381%

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Step-by-Step Solution: 3/7 + 11/21

Step 1

Find the Least Common Denominator (LCD)

Notice that 21 is an exact multiple of 7 (7 × 3 = 21). The Least Common Denominator (LCD) is simply 21, meaning we only need to scale one fraction.

LCD(7, 21) = 21

Step 2

Convert to Equivalent Fractions with Common Denominator 21

Multiply the numerator and denominator of 3/7 by 3, and multiply the numerator and denominator of 11/21 by 1 so both fractions share the common base 21.

3 × 3/7 × 3 = 9/21 and 11 × 1/21 × 1 = 11/21

Step 3

Add the Numerators

Now add the numerators (9 + 11 = 20) and keep the common denominator 21 unchanged.

9 + 11/21 = 20/21

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 20 and 21 is 1, confirming that 20/21 cannot be reduced further—it is already in its simplest irreducible form.

20/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 20 by denominator 21 produces a repeating decimal (approximately 0.952381, or 95.2381%).

20 ÷ 21 = 0.952381 (95.2381%)

Visual Representation

The diagram below illustrates 3/7 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`20/21`
Mixed Number Form	`20/21`
Decimal Form	`0.952381`
Percentage	`95.2381%`

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Frequently Asked Questions

What is 3/7 plus 11/21 as a fraction?

3/7 + 11/21 in simplest fraction form is 20/21.

What is 3/7 plus 11/21 as a decimal?

3/7 + 11/21 converted to a decimal is 0.952381.

What is 3/7 plus 11/21 as a percentage?

3/7 + 11/21 expressed as a percentage is 95.2381%.

Does 3/7 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.952381...) because the denominator contains prime factors other than 2 and 5.