What is 4/21 plus 2/3? (Answer: 6/7)

Exact Answer

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Problem: What is 4/21 plus 2/3?
Formula / Expression: 4/21 + 2/3
Final Answer: 6/7
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 21
Multiply the numerator and denominator of 4/21 by 1, and multiply the numerator and denominator of 2/3 by 7 so both fractions share the common base 21.
Working: 4 × 1/21 × 1 = 4/21 and 2 × 7/3 × 7 = 14/21

Step 3: Add the Numerators
Now add the numerators (4 + 14 = 18) and keep the common denominator 21 unchanged.
Working: 4 + 14/21 = 18/21

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 18 and 21, which is 3. Divide both the numerator and denominator by 3.
Working: 18 ÷ 3/21 ÷ 3 = 6/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 6 by denominator 7 produces a repeating decimal (approximately 0.857143, or 85.7143%).
Working: 6 ÷ 7 = 0.857143 (85.7143%)

Key Values:
- Simplified Fraction: 6/7
- Mixed Number Form: 6/7
- Decimal Value: 0.857143
- Percentage: 85.7143%

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Solved with FractionsCalc:
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4/21 + 2/3 = 6/7

Simplified Fraction

6/7

Mixed Number

Proper (6/7)

Decimal Value

0.857143

Percentage

85.7143%

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Step-by-Step Solution: 4/21 + 2/3

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 3) = 21

Step 2

Convert to Equivalent Fractions with Common Denominator 21

Multiply the numerator and denominator of 4/21 by 1, and multiply the numerator and denominator of 2/3 by 7 so both fractions share the common base 21.

4 × 1/21 × 1 = 4/21 and 2 × 7/3 × 7 = 14/21

Step 3

Add the Numerators

Now add the numerators (4 + 14 = 18) and keep the common denominator 21 unchanged.

4 + 14/21 = 18/21

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 18 and 21, which is 3. Divide both the numerator and denominator by 3.

18 ÷ 3/21 ÷ 3 = 6/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 6 by denominator 7 produces a repeating decimal (approximately 0.857143, or 85.7143%).

6 ÷ 7 = 0.857143 (85.7143%)

Visual Representation

The diagram below illustrates 4/21 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`6/7`
Mixed Number Form	`6/7`
Decimal Form	`0.857143`
Percentage	`85.7143%`

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Frequently Asked Questions

What is 4/21 plus 2/3 as a fraction?

4/21 + 2/3 in simplest fraction form is 6/7.

What is 4/21 plus 2/3 as a decimal?

4/21 + 2/3 converted to a decimal is 0.857143.

What is 4/21 plus 2/3 as a percentage?

4/21 + 2/3 expressed as a percentage is 85.7143%.

Does 4/21 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.857143...) because the denominator contains prime factors other than 2 and 5.