What is 6/21 plus 8/28? (Answer: 4/7)

Exact Answer

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Problem: What is 6/21 plus 8/28?
Formula / Expression: 6/21 + 8/28
Final Answer: 4/7
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 28 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 21 × 28 = 588, keeping the calculation simpler).
Working: LCD(21, 28) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 6/21 by 4, and multiply the numerator and denominator of 8/28 by 3 so both fractions share the common base 84.
Working: 6 × 4/21 × 4 = 24/84 and 8 × 3/28 × 3 = 24/84

Step 3: Add the Numerators
Now add the numerators (24 + 24 = 48) and keep the common denominator 84 unchanged.
Working: 24 + 24/84 = 48/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 48 and 84, which is 12. Divide both the numerator and denominator by 12.
Working: 48 ÷ 12/84 ÷ 12 = 4/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 7 produces a repeating decimal (approximately 0.571429, or 57.1429%).
Working: 4 ÷ 7 = 0.571429 (57.1429%)

Key Values:
- Simplified Fraction: 4/7
- Mixed Number Form: 4/7
- Decimal Value: 0.571429
- Percentage: 57.1429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-21-plus-8-28/
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6/21 + 8/28 = 4/7

Simplified Fraction

4/7

Mixed Number

Proper (4/7)

Decimal Value

0.571429

Percentage

57.1429%

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Step-by-Step Solution: 6/21 + 8/28

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 28 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 21 × 28 = 588, keeping the calculation simpler).

LCD(21, 28) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 6/21 by 4, and multiply the numerator and denominator of 8/28 by 3 so both fractions share the common base 84.

6 × 4/21 × 4 = 24/84 and 8 × 3/28 × 3 = 24/84

Step 3

Add the Numerators

Now add the numerators (24 + 24 = 48) and keep the common denominator 84 unchanged.

24 + 24/84 = 48/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 48 and 84, which is 12. Divide both the numerator and denominator by 12.

48 ÷ 12/84 ÷ 12 = 4/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 7 produces a repeating decimal (approximately 0.571429, or 57.1429%).

4 ÷ 7 = 0.571429 (57.1429%)

Visual Representation

The diagram below illustrates 6/21 plus 8/28 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/7`
Mixed Number Form	`4/7`
Decimal Form	`0.571429`
Percentage	`57.1429%`

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Frequently Asked Questions

What is 6/21 plus 8/28 as a fraction?

6/21 + 8/28 in simplest fraction form is 4/7.

What is 6/21 plus 8/28 as a decimal?

6/21 + 8/28 converted to a decimal is 0.571429.

What is 6/21 plus 8/28 as a percentage?

6/21 + 8/28 expressed as a percentage is 57.1429%.

Does 6/21 plus 8/28 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.571429...) because the denominator contains prime factors other than 2 and 5.