What is 1/21 plus 8/21?
1/21 plus 8/21 equals 3/7 (or 0.428571 in decimal form). Learn the step-by-step solution to add 1/21 and 8/21 using Least Common Denominator and simplification.
Exact Answer
1/21 + 8/21 = 3/7
Simplified Fraction
3/7
Mixed Number
Proper (3/7)
Decimal Value
0.428571
Percentage
42.8571%
Step-by-Step Solution: 1/21 + 8/21
Step 1
Check the Denominators (Like Fractions)
Both fractions already share the identical denominator (21). Because these are like fractions, no conversion to a common denominator is required—we directly add their numerators while keeping the denominator 21.
1/21 + 8/21
Step 2
Add the Numerators
Now add the numerators (1 + 8 = 9) and keep the common denominator 21 unchanged.
1 + 8/21 = 9/21
Step 3
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 9 and 21, which is 3. Divide both the numerator and denominator by 3.
9 ÷ 3/21 ÷ 3 = 3/7
Step 4
Decimal & Percentage Representation
Dividing the numerator 3 by denominator 7 produces a repeating decimal (approximately 0.428571, or 42.8571%).
3 ÷ 7 = 0.428571 (42.8571%)
Visual Representation
The diagram below illustrates 1/21 plus 8/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 3/7 |
| Mixed Number Form | 3/7 |
| Decimal Form | 0.428571 |
| Percentage | 42.8571% |
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Frequently Asked Questions
What is 1/21 plus 8/21 as a fraction?
1/21 + 8/21 in simplest fraction form is 3/7.
What is 1/21 plus 8/21 as a decimal?
1/21 + 8/21 converted to a decimal is 0.428571.
What is 1/21 plus 8/21 as a percentage?
1/21 + 8/21 expressed as a percentage is 42.8571%.
Does 1/21 plus 8/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.428571...) because the denominator contains prime factors other than 2 and 5.