What is 6/42 plus 6/21?
6/42 plus 6/21 equals 3/7 (or 0.428571 in decimal form). Learn the step-by-step solution to add 6/42 and 6/21 using Least Common Denominator and simplification.
Exact Answer
6/42 + 6/21 = 3/7
Simplified Fraction
3/7
Mixed Number
Proper (3/7)
Decimal Value
0.428571
Percentage
42.8571%
Step-by-Step Solution: 6/42 + 6/21
Step 1
Find the Least Common Denominator (LCD)
Notice that 42 is an exact multiple of 21 (21 × 2 = 42). The Least Common Denominator (LCD) is simply 42, meaning we only need to scale one fraction.
LCD(42, 21) = 42
Step 2
Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 6/42 by 1, and multiply the numerator and denominator of 6/21 by 2 so both fractions share the common base 42.
6 × 1/42 × 1 = 6/42 and 6 × 2/21 × 2 = 12/42
Step 3
Add the Numerators
Now add the numerators (6 + 12 = 18) and keep the common denominator 42 unchanged.
6 + 12/42 = 18/42
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 18 and 42, which is 6. Divide both the numerator and denominator by 6.
18 ÷ 6/42 ÷ 6 = 3/7
Step 5
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 6/42 plus 6/21 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 6/42 plus 6/21 as a fraction?
6/42 + 6/21 in simplest fraction form is 3/7.
What is 6/42 plus 6/21 as a decimal?
6/42 + 6/21 converted to a decimal is 0.428571.
What is 6/42 plus 6/21 as a percentage?
6/42 + 6/21 expressed as a percentage is 42.8571%.
Does 6/42 plus 6/21 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.