What is 7/42 plus 6/21?
7/42 plus 6/21 equals 19/42 (or 0.452381 in decimal form). Learn the step-by-step solution to add 7/42 and 6/21 using Least Common Denominator and simplification.
Exact Answer
7/42 + 6/21 = 19/42
Simplified Fraction
19/42
Mixed Number
Proper (19/42)
Decimal Value
0.452381
Percentage
45.2381%
Step-by-Step Solution: 7/42 + 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 7/42 by 1, and multiply the numerator and denominator of 6/21 by 2 so both fractions share the common base 42.
7 × 1/42 × 1 = 7/42 and 6 × 2/21 × 2 = 12/42
Step 3
Add the Numerators
Now add the numerators (7 + 12 = 19) and keep the common denominator 42 unchanged.
7 + 12/42 = 19/42
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 42 is 1, confirming that 19/42 cannot be reduced further—it is already in its simplest irreducible form.
19/42
Step 5
Decimal & Percentage Representation
Dividing the numerator 19 by denominator 42 produces a repeating decimal (approximately 0.452381, or 45.2381%).
19 ÷ 42 = 0.452381 (45.2381%)
Visual Representation
The diagram below illustrates 7/42 plus 6/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 19/42 |
| Mixed Number Form | 19/42 |
| Decimal Form | 0.452381 |
| Percentage | 45.2381% |
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Frequently Asked Questions
What is 7/42 plus 6/21 as a fraction?
7/42 + 6/21 in simplest fraction form is 19/42.
What is 7/42 plus 6/21 as a decimal?
7/42 + 6/21 converted to a decimal is 0.452381.
What is 7/42 plus 6/21 as a percentage?
7/42 + 6/21 expressed as a percentage is 45.2381%.
Does 7/42 plus 6/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.452381...) because the denominator contains prime factors other than 2 and 5.