What is 3/6 plus 4/7?
3/6 plus 4/7 equals 15/14 (or 1 1/14 as a mixed number) (or 1.071429 in decimal form). Learn the step-by-step solution to add 3/6 and 4/7 using Least Common Denominator and simplification.
Exact Answer
3/6 + 4/7 = 15/14
Simplified Fraction
15/14
Mixed Number
1 1/14
Decimal Value
1.071429
Percentage
107.1429%
Step-by-Step Solution: 3/6 + 4/7
Step 1
Find the Least Common Denominator (LCD)
The denominators 6 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 7 = 42.
LCD(6, 7) = 42
Step 2
Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 3/6 by 7, and multiply the numerator and denominator of 4/7 by 6 so both fractions share the common base 42.
3 × 7/6 × 7 = 21/42 and 4 × 6/7 × 6 = 24/42
Step 3
Add the Numerators
Now add the numerators (21 + 24 = 45) and keep the common denominator 42 unchanged.
21 + 24/42 = 45/42
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 45 and 42, which is 3. Divide both the numerator and denominator by 3.
45 ÷ 3/42 ÷ 3 = 15/14
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (15) is greater than the denominator (14), divide 15 by 14: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/14.
15/14 = 11/14
Step 6
Decimal & Percentage Representation
Dividing the numerator 15 by denominator 14 produces a repeating decimal (approximately 1.071429, or 107.1429%).
15 ÷ 14 = 1.071429 (107.1429%)
Visual Representation
The diagram below illustrates 3/6 plus 4/7 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 15/14 |
| Mixed Number Form | 1 1/14 |
| Decimal Form | 1.071429 |
| Percentage | 107.1429% |
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Frequently Asked Questions
What is 3/6 plus 4/7 as a fraction?
3/6 + 4/7 in simplest fraction form is 15/14 (or 1 1/14 as a mixed number).
What is 3/6 plus 4/7 as a decimal?
3/6 + 4/7 converted to a decimal is 1.071429.
What is 3/6 plus 4/7 as a percentage?
3/6 + 4/7 expressed as a percentage is 107.1429%.
How do you write 3/6 plus 4/7 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 15/14 can be written as the mixed number 1 1/14.
Does 3/6 plus 4/7 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.071429...) because the denominator contains prime factors other than 2 and 5.