What is 4/6 plus 5/7?
4/6 plus 5/7 equals 29/21 (or 1 8/21 as a mixed number) (or 1.380952 in decimal form). Learn the step-by-step solution to add 4/6 and 5/7 using Least Common Denominator and simplification.
Exact Answer
4/6 + 5/7 = 29/21
Simplified Fraction
29/21
Mixed Number
1 8/21
Decimal Value
1.380952
Percentage
138.0952%
Step-by-Step Solution: 4/6 + 5/7
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 4/6 by 7, and multiply the numerator and denominator of 5/7 by 6 so both fractions share the common base 42.
4 × 7/6 × 7 = 28/42 and 5 × 6/7 × 6 = 30/42
Step 3
Add the Numerators
Now add the numerators (28 + 30 = 58) and keep the common denominator 42 unchanged.
28 + 30/42 = 58/42
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 42, which is 2. Divide both the numerator and denominator by 2.
58 ÷ 2/42 ÷ 2 = 29/21
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (29) is greater than the denominator (21), divide 29 by 21: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/21.
29/21 = 18/21
Step 6
Decimal & Percentage Representation
Dividing the numerator 29 by denominator 21 produces a repeating decimal (approximately 1.380952, or 138.0952%).
29 ÷ 21 = 1.380952 (138.0952%)
Visual Representation
The diagram below illustrates 4/6 plus 5/7 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 29/21 |
| Mixed Number Form | 1 8/21 |
| Decimal Form | 1.380952 |
| Percentage | 138.0952% |
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Frequently Asked Questions
What is 4/6 plus 5/7 as a fraction?
4/6 + 5/7 in simplest fraction form is 29/21 (or 1 8/21 as a mixed number).
What is 4/6 plus 5/7 as a decimal?
4/6 + 5/7 converted to a decimal is 1.380952.
What is 4/6 plus 5/7 as a percentage?
4/6 + 5/7 expressed as a percentage is 138.0952%.
How do you write 4/6 plus 5/7 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 29/21 can be written as the mixed number 1 8/21.
Does 4/6 plus 5/7 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.380952...) because the denominator contains prime factors other than 2 and 5.