What is 3/7 plus 7/9? (Answer: 76/63)

Exact Answer

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Problem: What is 3/7 plus 7/9?
Formula / Expression: 3/7 + 7/9
Final Answer: 1 13/63 (76/63)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 9 = 63.
Working: LCD(7, 9) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 3/7 by 9, and multiply the numerator and denominator of 7/9 by 7 so both fractions share the common base 63.
Working: 3 × 9/7 × 9 = 27/63 and 7 × 7/9 × 7 = 49/63

Step 3: Add the Numerators
Now add the numerators (27 + 49 = 76) and keep the common denominator 63 unchanged.
Working: 27 + 49/63 = 76/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 76 and 63 is 1, confirming that 76/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 76/63

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (76) is greater than the denominator (63), divide 76 by 63: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/63.
Working: 76/63 = 1 13/63

Step 6: Decimal & Percentage Representation
Dividing the numerator 76 by denominator 63 produces a repeating decimal (approximately 1.206349, or 120.6349%).
Working: 76 ÷ 63 = 1.206349 (120.6349%)

Key Values:
- Simplified Fraction: 76/63
- Mixed Number Form: 1 13/63
- Decimal Value: 1.206349
- Percentage: 120.6349%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-7-plus-7-9/
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3/7 + 7/9 = 76/63

Simplified Fraction

76/63

Mixed Number

1 13/63

Decimal Value

1.206349

Percentage

120.6349%

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Step-by-Step Solution: 3/7 + 7/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 9 = 63.

LCD(7, 9) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 3/7 by 9, and multiply the numerator and denominator of 7/9 by 7 so both fractions share the common base 63.

3 × 9/7 × 9 = 27/63 and 7 × 7/9 × 7 = 49/63

Step 3

Add the Numerators

Now add the numerators (27 + 49 = 76) and keep the common denominator 63 unchanged.

27 + 49/63 = 76/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 76 and 63 is 1, confirming that 76/63 cannot be reduced further—it is already in its simplest irreducible form.

76/63

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (76) is greater than the denominator (63), divide 76 by 63: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/63.

76/63 = 113/63

Step 6

Decimal & Percentage Representation

Dividing the numerator 76 by denominator 63 produces a repeating decimal (approximately 1.206349, or 120.6349%).

76 ÷ 63 = 1.206349 (120.6349%)

Visual Representation

The diagram below illustrates 3/7 plus 7/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`76/63`
Mixed Number Form	`1 13/63`
Decimal Form	`1.206349`
Percentage	`120.6349%`

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Frequently Asked Questions

What is 3/7 plus 7/9 as a fraction?

3/7 + 7/9 in simplest fraction form is 76/63 (or 1 13/63 as a mixed number).

What is 3/7 plus 7/9 as a decimal?

3/7 + 7/9 converted to a decimal is 1.206349.

What is 3/7 plus 7/9 as a percentage?

3/7 + 7/9 expressed as a percentage is 120.6349%.

How do you write 3/7 plus 7/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 76/63 can be written as the mixed number 1 13/63.

Does 3/7 plus 7/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.206349...) because the denominator contains prime factors other than 2 and 5.