What is 5/7 plus 7/9? (Answer: 94/63)

Exact Answer

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Problem: What is 5/7 plus 7/9?
Formula / Expression: 5/7 + 7/9
Final Answer: 1 31/63 (94/63)
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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 5/7 by 9, and multiply the numerator and denominator of 7/9 by 7 so both fractions share the common base 63.
Working: 5 × 9/7 × 9 = 45/63 and 7 × 7/9 × 7 = 49/63

Step 3: Add the Numerators
Now add the numerators (45 + 49 = 94) and keep the common denominator 63 unchanged.
Working: 45 + 49/63 = 94/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 94 and 63 is 1, confirming that 94/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 94/63

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (94) is greater than the denominator (63), divide 94 by 63: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/63.
Working: 94/63 = 1 31/63

Step 6: Decimal & Percentage Representation
Dividing the numerator 94 by denominator 63 produces a repeating decimal (approximately 1.492063, or 149.2063%).
Working: 94 ÷ 63 = 1.492063 (149.2063%)

Key Values:
- Simplified Fraction: 94/63
- Mixed Number Form: 1 31/63
- Decimal Value: 1.492063
- Percentage: 149.2063%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-7-plus-7-9/
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5/7 + 7/9 = 94/63

Simplified Fraction

94/63

Mixed Number

1 31/63

Decimal Value

1.492063

Percentage

149.2063%

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Step-by-Step Solution: 5/7 + 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 5/7 by 9, and multiply the numerator and denominator of 7/9 by 7 so both fractions share the common base 63.

5 × 9/7 × 9 = 45/63 and 7 × 7/9 × 7 = 49/63

Step 3

Add the Numerators

Now add the numerators (45 + 49 = 94) and keep the common denominator 63 unchanged.

45 + 49/63 = 94/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 94 and 63 is 1, confirming that 94/63 cannot be reduced further—it is already in its simplest irreducible form.

94/63

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (94) is greater than the denominator (63), divide 94 by 63: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/63.

94/63 = 131/63

Step 6

Decimal & Percentage Representation

Dividing the numerator 94 by denominator 63 produces a repeating decimal (approximately 1.492063, or 149.2063%).

94 ÷ 63 = 1.492063 (149.2063%)

Visual Representation

The diagram below illustrates 5/7 plus 7/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`94/63`
Mixed Number Form	`1 31/63`
Decimal Form	`1.492063`
Percentage	`149.2063%`

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Frequently Asked Questions

What is 5/7 plus 7/9 as a fraction?

5/7 + 7/9 in simplest fraction form is 94/63 (or 1 31/63 as a mixed number).

What is 5/7 plus 7/9 as a decimal?

5/7 + 7/9 converted to a decimal is 1.492063.

What is 5/7 plus 7/9 as a percentage?

5/7 + 7/9 expressed as a percentage is 149.2063%.

How do you write 5/7 plus 7/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 94/63 can be written as the mixed number 1 31/63.

Does 5/7 plus 7/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.492063...) because the denominator contains prime factors other than 2 and 5.