What is 5/9 plus 4/7? (Answer: 71/63)

Exact Answer

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Problem: What is 5/9 plus 4/7?
Formula / Expression: 5/9 + 4/7
Final Answer: 1 8/63 (71/63)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 5/9 by 7, and multiply the numerator and denominator of 4/7 by 9 so both fractions share the common base 63.
Working: 5 × 7/9 × 7 = 35/63 and 4 × 9/7 × 9 = 36/63

Step 3: Add the Numerators
Now add the numerators (35 + 36 = 71) and keep the common denominator 63 unchanged.
Working: 35 + 36/63 = 71/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 63 is 1, confirming that 71/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/63

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (71) is greater than the denominator (63), divide 71 by 63: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/63.
Working: 71/63 = 1 8/63

Step 6: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 63 produces a repeating decimal (approximately 1.126984, or 112.6984%).
Working: 71 ÷ 63 = 1.126984 (112.6984%)

Key Values:
- Simplified Fraction: 71/63
- Mixed Number Form: 1 8/63
- Decimal Value: 1.126984
- Percentage: 112.6984%

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Solved with FractionsCalc:
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5/9 + 4/7 = 71/63

Simplified Fraction

71/63

Mixed Number

1 8/63

Decimal Value

1.126984

Percentage

112.6984%

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Step-by-Step Solution: 5/9 + 4/7

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 7) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 5/9 by 7, and multiply the numerator and denominator of 4/7 by 9 so both fractions share the common base 63.

5 × 7/9 × 7 = 35/63 and 4 × 9/7 × 9 = 36/63

Step 3

Add the Numerators

Now add the numerators (35 + 36 = 71) and keep the common denominator 63 unchanged.

35 + 36/63 = 71/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 63 is 1, confirming that 71/63 cannot be reduced further—it is already in its simplest irreducible form.

71/63

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (71) is greater than the denominator (63), divide 71 by 63: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/63.

71/63 = 18/63

Step 6

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 63 produces a repeating decimal (approximately 1.126984, or 112.6984%).

71 ÷ 63 = 1.126984 (112.6984%)

Visual Representation

The diagram below illustrates 5/9 plus 4/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/63`
Mixed Number Form	`1 8/63`
Decimal Form	`1.126984`
Percentage	`112.6984%`

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Frequently Asked Questions

What is 5/9 plus 4/7 as a fraction?

5/9 + 4/7 in simplest fraction form is 71/63 (or 1 8/63 as a mixed number).

What is 5/9 plus 4/7 as a decimal?

5/9 + 4/7 converted to a decimal is 1.126984.

What is 5/9 plus 4/7 as a percentage?

5/9 + 4/7 expressed as a percentage is 112.6984%.

How do you write 5/9 plus 4/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 71/63 can be written as the mixed number 1 8/63.

Does 5/9 plus 4/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.126984...) because the denominator contains prime factors other than 2 and 5.