What is 5/9 plus 7/10? (Answer: 113/90)

Exact Answer

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Problem: What is 5/9 plus 7/10?
Formula / Expression: 5/9 + 7/10
Final Answer: 1 23/90 (113/90)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 10 = 90.
Working: LCD(9, 10) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 5/9 by 10, and multiply the numerator and denominator of 7/10 by 9 so both fractions share the common base 90.
Working: 5 × 10/9 × 10 = 50/90 and 7 × 9/10 × 9 = 63/90

Step 3: Add the Numerators
Now add the numerators (50 + 63 = 113) and keep the common denominator 90 unchanged.
Working: 50 + 63/90 = 113/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 113 and 90 is 1, confirming that 113/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 113/90

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (113) is greater than the denominator (90), divide 113 by 90: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/90.
Working: 113/90 = 1 23/90

Step 6: Decimal & Percentage Representation
Dividing the numerator 113 by denominator 90 produces a repeating decimal (approximately 1.255556, or 125.5556%).
Working: 113 ÷ 90 = 1.255556 (125.5556%)

Key Values:
- Simplified Fraction: 113/90
- Mixed Number Form: 1 23/90
- Decimal Value: 1.255556
- Percentage: 125.5556%

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Solved with FractionsCalc:
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5/9 + 7/10 = 113/90

Simplified Fraction

113/90

Mixed Number

1 23/90

Decimal Value

1.255556

Percentage

125.5556%

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Step-by-Step Solution: 5/9 + 7/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 10 = 90.

LCD(9, 10) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 5/9 by 10, and multiply the numerator and denominator of 7/10 by 9 so both fractions share the common base 90.

5 × 10/9 × 10 = 50/90 and 7 × 9/10 × 9 = 63/90

Step 3

Add the Numerators

Now add the numerators (50 + 63 = 113) and keep the common denominator 90 unchanged.

50 + 63/90 = 113/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 113 and 90 is 1, confirming that 113/90 cannot be reduced further—it is already in its simplest irreducible form.

113/90

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (113) is greater than the denominator (90), divide 113 by 90: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/90.

113/90 = 123/90

Step 6

Decimal & Percentage Representation

Dividing the numerator 113 by denominator 90 produces a repeating decimal (approximately 1.255556, or 125.5556%).

113 ÷ 90 = 1.255556 (125.5556%)

Visual Representation

The diagram below illustrates 5/9 plus 7/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`113/90`
Mixed Number Form	`1 23/90`
Decimal Form	`1.255556`
Percentage	`125.5556%`

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Frequently Asked Questions

What is 5/9 plus 7/10 as a fraction?

5/9 + 7/10 in simplest fraction form is 113/90 (or 1 23/90 as a mixed number).

What is 5/9 plus 7/10 as a decimal?

5/9 + 7/10 converted to a decimal is 1.255556.

What is 5/9 plus 7/10 as a percentage?

5/9 + 7/10 expressed as a percentage is 125.5556%.

How do you write 5/9 plus 7/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 113/90 can be written as the mixed number 1 23/90.

Does 5/9 plus 7/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.255556...) because the denominator contains prime factors other than 2 and 5.