What is 5/10 plus 7/9? (Answer: 23/18)

Exact Answer

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Problem: What is 5/10 plus 7/9?
Formula / Expression: 5/10 + 7/9
Final Answer: 1 5/18 (23/18)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 5/10 by 9, and multiply the numerator and denominator of 7/9 by 10 so both fractions share the common base 90.
Working: 5 × 9/10 × 9 = 45/90 and 7 × 10/9 × 10 = 70/90

Step 3: Add the Numerators
Now add the numerators (45 + 70 = 115) and keep the common denominator 90 unchanged.
Working: 45 + 70/90 = 115/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 115 and 90, which is 5. Divide both the numerator and denominator by 5.
Working: 115 ÷ 5/90 ÷ 5 = 23/18

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (23) is greater than the denominator (18), divide 23 by 18: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/18.
Working: 23/18 = 1 5/18

Step 6: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 18 produces a repeating decimal (approximately 1.277778, or 127.7778%).
Working: 23 ÷ 18 = 1.277778 (127.7778%)

Key Values:
- Simplified Fraction: 23/18
- Mixed Number Form: 1 5/18
- Decimal Value: 1.277778
- Percentage: 127.7778%

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Solved with FractionsCalc:
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5/10 + 7/9 = 23/18

Simplified Fraction

23/18

Mixed Number

1 5/18

Decimal Value

1.277778

Percentage

127.7778%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(10, 9) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

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

5 × 9/10 × 9 = 45/90 and 7 × 10/9 × 10 = 70/90

Step 3

Add the Numerators

Now add the numerators (45 + 70 = 115) and keep the common denominator 90 unchanged.

45 + 70/90 = 115/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 115 and 90, which is 5. Divide both the numerator and denominator by 5.

115 ÷ 5/90 ÷ 5 = 23/18

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (23) is greater than the denominator (18), divide 23 by 18: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/18.

23/18 = 15/18

Step 6

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 18 produces a repeating decimal (approximately 1.277778, or 127.7778%).

23 ÷ 18 = 1.277778 (127.7778%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/18`
Mixed Number Form	`1 5/18`
Decimal Form	`1.277778`
Percentage	`127.7778%`

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Frequently Asked Questions

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

5/10 + 7/9 in simplest fraction form is 23/18 (or 1 5/18 as a mixed number).

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

5/10 + 7/9 converted to a decimal is 1.277778.

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

5/10 + 7/9 expressed as a percentage is 127.7778%.

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

Because the numerator is greater than the denominator, the improper fraction 23/18 can be written as the mixed number 1 5/18.

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

It results in a repeating decimal (approximately 1.277778...) because the denominator contains prime factors other than 2 and 5.