What is 2/9 plus 10/18? (Answer: 7/9)

Exact Answer

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Problem: What is 2/9 plus 10/18?
Formula / Expression: 2/9 + 10/18
Final Answer: 7/9
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 18 is an exact multiple of 9 (9 × 2 = 18). The Least Common Denominator (LCD) is simply 18, meaning we only need to scale one fraction.
Working: LCD(9, 18) = 18

Step 2: Convert to Equivalent Fractions with Common Denominator 18
Multiply the numerator and denominator of 2/9 by 2, and multiply the numerator and denominator of 10/18 by 1 so both fractions share the common base 18.
Working: 2 × 2/9 × 2 = 4/18 and 10 × 1/18 × 1 = 10/18

Step 3: Add the Numerators
Now add the numerators (4 + 10 = 14) and keep the common denominator 18 unchanged.
Working: 4 + 10/18 = 14/18

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 14 and 18, which is 2. Divide both the numerator and denominator by 2.
Working: 14 ÷ 2/18 ÷ 2 = 7/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 9 produces a repeating decimal (approximately 0.777778, or 77.7778%).
Working: 7 ÷ 9 = 0.777778 (77.7778%)

Key Values:
- Simplified Fraction: 7/9
- Mixed Number Form: 7/9
- Decimal Value: 0.777778
- Percentage: 77.7778%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-10-18/
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2/9 + 10/18 = 7/9

Simplified Fraction

7/9

Mixed Number

Proper (7/9)

Decimal Value

0.777778

Percentage

77.7778%

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Step-by-Step Solution: 2/9 + 10/18

Step 1

Find the Least Common Denominator (LCD)

Notice that 18 is an exact multiple of 9 (9 × 2 = 18). The Least Common Denominator (LCD) is simply 18, meaning we only need to scale one fraction.

LCD(9, 18) = 18

Step 2

Convert to Equivalent Fractions with Common Denominator 18

Multiply the numerator and denominator of 2/9 by 2, and multiply the numerator and denominator of 10/18 by 1 so both fractions share the common base 18.

2 × 2/9 × 2 = 4/18 and 10 × 1/18 × 1 = 10/18

Step 3

Add the Numerators

Now add the numerators (4 + 10 = 14) and keep the common denominator 18 unchanged.

4 + 10/18 = 14/18

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 14 and 18, which is 2. Divide both the numerator and denominator by 2.

14 ÷ 2/18 ÷ 2 = 7/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 9 produces a repeating decimal (approximately 0.777778, or 77.7778%).

7 ÷ 9 = 0.777778 (77.7778%)

Visual Representation

The diagram below illustrates 2/9 plus 10/18 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/9`
Mixed Number Form	`7/9`
Decimal Form	`0.777778`
Percentage	`77.7778%`

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Frequently Asked Questions

What is 2/9 plus 10/18 as a fraction?

2/9 + 10/18 in simplest fraction form is 7/9.

What is 2/9 plus 10/18 as a decimal?

2/9 + 10/18 converted to a decimal is 0.777778.

What is 2/9 plus 10/18 as a percentage?

2/9 + 10/18 expressed as a percentage is 77.7778%.

Does 2/9 plus 10/18 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.777778...) because the denominator contains prime factors other than 2 and 5.