What is 2/9 plus 10/16? (Answer: 61/72)

Exact Answer

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Problem: What is 2/9 plus 10/16?
Formula / Expression: 2/9 + 10/16
Final Answer: 61/72
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 16 = 144.
Working: LCD(9, 16) = 144

Step 2: Convert to Equivalent Fractions with Common Denominator 144
Multiply the numerator and denominator of 2/9 by 16, and multiply the numerator and denominator of 10/16 by 9 so both fractions share the common base 144.
Working: 2 × 16/9 × 16 = 32/144 and 10 × 9/16 × 9 = 90/144

Step 3: Add the Numerators
Now add the numerators (32 + 90 = 122) and keep the common denominator 144 unchanged.
Working: 32 + 90/144 = 122/144

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 122 and 144, which is 2. Divide both the numerator and denominator by 2.
Working: 122 ÷ 2/144 ÷ 2 = 61/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 72 produces a repeating decimal (approximately 0.847222, or 84.7222%).
Working: 61 ÷ 72 = 0.847222 (84.7222%)

Key Values:
- Simplified Fraction: 61/72
- Mixed Number Form: 61/72
- Decimal Value: 0.847222
- Percentage: 84.7222%

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Solved with FractionsCalc:
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2/9 + 10/16 = 61/72

Simplified Fraction

61/72

Mixed Number

Proper (61/72)

Decimal Value

0.847222

Percentage

84.7222%

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Step-by-Step Solution: 2/9 + 10/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 16 = 144.

LCD(9, 16) = 144

Step 2

Convert to Equivalent Fractions with Common Denominator 144

Multiply the numerator and denominator of 2/9 by 16, and multiply the numerator and denominator of 10/16 by 9 so both fractions share the common base 144.

2 × 16/9 × 16 = 32/144 and 10 × 9/16 × 9 = 90/144

Step 3

Add the Numerators

Now add the numerators (32 + 90 = 122) and keep the common denominator 144 unchanged.

32 + 90/144 = 122/144

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 122 and 144, which is 2. Divide both the numerator and denominator by 2.

122 ÷ 2/144 ÷ 2 = 61/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 72 produces a repeating decimal (approximately 0.847222, or 84.7222%).

61 ÷ 72 = 0.847222 (84.7222%)

Visual Representation

The diagram below illustrates 2/9 plus 10/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/72`
Mixed Number Form	`61/72`
Decimal Form	`0.847222`
Percentage	`84.7222%`

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Frequently Asked Questions

What is 2/9 plus 10/16 as a fraction?

2/9 + 10/16 in simplest fraction form is 61/72.

What is 2/9 plus 10/16 as a decimal?

2/9 + 10/16 converted to a decimal is 0.847222.

What is 2/9 plus 10/16 as a percentage?

2/9 + 10/16 expressed as a percentage is 84.7222%.

Does 2/9 plus 10/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.847222...) because the denominator contains prime factors other than 2 and 5.