What is 2/9 plus 7/10? (Answer: 83/90)

Exact Answer

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Problem: What is 2/9 plus 7/10?
Formula / Expression: 2/9 + 7/10
Final Answer: 83/90
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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 2/9 by 10, and multiply the numerator and denominator of 7/10 by 9 so both fractions share the common base 90.
Working: 2 × 10/9 × 10 = 20/90 and 7 × 9/10 × 9 = 63/90

Step 3: Add the Numerators
Now add the numerators (20 + 63 = 83) and keep the common denominator 90 unchanged.
Working: 20 + 63/90 = 83/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 83 and 90 is 1, confirming that 83/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 83/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 90 produces a repeating decimal (approximately 0.922222, or 92.2222%).
Working: 83 ÷ 90 = 0.922222 (92.2222%)

Key Values:
- Simplified Fraction: 83/90
- Mixed Number Form: 83/90
- Decimal Value: 0.922222
- Percentage: 92.2222%

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Solved with FractionsCalc:
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2/9 + 7/10 = 83/90

Simplified Fraction

83/90

Mixed Number

Proper (83/90)

Decimal Value

0.922222

Percentage

92.2222%

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Step-by-Step Solution: 2/9 + 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 2/9 by 10, and multiply the numerator and denominator of 7/10 by 9 so both fractions share the common base 90.

2 × 10/9 × 10 = 20/90 and 7 × 9/10 × 9 = 63/90

Step 3

Add the Numerators

Now add the numerators (20 + 63 = 83) and keep the common denominator 90 unchanged.

20 + 63/90 = 83/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 83 and 90 is 1, confirming that 83/90 cannot be reduced further—it is already in its simplest irreducible form.

83/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 90 produces a repeating decimal (approximately 0.922222, or 92.2222%).

83 ÷ 90 = 0.922222 (92.2222%)

Visual Representation

The diagram below illustrates 2/9 plus 7/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/90`
Mixed Number Form	`83/90`
Decimal Form	`0.922222`
Percentage	`92.2222%`

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Frequently Asked Questions

What is 2/9 plus 7/10 as a fraction?

2/9 + 7/10 in simplest fraction form is 83/90.

What is 2/9 plus 7/10 as a decimal?

2/9 + 7/10 converted to a decimal is 0.922222.

What is 2/9 plus 7/10 as a percentage?

2/9 + 7/10 expressed as a percentage is 92.2222%.

Does 2/9 plus 7/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.922222...) because the denominator contains prime factors other than 2 and 5.