What is 1/9 plus 7/10? (Answer: 73/90)

Exact Answer

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Problem: What is 1/9 plus 7/10?
Formula / Expression: 1/9 + 7/10
Final Answer: 73/90
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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 1/9 by 10, and multiply the numerator and denominator of 7/10 by 9 so both fractions share the common base 90.
Working: 1 × 10/9 × 10 = 10/90 and 7 × 9/10 × 9 = 63/90

Step 3: Add the Numerators
Now add the numerators (10 + 63 = 73) and keep the common denominator 90 unchanged.
Working: 10 + 63/90 = 73/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 73 and 90 is 1, confirming that 73/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 73/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 90 produces a repeating decimal (approximately 0.811111, or 81.1111%).
Working: 73 ÷ 90 = 0.811111 (81.1111%)

Key Values:
- Simplified Fraction: 73/90
- Mixed Number Form: 73/90
- Decimal Value: 0.811111
- Percentage: 81.1111%

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Solved with FractionsCalc:
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1/9 + 7/10 = 73/90

Simplified Fraction

73/90

Mixed Number

Proper (73/90)

Decimal Value

0.811111

Percentage

81.1111%

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Step-by-Step Solution: 1/9 + 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 1/9 by 10, and multiply the numerator and denominator of 7/10 by 9 so both fractions share the common base 90.

1 × 10/9 × 10 = 10/90 and 7 × 9/10 × 9 = 63/90

Step 3

Add the Numerators

Now add the numerators (10 + 63 = 73) and keep the common denominator 90 unchanged.

10 + 63/90 = 73/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 73 and 90 is 1, confirming that 73/90 cannot be reduced further—it is already in its simplest irreducible form.

73/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 90 produces a repeating decimal (approximately 0.811111, or 81.1111%).

73 ÷ 90 = 0.811111 (81.1111%)

Visual Representation

The diagram below illustrates 1/9 plus 7/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/90`
Mixed Number Form	`73/90`
Decimal Form	`0.811111`
Percentage	`81.1111%`

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Frequently Asked Questions

What is 1/9 plus 7/10 as a fraction?

1/9 + 7/10 in simplest fraction form is 73/90.

What is 1/9 plus 7/10 as a decimal?

1/9 + 7/10 converted to a decimal is 0.811111.

What is 1/9 plus 7/10 as a percentage?

1/9 + 7/10 expressed as a percentage is 81.1111%.

Does 1/9 plus 7/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.811111...) because the denominator contains prime factors other than 2 and 5.