What is 1/9 plus 7/8? (Answer: 71/72)

Exact Answer

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Problem: What is 1/9 plus 7/8?
Formula / Expression: 1/9 + 7/8
Final Answer: 71/72
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 8 = 72.
Working: LCD(9, 8) = 72

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 1/9 by 8, and multiply the numerator and denominator of 7/8 by 9 so both fractions share the common base 72.
Working: 1 × 8/9 × 8 = 8/72 and 7 × 9/8 × 9 = 63/72

Step 3: Add the Numerators
Now add the numerators (8 + 63 = 71) and keep the common denominator 72 unchanged.
Working: 8 + 63/72 = 71/72

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 72 is 1, confirming that 71/72 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 72 produces a repeating decimal (approximately 0.986111, or 98.6111%).
Working: 71 ÷ 72 = 0.986111 (98.6111%)

Key Values:
- Simplified Fraction: 71/72
- Mixed Number Form: 71/72
- Decimal Value: 0.986111
- Percentage: 98.6111%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-9-plus-7-8/
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1/9 + 7/8 = 71/72

Simplified Fraction

71/72

Mixed Number

Proper (71/72)

Decimal Value

0.986111

Percentage

98.6111%

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Step-by-Step Solution: 1/9 + 7/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 8 = 72.

LCD(9, 8) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 1/9 by 8, and multiply the numerator and denominator of 7/8 by 9 so both fractions share the common base 72.

1 × 8/9 × 8 = 8/72 and 7 × 9/8 × 9 = 63/72

Step 3

Add the Numerators

Now add the numerators (8 + 63 = 71) and keep the common denominator 72 unchanged.

8 + 63/72 = 71/72

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 72 is 1, confirming that 71/72 cannot be reduced further—it is already in its simplest irreducible form.

71/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 72 produces a repeating decimal (approximately 0.986111, or 98.6111%).

71 ÷ 72 = 0.986111 (98.6111%)

Visual Representation

The diagram below illustrates 1/9 plus 7/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/72`
Mixed Number Form	`71/72`
Decimal Form	`0.986111`
Percentage	`98.6111%`

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Frequently Asked Questions

What is 1/9 plus 7/8 as a fraction?

1/9 + 7/8 in simplest fraction form is 71/72.

What is 1/9 plus 7/8 as a decimal?

1/9 + 7/8 converted to a decimal is 0.986111.

What is 1/9 plus 7/8 as a percentage?

1/9 + 7/8 expressed as a percentage is 98.6111%.

Does 1/9 plus 7/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.986111...) because the denominator contains prime factors other than 2 and 5.