What is 7/9 plus 9/10? (Answer: 151/90)

Exact Answer

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Problem: What is 7/9 plus 9/10?
Formula / Expression: 7/9 + 9/10
Final Answer: 1 61/90 (151/90)
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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 7/9 by 10, and multiply the numerator and denominator of 9/10 by 9 so both fractions share the common base 90.
Working: 7 × 10/9 × 10 = 70/90 and 9 × 9/10 × 9 = 81/90

Step 3: Add the Numerators
Now add the numerators (70 + 81 = 151) and keep the common denominator 90 unchanged.
Working: 70 + 81/90 = 151/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 151 and 90 is 1, confirming that 151/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 151/90

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (151) is greater than the denominator (90), divide 151 by 90: it goes in 1 whole time(s) with a remainder of 61, giving the mixed number 1 61/90.
Working: 151/90 = 1 61/90

Step 6: Decimal & Percentage Representation
Dividing the numerator 151 by denominator 90 produces a repeating decimal (approximately 1.677778, or 167.7778%).
Working: 151 ÷ 90 = 1.677778 (167.7778%)

Key Values:
- Simplified Fraction: 151/90
- Mixed Number Form: 1 61/90
- Decimal Value: 1.677778
- Percentage: 167.7778%

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Solved with FractionsCalc:
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7/9 + 9/10 = 151/90

Simplified Fraction

151/90

Mixed Number

1 61/90

Decimal Value

1.677778

Percentage

167.7778%

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Step-by-Step Solution: 7/9 + 9/10

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 7/9 by 10, and multiply the numerator and denominator of 9/10 by 9 so both fractions share the common base 90.

7 × 10/9 × 10 = 70/90 and 9 × 9/10 × 9 = 81/90

Step 3

Add the Numerators

Now add the numerators (70 + 81 = 151) and keep the common denominator 90 unchanged.

70 + 81/90 = 151/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 151 and 90 is 1, confirming that 151/90 cannot be reduced further—it is already in its simplest irreducible form.

151/90

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (151) is greater than the denominator (90), divide 151 by 90: it goes in 1 whole time(s) with a remainder of 61, giving the mixed number 1 61/90.

151/90 = 161/90

Step 6

Decimal & Percentage Representation

Dividing the numerator 151 by denominator 90 produces a repeating decimal (approximately 1.677778, or 167.7778%).

151 ÷ 90 = 1.677778 (167.7778%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`151/90`
Mixed Number Form	`1 61/90`
Decimal Form	`1.677778`
Percentage	`167.7778%`

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Frequently Asked Questions

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

7/9 + 9/10 in simplest fraction form is 151/90 (or 1 61/90 as a mixed number).

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

7/9 + 9/10 converted to a decimal is 1.677778.

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

7/9 + 9/10 expressed as a percentage is 167.7778%.

How do you write 7/9 plus 9/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 151/90 can be written as the mixed number 1 61/90.

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

It results in a repeating decimal (approximately 1.677778...) because the denominator contains prime factors other than 2 and 5.