What is 7/10 plus 7/9? (Answer: 133/90)

Exact Answer

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Problem: What is 7/10 plus 7/9?
Formula / Expression: 7/10 + 7/9
Final Answer: 1 43/90 (133/90)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 9 = 90.
Working: LCD(10, 9) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 7/10 by 9, and multiply the numerator and denominator of 7/9 by 10 so both fractions share the common base 90.
Working: 7 × 9/10 × 9 = 63/90 and 7 × 10/9 × 10 = 70/90

Step 3: Add the Numerators
Now add the numerators (63 + 70 = 133) and keep the common denominator 90 unchanged.
Working: 63 + 70/90 = 133/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 133 and 90 is 1, confirming that 133/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 133/90

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (133) is greater than the denominator (90), divide 133 by 90: it goes in 1 whole time(s) with a remainder of 43, giving the mixed number 1 43/90.
Working: 133/90 = 1 43/90

Step 6: Decimal & Percentage Representation
Dividing the numerator 133 by denominator 90 produces a repeating decimal (approximately 1.477778, or 147.7778%).
Working: 133 ÷ 90 = 1.477778 (147.7778%)

Key Values:
- Simplified Fraction: 133/90
- Mixed Number Form: 1 43/90
- Decimal Value: 1.477778
- Percentage: 147.7778%

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Solved with FractionsCalc:
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7/10 + 7/9 = 133/90

Simplified Fraction

133/90

Mixed Number

1 43/90

Decimal Value

1.477778

Percentage

147.7778%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 9 = 90.

LCD(10, 9) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

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

7 × 9/10 × 9 = 63/90 and 7 × 10/9 × 10 = 70/90

Step 3

Add the Numerators

Now add the numerators (63 + 70 = 133) and keep the common denominator 90 unchanged.

63 + 70/90 = 133/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 133 and 90 is 1, confirming that 133/90 cannot be reduced further—it is already in its simplest irreducible form.

133/90

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (133) is greater than the denominator (90), divide 133 by 90: it goes in 1 whole time(s) with a remainder of 43, giving the mixed number 1 43/90.

133/90 = 143/90

Step 6

Decimal & Percentage Representation

Dividing the numerator 133 by denominator 90 produces a repeating decimal (approximately 1.477778, or 147.7778%).

133 ÷ 90 = 1.477778 (147.7778%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`133/90`
Mixed Number Form	`1 43/90`
Decimal Form	`1.477778`
Percentage	`147.7778%`

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Frequently Asked Questions

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

7/10 + 7/9 in simplest fraction form is 133/90 (or 1 43/90 as a mixed number).

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

7/10 + 7/9 converted to a decimal is 1.477778.

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

7/10 + 7/9 expressed as a percentage is 147.7778%.

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

Because the numerator is greater than the denominator, the improper fraction 133/90 can be written as the mixed number 1 43/90.

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

It results in a repeating decimal (approximately 1.477778...) because the denominator contains prime factors other than 2 and 5.