What is 10/22 plus 9/13? (Answer: 164/143)

Exact Answer

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Problem: What is 10/22 plus 9/13?
Formula / Expression: 10/22 + 9/13
Final Answer: 1 21/143 (164/143)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 13 = 286.
Working: LCD(22, 13) = 286

Step 2: Convert to Equivalent Fractions with Common Denominator 286
Multiply the numerator and denominator of 10/22 by 13, and multiply the numerator and denominator of 9/13 by 22 so both fractions share the common base 286.
Working: 10 × 13/22 × 13 = 130/286 and 9 × 22/13 × 22 = 198/286

Step 3: Add the Numerators
Now add the numerators (130 + 198 = 328) and keep the common denominator 286 unchanged.
Working: 130 + 198/286 = 328/286

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 328 and 286, which is 2. Divide both the numerator and denominator by 2.
Working: 328 ÷ 2/286 ÷ 2 = 164/143

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (164) is greater than the denominator (143), divide 164 by 143: it goes in 1 whole time(s) with a remainder of 21, giving the mixed number 1 21/143.
Working: 164/143 = 1 21/143

Step 6: Decimal & Percentage Representation
Dividing the numerator 164 by denominator 143 produces a repeating decimal (approximately 1.146853, or 114.6853%).
Working: 164 ÷ 143 = 1.146853 (114.6853%)

Key Values:
- Simplified Fraction: 164/143
- Mixed Number Form: 1 21/143
- Decimal Value: 1.146853
- Percentage: 114.6853%

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10/22 + 9/13 = 164/143

Simplified Fraction

164/143

Mixed Number

1 21/143

Decimal Value

1.146853

Percentage

114.6853%

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Step-by-Step Solution: 10/22 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 13 = 286.

LCD(22, 13) = 286

Step 2

Convert to Equivalent Fractions with Common Denominator 286

Multiply the numerator and denominator of 10/22 by 13, and multiply the numerator and denominator of 9/13 by 22 so both fractions share the common base 286.

10 × 13/22 × 13 = 130/286 and 9 × 22/13 × 22 = 198/286

Step 3

Add the Numerators

Now add the numerators (130 + 198 = 328) and keep the common denominator 286 unchanged.

130 + 198/286 = 328/286

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 328 and 286, which is 2. Divide both the numerator and denominator by 2.

328 ÷ 2/286 ÷ 2 = 164/143

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (164) is greater than the denominator (143), divide 164 by 143: it goes in 1 whole time(s) with a remainder of 21, giving the mixed number 1 21/143.

164/143 = 121/143

Step 6

Decimal & Percentage Representation

Dividing the numerator 164 by denominator 143 produces a repeating decimal (approximately 1.146853, or 114.6853%).

164 ÷ 143 = 1.146853 (114.6853%)

Visual Representation

The diagram below illustrates 10/22 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`164/143`
Mixed Number Form	`1 21/143`
Decimal Form	`1.146853`
Percentage	`114.6853%`

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Frequently Asked Questions

What is 10/22 plus 9/13 as a fraction?

10/22 + 9/13 in simplest fraction form is 164/143 (or 1 21/143 as a mixed number).

What is 10/22 plus 9/13 as a decimal?

10/22 + 9/13 converted to a decimal is 1.146853.

What is 10/22 plus 9/13 as a percentage?

10/22 + 9/13 expressed as a percentage is 114.6853%.

How do you write 10/22 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 164/143 can be written as the mixed number 1 21/143.

Does 10/22 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.146853...) because the denominator contains prime factors other than 2 and 5.