What is 18/28 plus 9/13? (Answer: 243/182)

Exact Answer

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Problem: What is 18/28 plus 9/13?
Formula / Expression: 18/28 + 9/13
Final Answer: 1 61/182 (243/182)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 28 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 28 × 13 = 364.
Working: LCD(28, 13) = 364

Step 2: Convert to Equivalent Fractions with Common Denominator 364
Multiply the numerator and denominator of 18/28 by 13, and multiply the numerator and denominator of 9/13 by 28 so both fractions share the common base 364.
Working: 18 × 13/28 × 13 = 234/364 and 9 × 28/13 × 28 = 252/364

Step 3: Add the Numerators
Now add the numerators (234 + 252 = 486) and keep the common denominator 364 unchanged.
Working: 234 + 252/364 = 486/364

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 486 and 364, which is 2. Divide both the numerator and denominator by 2.
Working: 486 ÷ 2/364 ÷ 2 = 243/182

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (243) is greater than the denominator (182), divide 243 by 182: it goes in 1 whole time(s) with a remainder of 61, giving the mixed number 1 61/182.
Working: 243/182 = 1 61/182

Step 6: Decimal & Percentage Representation
Dividing the numerator 243 by denominator 182 produces a repeating decimal (approximately 1.335165, or 133.5165%).
Working: 243 ÷ 182 = 1.335165 (133.5165%)

Key Values:
- Simplified Fraction: 243/182
- Mixed Number Form: 1 61/182
- Decimal Value: 1.335165
- Percentage: 133.5165%

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18/28 + 9/13 = 243/182

Simplified Fraction

243/182

Mixed Number

1 61/182

Decimal Value

1.335165

Percentage

133.5165%

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Step-by-Step Solution: 18/28 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 28 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 28 × 13 = 364.

LCD(28, 13) = 364

Step 2

Convert to Equivalent Fractions with Common Denominator 364

Multiply the numerator and denominator of 18/28 by 13, and multiply the numerator and denominator of 9/13 by 28 so both fractions share the common base 364.

18 × 13/28 × 13 = 234/364 and 9 × 28/13 × 28 = 252/364

Step 3

Add the Numerators

Now add the numerators (234 + 252 = 486) and keep the common denominator 364 unchanged.

234 + 252/364 = 486/364

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 486 and 364, which is 2. Divide both the numerator and denominator by 2.

486 ÷ 2/364 ÷ 2 = 243/182

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (243) is greater than the denominator (182), divide 243 by 182: it goes in 1 whole time(s) with a remainder of 61, giving the mixed number 1 61/182.

243/182 = 161/182

Step 6

Decimal & Percentage Representation

Dividing the numerator 243 by denominator 182 produces a repeating decimal (approximately 1.335165, or 133.5165%).

243 ÷ 182 = 1.335165 (133.5165%)

Visual Representation

The diagram below illustrates 18/28 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`243/182`
Mixed Number Form	`1 61/182`
Decimal Form	`1.335165`
Percentage	`133.5165%`

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Frequently Asked Questions

What is 18/28 plus 9/13 as a fraction?

18/28 + 9/13 in simplest fraction form is 243/182 (or 1 61/182 as a mixed number).

What is 18/28 plus 9/13 as a decimal?

18/28 + 9/13 converted to a decimal is 1.335165.

What is 18/28 plus 9/13 as a percentage?

18/28 + 9/13 expressed as a percentage is 133.5165%.

How do you write 18/28 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 243/182 can be written as the mixed number 1 61/182.

Does 18/28 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.335165...) because the denominator contains prime factors other than 2 and 5.