What is 22/48 plus 9/13? (Answer: 359/312)

Exact Answer

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Problem: What is 22/48 plus 9/13?
Formula / Expression: 22/48 + 9/13
Final Answer: 1 47/312 (359/312)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 48 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 48 × 13 = 624.
Working: LCD(48, 13) = 624

Step 2: Convert to Equivalent Fractions with Common Denominator 624
Multiply the numerator and denominator of 22/48 by 13, and multiply the numerator and denominator of 9/13 by 48 so both fractions share the common base 624.
Working: 22 × 13/48 × 13 = 286/624 and 9 × 48/13 × 48 = 432/624

Step 3: Add the Numerators
Now add the numerators (286 + 432 = 718) and keep the common denominator 624 unchanged.
Working: 286 + 432/624 = 718/624

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 718 and 624, which is 2. Divide both the numerator and denominator by 2.
Working: 718 ÷ 2/624 ÷ 2 = 359/312

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (359) is greater than the denominator (312), divide 359 by 312: it goes in 1 whole time(s) with a remainder of 47, giving the mixed number 1 47/312.
Working: 359/312 = 1 47/312

Step 6: Decimal & Percentage Representation
Dividing the numerator 359 by denominator 312 produces a repeating decimal (approximately 1.150641, or 115.0641%).
Working: 359 ÷ 312 = 1.150641 (115.0641%)

Key Values:
- Simplified Fraction: 359/312
- Mixed Number Form: 1 47/312
- Decimal Value: 1.150641
- Percentage: 115.0641%

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Solved with FractionsCalc:
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22/48 + 9/13 = 359/312

Simplified Fraction

359/312

Mixed Number

1 47/312

Decimal Value

1.150641

Percentage

115.0641%

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Step-by-Step Solution: 22/48 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 48 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 48 × 13 = 624.

LCD(48, 13) = 624

Step 2

Convert to Equivalent Fractions with Common Denominator 624

Multiply the numerator and denominator of 22/48 by 13, and multiply the numerator and denominator of 9/13 by 48 so both fractions share the common base 624.

22 × 13/48 × 13 = 286/624 and 9 × 48/13 × 48 = 432/624

Step 3

Add the Numerators

Now add the numerators (286 + 432 = 718) and keep the common denominator 624 unchanged.

286 + 432/624 = 718/624

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 718 and 624, which is 2. Divide both the numerator and denominator by 2.

718 ÷ 2/624 ÷ 2 = 359/312

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (359) is greater than the denominator (312), divide 359 by 312: it goes in 1 whole time(s) with a remainder of 47, giving the mixed number 1 47/312.

359/312 = 147/312

Step 6

Decimal & Percentage Representation

Dividing the numerator 359 by denominator 312 produces a repeating decimal (approximately 1.150641, or 115.0641%).

359 ÷ 312 = 1.150641 (115.0641%)

Visual Representation

The diagram below illustrates 22/48 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`359/312`
Mixed Number Form	`1 47/312`
Decimal Form	`1.150641`
Percentage	`115.0641%`

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Frequently Asked Questions

What is 22/48 plus 9/13 as a fraction?

22/48 + 9/13 in simplest fraction form is 359/312 (or 1 47/312 as a mixed number).

What is 22/48 plus 9/13 as a decimal?

22/48 + 9/13 converted to a decimal is 1.150641.

What is 22/48 plus 9/13 as a percentage?

22/48 + 9/13 expressed as a percentage is 115.0641%.

How do you write 22/48 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 359/312 can be written as the mixed number 1 47/312.

Does 22/48 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.150641...) because the denominator contains prime factors other than 2 and 5.