What is 23/44 plus 12/21? (Answer: 337/308)

Exact Answer

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Problem: What is 23/44 plus 12/21?
Formula / Expression: 23/44 + 12/21
Final Answer: 1 29/308 (337/308)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 44 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 44 × 21 = 924.
Working: LCD(44, 21) = 924

Step 2: Convert to Equivalent Fractions with Common Denominator 924
Multiply the numerator and denominator of 23/44 by 21, and multiply the numerator and denominator of 12/21 by 44 so both fractions share the common base 924.
Working: 23 × 21/44 × 21 = 483/924 and 12 × 44/21 × 44 = 528/924

Step 3: Add the Numerators
Now add the numerators (483 + 528 = 1011) and keep the common denominator 924 unchanged.
Working: 483 + 528/924 = 1011/924

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 1011 and 924, which is 3. Divide both the numerator and denominator by 3.
Working: 1011 ÷ 3/924 ÷ 3 = 337/308

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (337) is greater than the denominator (308), divide 337 by 308: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/308.
Working: 337/308 = 1 29/308

Step 6: Decimal & Percentage Representation
Dividing the numerator 337 by denominator 308 produces a repeating decimal (approximately 1.094156, or 109.4156%).
Working: 337 ÷ 308 = 1.094156 (109.4156%)

Key Values:
- Simplified Fraction: 337/308
- Mixed Number Form: 1 29/308
- Decimal Value: 1.094156
- Percentage: 109.4156%

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23/44 + 12/21 = 337/308

Simplified Fraction

337/308

Mixed Number

1 29/308

Decimal Value

1.094156

Percentage

109.4156%

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Step-by-Step Solution: 23/44 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 44 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 44 × 21 = 924.

LCD(44, 21) = 924

Step 2

Convert to Equivalent Fractions with Common Denominator 924

Multiply the numerator and denominator of 23/44 by 21, and multiply the numerator and denominator of 12/21 by 44 so both fractions share the common base 924.

23 × 21/44 × 21 = 483/924 and 12 × 44/21 × 44 = 528/924

Step 3

Add the Numerators

Now add the numerators (483 + 528 = 1011) and keep the common denominator 924 unchanged.

483 + 528/924 = 1011/924

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 1011 and 924, which is 3. Divide both the numerator and denominator by 3.

1011 ÷ 3/924 ÷ 3 = 337/308

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (337) is greater than the denominator (308), divide 337 by 308: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/308.

337/308 = 129/308

Step 6

Decimal & Percentage Representation

Dividing the numerator 337 by denominator 308 produces a repeating decimal (approximately 1.094156, or 109.4156%).

337 ÷ 308 = 1.094156 (109.4156%)

Visual Representation

The diagram below illustrates 23/44 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`337/308`
Mixed Number Form	`1 29/308`
Decimal Form	`1.094156`
Percentage	`109.4156%`

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Frequently Asked Questions

What is 23/44 plus 12/21 as a fraction?

23/44 + 12/21 in simplest fraction form is 337/308 (or 1 29/308 as a mixed number).

What is 23/44 plus 12/21 as a decimal?

23/44 + 12/21 converted to a decimal is 1.094156.

What is 23/44 plus 12/21 as a percentage?

23/44 + 12/21 expressed as a percentage is 109.4156%.

How do you write 23/44 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 337/308 can be written as the mixed number 1 29/308.

Does 23/44 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.094156...) because the denominator contains prime factors other than 2 and 5.