What is 22/43 plus 12/21? (Answer: 326/301)

Exact Answer

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Problem: What is 22/43 plus 12/21?
Formula / Expression: 22/43 + 12/21
Final Answer: 1 25/301 (326/301)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 43 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 43 × 21 = 903.
Working: LCD(43, 21) = 903

Step 2: Convert to Equivalent Fractions with Common Denominator 903
Multiply the numerator and denominator of 22/43 by 21, and multiply the numerator and denominator of 12/21 by 43 so both fractions share the common base 903.
Working: 22 × 21/43 × 21 = 462/903 and 12 × 43/21 × 43 = 516/903

Step 3: Add the Numerators
Now add the numerators (462 + 516 = 978) and keep the common denominator 903 unchanged.
Working: 462 + 516/903 = 978/903

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 978 and 903, which is 3. Divide both the numerator and denominator by 3.
Working: 978 ÷ 3/903 ÷ 3 = 326/301

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (326) is greater than the denominator (301), divide 326 by 301: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/301.
Working: 326/301 = 1 25/301

Step 6: Decimal & Percentage Representation
Dividing the numerator 326 by denominator 301 produces a repeating decimal (approximately 1.083056, or 108.3056%).
Working: 326 ÷ 301 = 1.083056 (108.3056%)

Key Values:
- Simplified Fraction: 326/301
- Mixed Number Form: 1 25/301
- Decimal Value: 1.083056
- Percentage: 108.3056%

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Solved with FractionsCalc:
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22/43 + 12/21 = 326/301

Simplified Fraction

326/301

Mixed Number

1 25/301

Decimal Value

1.083056

Percentage

108.3056%

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Step-by-Step Solution: 22/43 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 43 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 43 × 21 = 903.

LCD(43, 21) = 903

Step 2

Convert to Equivalent Fractions with Common Denominator 903

Multiply the numerator and denominator of 22/43 by 21, and multiply the numerator and denominator of 12/21 by 43 so both fractions share the common base 903.

22 × 21/43 × 21 = 462/903 and 12 × 43/21 × 43 = 516/903

Step 3

Add the Numerators

Now add the numerators (462 + 516 = 978) and keep the common denominator 903 unchanged.

462 + 516/903 = 978/903

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 978 and 903, which is 3. Divide both the numerator and denominator by 3.

978 ÷ 3/903 ÷ 3 = 326/301

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (326) is greater than the denominator (301), divide 326 by 301: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/301.

326/301 = 125/301

Step 6

Decimal & Percentage Representation

Dividing the numerator 326 by denominator 301 produces a repeating decimal (approximately 1.083056, or 108.3056%).

326 ÷ 301 = 1.083056 (108.3056%)

Visual Representation

The diagram below illustrates 22/43 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`326/301`
Mixed Number Form	`1 25/301`
Decimal Form	`1.083056`
Percentage	`108.3056%`

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Frequently Asked Questions

What is 22/43 plus 12/21 as a fraction?

22/43 + 12/21 in simplest fraction form is 326/301 (or 1 25/301 as a mixed number).

What is 22/43 plus 12/21 as a decimal?

22/43 + 12/21 converted to a decimal is 1.083056.

What is 22/43 plus 12/21 as a percentage?

22/43 + 12/21 expressed as a percentage is 108.3056%.

How do you write 22/43 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 326/301 can be written as the mixed number 1 25/301.

Does 22/43 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.083056...) because the denominator contains prime factors other than 2 and 5.