What is 10/23 plus 12/21? (Answer: 162/161)

Exact Answer

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Problem: What is 10/23 plus 12/21?
Formula / Expression: 10/23 + 12/21
Final Answer: 1 1/161 (162/161)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 21 = 483.
Working: LCD(23, 21) = 483

Step 2: Convert to Equivalent Fractions with Common Denominator 483
Multiply the numerator and denominator of 10/23 by 21, and multiply the numerator and denominator of 12/21 by 23 so both fractions share the common base 483.
Working: 10 × 21/23 × 21 = 210/483 and 12 × 23/21 × 23 = 276/483

Step 3: Add the Numerators
Now add the numerators (210 + 276 = 486) and keep the common denominator 483 unchanged.
Working: 210 + 276/483 = 486/483

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 486 and 483, which is 3. Divide both the numerator and denominator by 3.
Working: 486 ÷ 3/483 ÷ 3 = 162/161

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (162) is greater than the denominator (161), divide 162 by 161: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/161.
Working: 162/161 = 1 1/161

Step 6: Decimal & Percentage Representation
Dividing the numerator 162 by denominator 161 produces a repeating decimal (approximately 1.006211, or 100.6211%).
Working: 162 ÷ 161 = 1.006211 (100.6211%)

Key Values:
- Simplified Fraction: 162/161
- Mixed Number Form: 1 1/161
- Decimal Value: 1.006211
- Percentage: 100.6211%

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Solved with FractionsCalc:
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10/23 + 12/21 = 162/161

Simplified Fraction

162/161

Mixed Number

1 1/161

Decimal Value

1.006211

Percentage

100.6211%

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Step-by-Step Solution: 10/23 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 21 = 483.

LCD(23, 21) = 483

Step 2

Convert to Equivalent Fractions with Common Denominator 483

Multiply the numerator and denominator of 10/23 by 21, and multiply the numerator and denominator of 12/21 by 23 so both fractions share the common base 483.

10 × 21/23 × 21 = 210/483 and 12 × 23/21 × 23 = 276/483

Step 3

Add the Numerators

Now add the numerators (210 + 276 = 486) and keep the common denominator 483 unchanged.

210 + 276/483 = 486/483

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 486 and 483, which is 3. Divide both the numerator and denominator by 3.

486 ÷ 3/483 ÷ 3 = 162/161

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (162) is greater than the denominator (161), divide 162 by 161: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/161.

162/161 = 11/161

Step 6

Decimal & Percentage Representation

Dividing the numerator 162 by denominator 161 produces a repeating decimal (approximately 1.006211, or 100.6211%).

162 ÷ 161 = 1.006211 (100.6211%)

Visual Representation

The diagram below illustrates 10/23 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`162/161`
Mixed Number Form	`1 1/161`
Decimal Form	`1.006211`
Percentage	`100.6211%`

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Frequently Asked Questions

What is 10/23 plus 12/21 as a fraction?

10/23 + 12/21 in simplest fraction form is 162/161 (or 1 1/161 as a mixed number).

What is 10/23 plus 12/21 as a decimal?

10/23 + 12/21 converted to a decimal is 1.006211.

What is 10/23 plus 12/21 as a percentage?

10/23 + 12/21 expressed as a percentage is 100.6211%.

How do you write 10/23 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 162/161 can be written as the mixed number 1 1/161.

Does 10/23 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.006211...) because the denominator contains prime factors other than 2 and 5.