What is 10/22 plus 12/21? (Answer: 79/77)

Exact Answer

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Problem: What is 10/22 plus 12/21?
Formula / Expression: 10/22 + 12/21
Final Answer: 1 2/77 (79/77)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 21 = 462.
Working: LCD(22, 21) = 462

Step 2: Convert to Equivalent Fractions with Common Denominator 462
Multiply the numerator and denominator of 10/22 by 21, and multiply the numerator and denominator of 12/21 by 22 so both fractions share the common base 462.
Working: 10 × 21/22 × 21 = 210/462 and 12 × 22/21 × 22 = 264/462

Step 3: Add the Numerators
Now add the numerators (210 + 264 = 474) and keep the common denominator 462 unchanged.
Working: 210 + 264/462 = 474/462

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 474 and 462, which is 6. Divide both the numerator and denominator by 6.
Working: 474 ÷ 6/462 ÷ 6 = 79/77

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (79) is greater than the denominator (77), divide 79 by 77: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/77.
Working: 79/77 = 1 2/77

Step 6: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 77 produces a repeating decimal (approximately 1.025974, or 102.5974%).
Working: 79 ÷ 77 = 1.025974 (102.5974%)

Key Values:
- Simplified Fraction: 79/77
- Mixed Number Form: 1 2/77
- Decimal Value: 1.025974
- Percentage: 102.5974%

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Solved with FractionsCalc:
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10/22 + 12/21 = 79/77

Simplified Fraction

79/77

Mixed Number

1 2/77

Decimal Value

1.025974

Percentage

102.5974%

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Step-by-Step Solution: 10/22 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 21 = 462.

LCD(22, 21) = 462

Step 2

Convert to Equivalent Fractions with Common Denominator 462

Multiply the numerator and denominator of 10/22 by 21, and multiply the numerator and denominator of 12/21 by 22 so both fractions share the common base 462.

10 × 21/22 × 21 = 210/462 and 12 × 22/21 × 22 = 264/462

Step 3

Add the Numerators

Now add the numerators (210 + 264 = 474) and keep the common denominator 462 unchanged.

210 + 264/462 = 474/462

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 474 and 462, which is 6. Divide both the numerator and denominator by 6.

474 ÷ 6/462 ÷ 6 = 79/77

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (79) is greater than the denominator (77), divide 79 by 77: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/77.

79/77 = 12/77

Step 6

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 77 produces a repeating decimal (approximately 1.025974, or 102.5974%).

79 ÷ 77 = 1.025974 (102.5974%)

Visual Representation

The diagram below illustrates 10/22 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/77`
Mixed Number Form	`1 2/77`
Decimal Form	`1.025974`
Percentage	`102.5974%`

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Frequently Asked Questions

What is 10/22 plus 12/21 as a fraction?

10/22 + 12/21 in simplest fraction form is 79/77 (or 1 2/77 as a mixed number).

What is 10/22 plus 12/21 as a decimal?

10/22 + 12/21 converted to a decimal is 1.025974.

What is 10/22 plus 12/21 as a percentage?

10/22 + 12/21 expressed as a percentage is 102.5974%.

How do you write 10/22 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 79/77 can be written as the mixed number 1 2/77.

Does 10/22 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.025974...) because the denominator contains prime factors other than 2 and 5.