What is 7/21 plus 8/22? (Answer: 23/33)

Exact Answer

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Problem: What is 7/21 plus 8/22?
Formula / Expression: 7/21 + 8/22
Final Answer: 23/33
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 462
Multiply the numerator and denominator of 7/21 by 22, and multiply the numerator and denominator of 8/22 by 21 so both fractions share the common base 462.
Working: 7 × 22/21 × 22 = 154/462 and 8 × 21/22 × 21 = 168/462

Step 3: Add the Numerators
Now add the numerators (154 + 168 = 322) and keep the common denominator 462 unchanged.
Working: 154 + 168/462 = 322/462

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 322 and 462, which is 14. Divide both the numerator and denominator by 14.
Working: 322 ÷ 14/462 ÷ 14 = 23/33

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 33 produces a repeating decimal (approximately 0.69697, or 69.697%).
Working: 23 ÷ 33 = 0.69697 (69.697%)

Key Values:
- Simplified Fraction: 23/33
- Mixed Number Form: 23/33
- Decimal Value: 0.69697
- Percentage: 69.697%

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Solved with FractionsCalc:
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7/21 + 8/22 = 23/33

Simplified Fraction

23/33

Mixed Number

Proper (23/33)

Decimal Value

0.69697

Percentage

69.697%

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Step-by-Step Solution: 7/21 + 8/22

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 22) = 462

Step 2

Convert to Equivalent Fractions with Common Denominator 462

Multiply the numerator and denominator of 7/21 by 22, and multiply the numerator and denominator of 8/22 by 21 so both fractions share the common base 462.

7 × 22/21 × 22 = 154/462 and 8 × 21/22 × 21 = 168/462

Step 3

Add the Numerators

Now add the numerators (154 + 168 = 322) and keep the common denominator 462 unchanged.

154 + 168/462 = 322/462

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 322 and 462, which is 14. Divide both the numerator and denominator by 14.

322 ÷ 14/462 ÷ 14 = 23/33

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 33 produces a repeating decimal (approximately 0.69697, or 69.697%).

23 ÷ 33 = 0.69697 (69.697%)

Visual Representation

The diagram below illustrates 7/21 plus 8/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/33`
Mixed Number Form	`23/33`
Decimal Form	`0.69697`
Percentage	`69.697%`

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Frequently Asked Questions

What is 7/21 plus 8/22 as a fraction?

7/21 + 8/22 in simplest fraction form is 23/33.

What is 7/21 plus 8/22 as a decimal?

7/21 + 8/22 converted to a decimal is 0.69697.

What is 7/21 plus 8/22 as a percentage?

7/21 + 8/22 expressed as a percentage is 69.697%.

Does 7/21 plus 8/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.69697...) because the denominator contains prime factors other than 2 and 5.