What is 10/21 plus 10/20? (Answer: 41/42)

Exact Answer

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Problem: What is 10/21 plus 10/20?
Formula / Expression: 10/21 + 10/20
Final Answer: 41/42
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 20 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 20 = 420.
Working: LCD(21, 20) = 420

Step 2: Convert to Equivalent Fractions with Common Denominator 420
Multiply the numerator and denominator of 10/21 by 20, and multiply the numerator and denominator of 10/20 by 21 so both fractions share the common base 420.
Working: 10 × 20/21 × 20 = 200/420 and 10 × 21/20 × 21 = 210/420

Step 3: Add the Numerators
Now add the numerators (200 + 210 = 410) and keep the common denominator 420 unchanged.
Working: 200 + 210/420 = 410/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 410 and 420, which is 10. Divide both the numerator and denominator by 10.
Working: 410 ÷ 10/420 ÷ 10 = 41/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 42 produces a repeating decimal (approximately 0.97619, or 97.619%).
Working: 41 ÷ 42 = 0.97619 (97.619%)

Key Values:
- Simplified Fraction: 41/42
- Mixed Number Form: 41/42
- Decimal Value: 0.97619
- Percentage: 97.619%

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Solved with FractionsCalc:
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10/21 + 10/20 = 41/42

Simplified Fraction

41/42

Mixed Number

Proper (41/42)

Decimal Value

0.97619

Percentage

97.619%

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Step-by-Step Solution: 10/21 + 10/20

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 20 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 20 = 420.

LCD(21, 20) = 420

Step 2

Convert to Equivalent Fractions with Common Denominator 420

Multiply the numerator and denominator of 10/21 by 20, and multiply the numerator and denominator of 10/20 by 21 so both fractions share the common base 420.

10 × 20/21 × 20 = 200/420 and 10 × 21/20 × 21 = 210/420

Step 3

Add the Numerators

Now add the numerators (200 + 210 = 410) and keep the common denominator 420 unchanged.

200 + 210/420 = 410/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 410 and 420, which is 10. Divide both the numerator and denominator by 10.

410 ÷ 10/420 ÷ 10 = 41/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 42 produces a repeating decimal (approximately 0.97619, or 97.619%).

41 ÷ 42 = 0.97619 (97.619%)

Visual Representation

The diagram below illustrates 10/21 plus 10/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/42`
Mixed Number Form	`41/42`
Decimal Form	`0.97619`
Percentage	`97.619%`

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Frequently Asked Questions

What is 10/21 plus 10/20 as a fraction?

10/21 + 10/20 in simplest fraction form is 41/42.

What is 10/21 plus 10/20 as a decimal?

10/21 + 10/20 converted to a decimal is 0.97619.

What is 10/21 plus 10/20 as a percentage?

10/21 + 10/20 expressed as a percentage is 97.619%.

Does 10/21 plus 10/20 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.97619...) because the denominator contains prime factors other than 2 and 5.