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

Exact Answer

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

Step 1: Find the Least Common Denominator (LCD)
Notice that 42 is an exact multiple of 21 (21 × 2 = 42). The Least Common Denominator (LCD) is simply 42, meaning we only need to scale one fraction.
Working: LCD(21, 42) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 10/21 by 2, and multiply the numerator and denominator of 20/42 by 1 so both fractions share the common base 42.
Working: 10 × 2/21 × 2 = 20/42 and 20 × 1/42 × 1 = 20/42

Step 3: Add the Numerators
Now add the numerators (20 + 20 = 40) and keep the common denominator 42 unchanged.
Working: 20 + 20/42 = 40/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 40 and 42, which is 2. Divide both the numerator and denominator by 2.
Working: 40 ÷ 2/42 ÷ 2 = 20/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 20 by denominator 21 produces a repeating decimal (approximately 0.952381, or 95.2381%).
Working: 20 ÷ 21 = 0.952381 (95.2381%)

Key Values:
- Simplified Fraction: 20/21
- Mixed Number Form: 20/21
- Decimal Value: 0.952381
- Percentage: 95.2381%

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

Simplified Fraction

20/21

Mixed Number

Proper (20/21)

Decimal Value

0.952381

Percentage

95.2381%

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Step-by-Step Solution: 10/21 + 20/42

Step 1

Find the Least Common Denominator (LCD)

Notice that 42 is an exact multiple of 21 (21 × 2 = 42). The Least Common Denominator (LCD) is simply 42, meaning we only need to scale one fraction.

LCD(21, 42) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 10/21 by 2, and multiply the numerator and denominator of 20/42 by 1 so both fractions share the common base 42.

10 × 2/21 × 2 = 20/42 and 20 × 1/42 × 1 = 20/42

Step 3

Add the Numerators

Now add the numerators (20 + 20 = 40) and keep the common denominator 42 unchanged.

20 + 20/42 = 40/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 40 and 42, which is 2. Divide both the numerator and denominator by 2.

40 ÷ 2/42 ÷ 2 = 20/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 20 by denominator 21 produces a repeating decimal (approximately 0.952381, or 95.2381%).

20 ÷ 21 = 0.952381 (95.2381%)

Visual Representation

The diagram below illustrates 10/21 plus 20/42 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`20/21`
Mixed Number Form	`20/21`
Decimal Form	`0.952381`
Percentage	`95.2381%`

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Frequently Asked Questions

What is 10/21 plus 20/42 as a fraction?

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

What is 10/21 plus 20/42 as a decimal?

10/21 + 20/42 converted to a decimal is 0.952381.

What is 10/21 plus 20/42 as a percentage?

10/21 + 20/42 expressed as a percentage is 95.2381%.

Does 10/21 plus 20/42 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.952381...) because the denominator contains prime factors other than 2 and 5.