What is 10/42 plus 6/21? (Answer: 11/21)

Exact Answer

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Problem: What is 10/42 plus 6/21?
Formula / Expression: 10/42 + 6/21
Final Answer: 11/21
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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(42, 21) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 10/42 by 1, and multiply the numerator and denominator of 6/21 by 2 so both fractions share the common base 42.
Working: 10 × 1/42 × 1 = 10/42 and 6 × 2/21 × 2 = 12/42

Step 3: Add the Numerators
Now add the numerators (10 + 12 = 22) and keep the common denominator 42 unchanged.
Working: 10 + 12/42 = 22/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 22 and 42, which is 2. Divide both the numerator and denominator by 2.
Working: 22 ÷ 2/42 ÷ 2 = 11/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 21 produces a repeating decimal (approximately 0.52381, or 52.381%).
Working: 11 ÷ 21 = 0.52381 (52.381%)

Key Values:
- Simplified Fraction: 11/21
- Mixed Number Form: 11/21
- Decimal Value: 0.52381
- Percentage: 52.381%

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Solved with FractionsCalc:
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10/42 + 6/21 = 11/21

Simplified Fraction

11/21

Mixed Number

Proper (11/21)

Decimal Value

0.52381

Percentage

52.381%

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Step-by-Step Solution: 10/42 + 6/21

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(42, 21) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 10/42 by 1, and multiply the numerator and denominator of 6/21 by 2 so both fractions share the common base 42.

10 × 1/42 × 1 = 10/42 and 6 × 2/21 × 2 = 12/42

Step 3

Add the Numerators

Now add the numerators (10 + 12 = 22) and keep the common denominator 42 unchanged.

10 + 12/42 = 22/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 22 and 42, which is 2. Divide both the numerator and denominator by 2.

22 ÷ 2/42 ÷ 2 = 11/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 21 produces a repeating decimal (approximately 0.52381, or 52.381%).

11 ÷ 21 = 0.52381 (52.381%)

Visual Representation

The diagram below illustrates 10/42 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/21`
Mixed Number Form	`11/21`
Decimal Form	`0.52381`
Percentage	`52.381%`

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Frequently Asked Questions

What is 10/42 plus 6/21 as a fraction?

10/42 + 6/21 in simplest fraction form is 11/21.

What is 10/42 plus 6/21 as a decimal?

10/42 + 6/21 converted to a decimal is 0.52381.

What is 10/42 plus 6/21 as a percentage?

10/42 + 6/21 expressed as a percentage is 52.381%.

Does 10/42 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.52381...) because the denominator contains prime factors other than 2 and 5.