What is 4/42 plus 11/21? (Answer: 13/21)

Exact Answer

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Problem: What is 4/42 plus 11/21?
Formula / Expression: 4/42 + 11/21
Final Answer: 13/21
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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 4/42 by 1, and multiply the numerator and denominator of 11/21 by 2 so both fractions share the common base 42.
Working: 4 × 1/42 × 1 = 4/42 and 11 × 2/21 × 2 = 22/42

Step 3: Add the Numerators
Now add the numerators (4 + 22 = 26) and keep the common denominator 42 unchanged.
Working: 4 + 22/42 = 26/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 26 and 42, which is 2. Divide both the numerator and denominator by 2.
Working: 26 ÷ 2/42 ÷ 2 = 13/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 21 produces a repeating decimal (approximately 0.619048, or 61.9048%).
Working: 13 ÷ 21 = 0.619048 (61.9048%)

Key Values:
- Simplified Fraction: 13/21
- Mixed Number Form: 13/21
- Decimal Value: 0.619048
- Percentage: 61.9048%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-42-plus-11-21/
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4/42 + 11/21 = 13/21

Simplified Fraction

13/21

Mixed Number

Proper (13/21)

Decimal Value

0.619048

Percentage

61.9048%

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Step-by-Step Solution: 4/42 + 11/21

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 4/42 by 1, and multiply the numerator and denominator of 11/21 by 2 so both fractions share the common base 42.

4 × 1/42 × 1 = 4/42 and 11 × 2/21 × 2 = 22/42

Step 3

Add the Numerators

Now add the numerators (4 + 22 = 26) and keep the common denominator 42 unchanged.

4 + 22/42 = 26/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 26 and 42, which is 2. Divide both the numerator and denominator by 2.

26 ÷ 2/42 ÷ 2 = 13/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 21 produces a repeating decimal (approximately 0.619048, or 61.9048%).

13 ÷ 21 = 0.619048 (61.9048%)

Visual Representation

The diagram below illustrates 4/42 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/21`
Mixed Number Form	`13/21`
Decimal Form	`0.619048`
Percentage	`61.9048%`

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Frequently Asked Questions

What is 4/42 plus 11/21 as a fraction?

4/42 + 11/21 in simplest fraction form is 13/21.

What is 4/42 plus 11/21 as a decimal?

4/42 + 11/21 converted to a decimal is 0.619048.

What is 4/42 plus 11/21 as a percentage?

4/42 + 11/21 expressed as a percentage is 61.9048%.

Does 4/42 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.619048...) because the denominator contains prime factors other than 2 and 5.