What is 2/4 plus 11/21? (Answer: 43/42)

Exact Answer

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Problem: What is 2/4 plus 11/21?
Formula / Expression: 2/4 + 11/21
Final Answer: 1 1/42 (43/42)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 4 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 21 = 84.
Working: LCD(4, 21) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 2/4 by 21, and multiply the numerator and denominator of 11/21 by 4 so both fractions share the common base 84.
Working: 2 × 21/4 × 21 = 42/84 and 11 × 4/21 × 4 = 44/84

Step 3: Add the Numerators
Now add the numerators (42 + 44 = 86) and keep the common denominator 84 unchanged.
Working: 42 + 44/84 = 86/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 86 and 84, which is 2. Divide both the numerator and denominator by 2.
Working: 86 ÷ 2/84 ÷ 2 = 43/42

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (43) is greater than the denominator (42), divide 43 by 42: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/42.
Working: 43/42 = 1 1/42

Step 6: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 42 produces a repeating decimal (approximately 1.02381, or 102.381%).
Working: 43 ÷ 42 = 1.02381 (102.381%)

Key Values:
- Simplified Fraction: 43/42
- Mixed Number Form: 1 1/42
- Decimal Value: 1.02381
- Percentage: 102.381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-4-plus-11-21/
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2/4 + 11/21 = 43/42

Simplified Fraction

43/42

Mixed Number

1 1/42

Decimal Value

1.02381

Percentage

102.381%

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Step-by-Step Solution: 2/4 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 4 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 21 = 84.

LCD(4, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 2/4 by 21, and multiply the numerator and denominator of 11/21 by 4 so both fractions share the common base 84.

2 × 21/4 × 21 = 42/84 and 11 × 4/21 × 4 = 44/84

Step 3

Add the Numerators

Now add the numerators (42 + 44 = 86) and keep the common denominator 84 unchanged.

42 + 44/84 = 86/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 86 and 84, which is 2. Divide both the numerator and denominator by 2.

86 ÷ 2/84 ÷ 2 = 43/42

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (43) is greater than the denominator (42), divide 43 by 42: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/42.

43/42 = 11/42

Step 6

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 42 produces a repeating decimal (approximately 1.02381, or 102.381%).

43 ÷ 42 = 1.02381 (102.381%)

Visual Representation

The diagram below illustrates 2/4 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/42`
Mixed Number Form	`1 1/42`
Decimal Form	`1.02381`
Percentage	`102.381%`

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Frequently Asked Questions

What is 2/4 plus 11/21 as a fraction?

2/4 + 11/21 in simplest fraction form is 43/42 (or 1 1/42 as a mixed number).

What is 2/4 plus 11/21 as a decimal?

2/4 + 11/21 converted to a decimal is 1.02381.

What is 2/4 plus 11/21 as a percentage?

2/4 + 11/21 expressed as a percentage is 102.381%.

How do you write 2/4 plus 11/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 43/42 can be written as the mixed number 1 1/42.

Does 2/4 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.02381...) because the denominator contains prime factors other than 2 and 5.