What is 2/21 plus 3/24? (Answer: 37/168)

Exact Answer

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Problem: What is 2/21 plus 3/24?
Formula / Expression: 2/21 + 3/24
Final Answer: 37/168
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 24 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 21 × 24 = 504, keeping the calculation simpler).
Working: LCD(21, 24) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 2/21 by 8, and multiply the numerator and denominator of 3/24 by 7 so both fractions share the common base 168.
Working: 2 × 8/21 × 8 = 16/168 and 3 × 7/24 × 7 = 21/168

Step 3: Add the Numerators
Now add the numerators (16 + 21 = 37) and keep the common denominator 168 unchanged.
Working: 16 + 21/168 = 37/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 168 is 1, confirming that 37/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 168 produces a repeating decimal (approximately 0.220238, or 22.0238%).
Working: 37 ÷ 168 = 0.220238 (22.0238%)

Key Values:
- Simplified Fraction: 37/168
- Mixed Number Form: 37/168
- Decimal Value: 0.220238
- Percentage: 22.0238%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-21-plus-3-24/
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2/21 + 3/24 = 37/168

Simplified Fraction

37/168

Mixed Number

Proper (37/168)

Decimal Value

0.220238

Percentage

22.0238%

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Step-by-Step Solution: 2/21 + 3/24

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 24 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 21 × 24 = 504, keeping the calculation simpler).

LCD(21, 24) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 2/21 by 8, and multiply the numerator and denominator of 3/24 by 7 so both fractions share the common base 168.

2 × 8/21 × 8 = 16/168 and 3 × 7/24 × 7 = 21/168

Step 3

Add the Numerators

Now add the numerators (16 + 21 = 37) and keep the common denominator 168 unchanged.

16 + 21/168 = 37/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 168 is 1, confirming that 37/168 cannot be reduced further—it is already in its simplest irreducible form.

37/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 168 produces a repeating decimal (approximately 0.220238, or 22.0238%).

37 ÷ 168 = 0.220238 (22.0238%)

Visual Representation

The diagram below illustrates 2/21 plus 3/24 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/168`
Mixed Number Form	`37/168`
Decimal Form	`0.220238`
Percentage	`22.0238%`

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Frequently Asked Questions

What is 2/21 plus 3/24 as a fraction?

2/21 + 3/24 in simplest fraction form is 37/168.

What is 2/21 plus 3/24 as a decimal?

2/21 + 3/24 converted to a decimal is 0.220238.

What is 2/21 plus 3/24 as a percentage?

2/21 + 3/24 expressed as a percentage is 22.0238%.

Does 2/21 plus 3/24 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.220238...) because the denominator contains prime factors other than 2 and 5.