What is 2/24 plus 3/21? (Answer: 19/84)

Exact Answer

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Problem: What is 2/24 plus 3/21?
Formula / Expression: 2/24 + 3/21
Final Answer: 19/84
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 2/24 by 7, and multiply the numerator and denominator of 3/21 by 8 so both fractions share the common base 168.
Working: 2 × 7/24 × 7 = 14/168 and 3 × 8/21 × 8 = 24/168

Step 3: Add the Numerators
Now add the numerators (14 + 24 = 38) and keep the common denominator 168 unchanged.
Working: 14 + 24/168 = 38/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 38 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: 38 ÷ 2/168 ÷ 2 = 19/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 84 produces a repeating decimal (approximately 0.22619, or 22.619%).
Working: 19 ÷ 84 = 0.22619 (22.619%)

Key Values:
- Simplified Fraction: 19/84
- Mixed Number Form: 19/84
- Decimal Value: 0.22619
- Percentage: 22.619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-24-plus-3-21/
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2/24 + 3/21 = 19/84

Simplified Fraction

19/84

Mixed Number

Proper (19/84)

Decimal Value

0.22619

Percentage

22.619%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(24, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

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

2 × 7/24 × 7 = 14/168 and 3 × 8/21 × 8 = 24/168

Step 3

Add the Numerators

Now add the numerators (14 + 24 = 38) and keep the common denominator 168 unchanged.

14 + 24/168 = 38/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 38 and 168, which is 2. Divide both the numerator and denominator by 2.

38 ÷ 2/168 ÷ 2 = 19/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 84 produces a repeating decimal (approximately 0.22619, or 22.619%).

19 ÷ 84 = 0.22619 (22.619%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/84`
Mixed Number Form	`19/84`
Decimal Form	`0.22619`
Percentage	`22.619%`

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Frequently Asked Questions

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

2/24 + 3/21 in simplest fraction form is 19/84.

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

2/24 + 3/21 converted to a decimal is 0.22619.

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

2/24 + 3/21 expressed as a percentage is 22.619%.

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

It results in a repeating decimal (approximately 0.22619...) because the denominator contains prime factors other than 2 and 5.