What is 3/21 plus 4/24? (Answer: 13/42)

Exact Answer

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Problem: What is 3/21 plus 4/24?
Formula / Expression: 3/21 + 4/24
Final Answer: 13/42
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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 3/21 by 8, and multiply the numerator and denominator of 4/24 by 7 so both fractions share the common base 168.
Working: 3 × 8/21 × 8 = 24/168 and 4 × 7/24 × 7 = 28/168

Step 3: Add the Numerators
Now add the numerators (24 + 28 = 52) and keep the common denominator 168 unchanged.
Working: 24 + 28/168 = 52/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 52 and 168, which is 4. Divide both the numerator and denominator by 4.
Working: 52 ÷ 4/168 ÷ 4 = 13/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 42 produces a repeating decimal (approximately 0.309524, or 30.9524%).
Working: 13 ÷ 42 = 0.309524 (30.9524%)

Key Values:
- Simplified Fraction: 13/42
- Mixed Number Form: 13/42
- Decimal Value: 0.309524
- Percentage: 30.9524%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-21-plus-4-24/
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3/21 + 4/24 = 13/42

Simplified Fraction

13/42

Mixed Number

Proper (13/42)

Decimal Value

0.309524

Percentage

30.9524%

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Step-by-Step Solution: 3/21 + 4/24

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 3/21 by 8, and multiply the numerator and denominator of 4/24 by 7 so both fractions share the common base 168.

3 × 8/21 × 8 = 24/168 and 4 × 7/24 × 7 = 28/168

Step 3

Add the Numerators

Now add the numerators (24 + 28 = 52) and keep the common denominator 168 unchanged.

24 + 28/168 = 52/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 52 and 168, which is 4. Divide both the numerator and denominator by 4.

52 ÷ 4/168 ÷ 4 = 13/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 42 produces a repeating decimal (approximately 0.309524, or 30.9524%).

13 ÷ 42 = 0.309524 (30.9524%)

Visual Representation

The diagram below illustrates 3/21 plus 4/24 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/42`
Mixed Number Form	`13/42`
Decimal Form	`0.309524`
Percentage	`30.9524%`

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Frequently Asked Questions

What is 3/21 plus 4/24 as a fraction?

3/21 + 4/24 in simplest fraction form is 13/42.

What is 3/21 plus 4/24 as a decimal?

3/21 + 4/24 converted to a decimal is 0.309524.

What is 3/21 plus 4/24 as a percentage?

3/21 + 4/24 expressed as a percentage is 30.9524%.

Does 3/21 plus 4/24 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.309524...) because the denominator contains prime factors other than 2 and 5.