What is 1/24 plus 4/21? (Answer: 13/56)

Exact Answer

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Problem: What is 1/24 plus 4/21?
Formula / Expression: 1/24 + 4/21
Final Answer: 13/56
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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 1/24 by 7, and multiply the numerator and denominator of 4/21 by 8 so both fractions share the common base 168.
Working: 1 × 7/24 × 7 = 7/168 and 4 × 8/21 × 8 = 32/168

Step 3: Add the Numerators
Now add the numerators (7 + 32 = 39) and keep the common denominator 168 unchanged.
Working: 7 + 32/168 = 39/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 39 and 168, which is 3. Divide both the numerator and denominator by 3.
Working: 39 ÷ 3/168 ÷ 3 = 13/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 56 produces a repeating decimal (approximately 0.232143, or 23.2143%).
Working: 13 ÷ 56 = 0.232143 (23.2143%)

Key Values:
- Simplified Fraction: 13/56
- Mixed Number Form: 13/56
- Decimal Value: 0.232143
- Percentage: 23.2143%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-24-plus-4-21/
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1/24 + 4/21 = 13/56

Simplified Fraction

13/56

Mixed Number

Proper (13/56)

Decimal Value

0.232143

Percentage

23.2143%

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Step-by-Step Solution: 1/24 + 4/21

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 1/24 by 7, and multiply the numerator and denominator of 4/21 by 8 so both fractions share the common base 168.

1 × 7/24 × 7 = 7/168 and 4 × 8/21 × 8 = 32/168

Step 3

Add the Numerators

Now add the numerators (7 + 32 = 39) and keep the common denominator 168 unchanged.

7 + 32/168 = 39/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 39 and 168, which is 3. Divide both the numerator and denominator by 3.

39 ÷ 3/168 ÷ 3 = 13/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 56 produces a repeating decimal (approximately 0.232143, or 23.2143%).

13 ÷ 56 = 0.232143 (23.2143%)

Visual Representation

The diagram below illustrates 1/24 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/56`
Mixed Number Form	`13/56`
Decimal Form	`0.232143`
Percentage	`23.2143%`

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Frequently Asked Questions

What is 1/24 plus 4/21 as a fraction?

1/24 + 4/21 in simplest fraction form is 13/56.

What is 1/24 plus 4/21 as a decimal?

1/24 + 4/21 converted to a decimal is 0.232143.

What is 1/24 plus 4/21 as a percentage?

1/24 + 4/21 expressed as a percentage is 23.2143%.

Does 1/24 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.232143...) because the denominator contains prime factors other than 2 and 5.