What is 4/21 plus 12/63? (Answer: 8/21)

Exact Answer

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Problem: What is 4/21 plus 12/63?
Formula / Expression: 4/21 + 12/63
Final Answer: 8/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 63 is an exact multiple of 21 (21 × 3 = 63). The Least Common Denominator (LCD) is simply 63, meaning we only need to scale one fraction.
Working: LCD(21, 63) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 4/21 by 3, and multiply the numerator and denominator of 12/63 by 1 so both fractions share the common base 63.
Working: 4 × 3/21 × 3 = 12/63 and 12 × 1/63 × 1 = 12/63

Step 3: Add the Numerators
Now add the numerators (12 + 12 = 24) and keep the common denominator 63 unchanged.
Working: 12 + 12/63 = 24/63

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 24 and 63, which is 3. Divide both the numerator and denominator by 3.
Working: 24 ÷ 3/63 ÷ 3 = 8/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 21 produces a repeating decimal (approximately 0.380952, or 38.0952%).
Working: 8 ÷ 21 = 0.380952 (38.0952%)

Key Values:
- Simplified Fraction: 8/21
- Mixed Number Form: 8/21
- Decimal Value: 0.380952
- Percentage: 38.0952%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-21-plus-12-63/
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4/21 + 12/63 = 8/21

Simplified Fraction

8/21

Mixed Number

Proper (8/21)

Decimal Value

0.380952

Percentage

38.0952%

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Step-by-Step Solution: 4/21 + 12/63

Step 1

Find the Least Common Denominator (LCD)

Notice that 63 is an exact multiple of 21 (21 × 3 = 63). The Least Common Denominator (LCD) is simply 63, meaning we only need to scale one fraction.

LCD(21, 63) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 4/21 by 3, and multiply the numerator and denominator of 12/63 by 1 so both fractions share the common base 63.

4 × 3/21 × 3 = 12/63 and 12 × 1/63 × 1 = 12/63

Step 3

Add the Numerators

Now add the numerators (12 + 12 = 24) and keep the common denominator 63 unchanged.

12 + 12/63 = 24/63

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 24 and 63, which is 3. Divide both the numerator and denominator by 3.

24 ÷ 3/63 ÷ 3 = 8/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 21 produces a repeating decimal (approximately 0.380952, or 38.0952%).

8 ÷ 21 = 0.380952 (38.0952%)

Visual Representation

The diagram below illustrates 4/21 plus 12/63 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/21`
Mixed Number Form	`8/21`
Decimal Form	`0.380952`
Percentage	`38.0952%`

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Frequently Asked Questions

What is 4/21 plus 12/63 as a fraction?

4/21 + 12/63 in simplest fraction form is 8/21.

What is 4/21 plus 12/63 as a decimal?

4/21 + 12/63 converted to a decimal is 0.380952.

What is 4/21 plus 12/63 as a percentage?

4/21 + 12/63 expressed as a percentage is 38.0952%.

Does 4/21 plus 12/63 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.380952...) because the denominator contains prime factors other than 2 and 5.