What is 4/49 plus 12/21? (Answer: 32/49)

Exact Answer

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Problem: What is 4/49 plus 12/21?
Formula / Expression: 4/49 + 12/21
Final Answer: 32/49
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 49 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 49 × 21 = 1029, keeping the calculation simpler).
Working: LCD(49, 21) = 147

Step 2: Convert to Equivalent Fractions with Common Denominator 147
Multiply the numerator and denominator of 4/49 by 3, and multiply the numerator and denominator of 12/21 by 7 so both fractions share the common base 147.
Working: 4 × 3/49 × 3 = 12/147 and 12 × 7/21 × 7 = 84/147

Step 3: Add the Numerators
Now add the numerators (12 + 84 = 96) and keep the common denominator 147 unchanged.
Working: 12 + 84/147 = 96/147

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 96 and 147, which is 3. Divide both the numerator and denominator by 3.
Working: 96 ÷ 3/147 ÷ 3 = 32/49

Step 5: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 49 produces a repeating decimal (approximately 0.653061, or 65.3061%).
Working: 32 ÷ 49 = 0.653061 (65.3061%)

Key Values:
- Simplified Fraction: 32/49
- Mixed Number Form: 32/49
- Decimal Value: 0.653061
- Percentage: 65.3061%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-49-plus-12-21/
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4/49 + 12/21 = 32/49

Simplified Fraction

32/49

Mixed Number

Proper (32/49)

Decimal Value

0.653061

Percentage

65.3061%

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Step-by-Step Solution: 4/49 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 49 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 49 × 21 = 1029, keeping the calculation simpler).

LCD(49, 21) = 147

Step 2

Convert to Equivalent Fractions with Common Denominator 147

Multiply the numerator and denominator of 4/49 by 3, and multiply the numerator and denominator of 12/21 by 7 so both fractions share the common base 147.

4 × 3/49 × 3 = 12/147 and 12 × 7/21 × 7 = 84/147

Step 3

Add the Numerators

Now add the numerators (12 + 84 = 96) and keep the common denominator 147 unchanged.

12 + 84/147 = 96/147

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 96 and 147, which is 3. Divide both the numerator and denominator by 3.

96 ÷ 3/147 ÷ 3 = 32/49

Step 5

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 49 produces a repeating decimal (approximately 0.653061, or 65.3061%).

32 ÷ 49 = 0.653061 (65.3061%)

Visual Representation

The diagram below illustrates 4/49 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/49`
Mixed Number Form	`32/49`
Decimal Form	`0.653061`
Percentage	`65.3061%`

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Frequently Asked Questions

What is 4/49 plus 12/21 as a fraction?

4/49 + 12/21 in simplest fraction form is 32/49.

What is 4/49 plus 12/21 as a decimal?

4/49 + 12/21 converted to a decimal is 0.653061.

What is 4/49 plus 12/21 as a percentage?

4/49 + 12/21 expressed as a percentage is 65.3061%.

Does 4/49 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.653061...) because the denominator contains prime factors other than 2 and 5.