What is 3/49 plus 2/21? (Answer: 23/147)

Exact Answer

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Problem: What is 3/49 plus 2/21?
Formula / Expression: 3/49 + 2/21
Final Answer: 23/147
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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 3/49 by 3, and multiply the numerator and denominator of 2/21 by 7 so both fractions share the common base 147.
Working: 3 × 3/49 × 3 = 9/147 and 2 × 7/21 × 7 = 14/147

Step 3: Add the Numerators
Now add the numerators (9 + 14 = 23) and keep the common denominator 147 unchanged.
Working: 9 + 14/147 = 23/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 147 is 1, confirming that 23/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 147 produces a repeating decimal (approximately 0.156463, or 15.6463%).
Working: 23 ÷ 147 = 0.156463 (15.6463%)

Key Values:
- Simplified Fraction: 23/147
- Mixed Number Form: 23/147
- Decimal Value: 0.156463
- Percentage: 15.6463%

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3/49 + 2/21 = 23/147

Simplified Fraction

23/147

Mixed Number

Proper (23/147)

Decimal Value

0.156463

Percentage

15.6463%

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Step-by-Step Solution: 3/49 + 2/21

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 3/49 by 3, and multiply the numerator and denominator of 2/21 by 7 so both fractions share the common base 147.

3 × 3/49 × 3 = 9/147 and 2 × 7/21 × 7 = 14/147

Step 3

Add the Numerators

Now add the numerators (9 + 14 = 23) and keep the common denominator 147 unchanged.

9 + 14/147 = 23/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 147 is 1, confirming that 23/147 cannot be reduced further—it is already in its simplest irreducible form.

23/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 147 produces a repeating decimal (approximately 0.156463, or 15.6463%).

23 ÷ 147 = 0.156463 (15.6463%)

Visual Representation

The diagram below illustrates 3/49 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/147`
Mixed Number Form	`23/147`
Decimal Form	`0.156463`
Percentage	`15.6463%`

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Frequently Asked Questions

What is 3/49 plus 2/21 as a fraction?

3/49 + 2/21 in simplest fraction form is 23/147.

What is 3/49 plus 2/21 as a decimal?

3/49 + 2/21 converted to a decimal is 0.156463.

What is 3/49 plus 2/21 as a percentage?

3/49 + 2/21 expressed as a percentage is 15.6463%.

Does 3/49 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.156463...) because the denominator contains prime factors other than 2 and 5.