What is 4/49 plus 3/21? (Answer: 11/49)

Exact Answer

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Problem: What is 4/49 plus 3/21?
Formula / Expression: 4/49 + 3/21
Final Answer: 11/49
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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 3/21 by 7 so both fractions share the common base 147.
Working: 4 × 3/49 × 3 = 12/147 and 3 × 7/21 × 7 = 21/147

Step 3: Add the Numerators
Now add the numerators (12 + 21 = 33) and keep the common denominator 147 unchanged.
Working: 12 + 21/147 = 33/147

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 33 and 147, which is 3. Divide both the numerator and denominator by 3.
Working: 33 ÷ 3/147 ÷ 3 = 11/49

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 49 produces a repeating decimal (approximately 0.22449, or 22.449%).
Working: 11 ÷ 49 = 0.22449 (22.449%)

Key Values:
- Simplified Fraction: 11/49
- Mixed Number Form: 11/49
- Decimal Value: 0.22449
- Percentage: 22.449%

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Solved with FractionsCalc:
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4/49 + 3/21 = 11/49

Simplified Fraction

11/49

Mixed Number

Proper (11/49)

Decimal Value

0.22449

Percentage

22.449%

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Step-by-Step Solution: 4/49 + 3/21

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 3/21 by 7 so both fractions share the common base 147.

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

Step 3

Add the Numerators

Now add the numerators (12 + 21 = 33) and keep the common denominator 147 unchanged.

12 + 21/147 = 33/147

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 33 and 147, which is 3. Divide both the numerator and denominator by 3.

33 ÷ 3/147 ÷ 3 = 11/49

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 49 produces a repeating decimal (approximately 0.22449, or 22.449%).

11 ÷ 49 = 0.22449 (22.449%)

Visual Representation

The diagram below illustrates 4/49 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/49`
Mixed Number Form	`11/49`
Decimal Form	`0.22449`
Percentage	`22.449%`

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Frequently Asked Questions

What is 4/49 plus 3/21 as a fraction?

4/49 + 3/21 in simplest fraction form is 11/49.

What is 4/49 plus 3/21 as a decimal?

4/49 + 3/21 converted to a decimal is 0.22449.

What is 4/49 plus 3/21 as a percentage?

4/49 + 3/21 expressed as a percentage is 22.449%.

Does 4/49 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.22449...) because the denominator contains prime factors other than 2 and 5.