What is 4/49 plus 9/21? (Answer: 25/49)

Exact Answer

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Problem: What is 4/49 plus 9/21?
Formula / Expression: 4/49 + 9/21
Final Answer: 25/49
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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 9/21 by 7 so both fractions share the common base 147.
Working: 4 × 3/49 × 3 = 12/147 and 9 × 7/21 × 7 = 63/147

Step 3: Add the Numerators
Now add the numerators (12 + 63 = 75) and keep the common denominator 147 unchanged.
Working: 12 + 63/147 = 75/147

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 75 and 147, which is 3. Divide both the numerator and denominator by 3.
Working: 75 ÷ 3/147 ÷ 3 = 25/49

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 49 produces a repeating decimal (approximately 0.510204, or 51.0204%).
Working: 25 ÷ 49 = 0.510204 (51.0204%)

Key Values:
- Simplified Fraction: 25/49
- Mixed Number Form: 25/49
- Decimal Value: 0.510204
- Percentage: 51.0204%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-49-plus-9-21/
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4/49 + 9/21 = 25/49

Simplified Fraction

25/49

Mixed Number

Proper (25/49)

Decimal Value

0.510204

Percentage

51.0204%

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Step-by-Step Solution: 4/49 + 9/21

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 9/21 by 7 so both fractions share the common base 147.

4 × 3/49 × 3 = 12/147 and 9 × 7/21 × 7 = 63/147

Step 3

Add the Numerators

Now add the numerators (12 + 63 = 75) and keep the common denominator 147 unchanged.

12 + 63/147 = 75/147

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 75 and 147, which is 3. Divide both the numerator and denominator by 3.

75 ÷ 3/147 ÷ 3 = 25/49

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 49 produces a repeating decimal (approximately 0.510204, or 51.0204%).

25 ÷ 49 = 0.510204 (51.0204%)

Visual Representation

The diagram below illustrates 4/49 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/49`
Mixed Number Form	`25/49`
Decimal Form	`0.510204`
Percentage	`51.0204%`

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Frequently Asked Questions

What is 4/49 plus 9/21 as a fraction?

4/49 + 9/21 in simplest fraction form is 25/49.

What is 4/49 plus 9/21 as a decimal?

4/49 + 9/21 converted to a decimal is 0.510204.

What is 4/49 plus 9/21 as a percentage?

4/49 + 9/21 expressed as a percentage is 51.0204%.

Does 4/49 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.510204...) because the denominator contains prime factors other than 2 and 5.