What is 1/49 plus 4/21? (Answer: 31/147)

Exact Answer

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Problem: What is 1/49 plus 4/21?
Formula / Expression: 1/49 + 4/21
Final Answer: 31/147
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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 1/49 by 3, and multiply the numerator and denominator of 4/21 by 7 so both fractions share the common base 147.
Working: 1 × 3/49 × 3 = 3/147 and 4 × 7/21 × 7 = 28/147

Step 3: Add the Numerators
Now add the numerators (3 + 28 = 31) and keep the common denominator 147 unchanged.
Working: 3 + 28/147 = 31/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 147 is 1, confirming that 31/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 147 produces a repeating decimal (approximately 0.210884, or 21.0884%).
Working: 31 ÷ 147 = 0.210884 (21.0884%)

Key Values:
- Simplified Fraction: 31/147
- Mixed Number Form: 31/147
- Decimal Value: 0.210884
- Percentage: 21.0884%

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1/49 + 4/21 = 31/147

Simplified Fraction

31/147

Mixed Number

Proper (31/147)

Decimal Value

0.210884

Percentage

21.0884%

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Step-by-Step Solution: 1/49 + 4/21

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 1/49 by 3, and multiply the numerator and denominator of 4/21 by 7 so both fractions share the common base 147.

1 × 3/49 × 3 = 3/147 and 4 × 7/21 × 7 = 28/147

Step 3

Add the Numerators

Now add the numerators (3 + 28 = 31) and keep the common denominator 147 unchanged.

3 + 28/147 = 31/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 147 is 1, confirming that 31/147 cannot be reduced further—it is already in its simplest irreducible form.

31/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 147 produces a repeating decimal (approximately 0.210884, or 21.0884%).

31 ÷ 147 = 0.210884 (21.0884%)

Visual Representation

The diagram below illustrates 1/49 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/147`
Mixed Number Form	`31/147`
Decimal Form	`0.210884`
Percentage	`21.0884%`

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Frequently Asked Questions

What is 1/49 plus 4/21 as a fraction?

1/49 + 4/21 in simplest fraction form is 31/147.

What is 1/49 plus 4/21 as a decimal?

1/49 + 4/21 converted to a decimal is 0.210884.

What is 1/49 plus 4/21 as a percentage?

1/49 + 4/21 expressed as a percentage is 21.0884%.

Does 1/49 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.210884...) because the denominator contains prime factors other than 2 and 5.