What is 3/21 plus 7/49? (Answer: 2/7)

Exact Answer

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Problem: What is 3/21 plus 7/49?
Formula / Expression: 3/21 + 7/49
Final Answer: 2/7
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Step-by-Step Solution:

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

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

Step 3: Add the Numerators
Now add the numerators (21 + 21 = 42) and keep the common denominator 147 unchanged.
Working: 21 + 21/147 = 42/147

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 147, which is 21. Divide both the numerator and denominator by 21.
Working: 42 ÷ 21/147 ÷ 21 = 2/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 7 produces a repeating decimal (approximately 0.285714, or 28.5714%).
Working: 2 ÷ 7 = 0.285714 (28.5714%)

Key Values:
- Simplified Fraction: 2/7
- Mixed Number Form: 2/7
- Decimal Value: 0.285714
- Percentage: 28.5714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-21-plus-7-49/
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3/21 + 7/49 = 2/7

Simplified Fraction

2/7

Mixed Number

Proper (2/7)

Decimal Value

0.285714

Percentage

28.5714%

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Step-by-Step Solution: 3/21 + 7/49

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 49) = 147

Step 2

Convert to Equivalent Fractions with Common Denominator 147

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

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

Step 3

Add the Numerators

Now add the numerators (21 + 21 = 42) and keep the common denominator 147 unchanged.

21 + 21/147 = 42/147

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 147, which is 21. Divide both the numerator and denominator by 21.

42 ÷ 21/147 ÷ 21 = 2/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 7 produces a repeating decimal (approximately 0.285714, or 28.5714%).

2 ÷ 7 = 0.285714 (28.5714%)

Visual Representation

The diagram below illustrates 3/21 plus 7/49 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/7`
Mixed Number Form	`2/7`
Decimal Form	`0.285714`
Percentage	`28.5714%`

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Frequently Asked Questions

What is 3/21 plus 7/49 as a fraction?

3/21 + 7/49 in simplest fraction form is 2/7.

What is 3/21 plus 7/49 as a decimal?

3/21 + 7/49 converted to a decimal is 0.285714.

What is 3/21 plus 7/49 as a percentage?

3/21 + 7/49 expressed as a percentage is 28.5714%.

Does 3/21 plus 7/49 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.285714...) because the denominator contains prime factors other than 2 and 5.