What is 6/21 plus 14/49? (Answer: 4/7)

Exact Answer

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Problem: What is 6/21 plus 14/49?
Formula / Expression: 6/21 + 14/49
Final Answer: 4/7
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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 6/21 by 7, and multiply the numerator and denominator of 14/49 by 3 so both fractions share the common base 147.
Working: 6 × 7/21 × 7 = 42/147 and 14 × 3/49 × 3 = 42/147

Step 3: Add the Numerators
Now add the numerators (42 + 42 = 84) and keep the common denominator 147 unchanged.
Working: 42 + 42/147 = 84/147

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 84 and 147, which is 21. Divide both the numerator and denominator by 21.
Working: 84 ÷ 21/147 ÷ 21 = 4/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 7 produces a repeating decimal (approximately 0.571429, or 57.1429%).
Working: 4 ÷ 7 = 0.571429 (57.1429%)

Key Values:
- Simplified Fraction: 4/7
- Mixed Number Form: 4/7
- Decimal Value: 0.571429
- Percentage: 57.1429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-21-plus-14-49/
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6/21 + 14/49 = 4/7

Simplified Fraction

4/7

Mixed Number

Proper (4/7)

Decimal Value

0.571429

Percentage

57.1429%

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Step-by-Step Solution: 6/21 + 14/49

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 6/21 by 7, and multiply the numerator and denominator of 14/49 by 3 so both fractions share the common base 147.

6 × 7/21 × 7 = 42/147 and 14 × 3/49 × 3 = 42/147

Step 3

Add the Numerators

Now add the numerators (42 + 42 = 84) and keep the common denominator 147 unchanged.

42 + 42/147 = 84/147

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 84 and 147, which is 21. Divide both the numerator and denominator by 21.

84 ÷ 21/147 ÷ 21 = 4/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 7 produces a repeating decimal (approximately 0.571429, or 57.1429%).

4 ÷ 7 = 0.571429 (57.1429%)

Visual Representation

The diagram below illustrates 6/21 plus 14/49 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/7`
Mixed Number Form	`4/7`
Decimal Form	`0.571429`
Percentage	`57.1429%`

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Frequently Asked Questions

What is 6/21 plus 14/49 as a fraction?

6/21 + 14/49 in simplest fraction form is 4/7.

What is 6/21 plus 14/49 as a decimal?

6/21 + 14/49 converted to a decimal is 0.571429.

What is 6/21 plus 14/49 as a percentage?

6/21 + 14/49 expressed as a percentage is 57.1429%.

Does 6/21 plus 14/49 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.571429...) because the denominator contains prime factors other than 2 and 5.