What is 6/49 plus 4/21? (Answer: 46/147)

Exact Answer

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Problem: What is 6/49 plus 4/21?
Formula / Expression: 6/49 + 4/21
Final Answer: 46/147
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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 6/49 by 3, and multiply the numerator and denominator of 4/21 by 7 so both fractions share the common base 147.
Working: 6 × 3/49 × 3 = 18/147 and 4 × 7/21 × 7 = 28/147

Step 3: Add the Numerators
Now add the numerators (18 + 28 = 46) and keep the common denominator 147 unchanged.
Working: 18 + 28/147 = 46/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 46 and 147 is 1, confirming that 46/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 46/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 46 by denominator 147 produces a repeating decimal (approximately 0.312925, or 31.2925%).
Working: 46 ÷ 147 = 0.312925 (31.2925%)

Key Values:
- Simplified Fraction: 46/147
- Mixed Number Form: 46/147
- Decimal Value: 0.312925
- Percentage: 31.2925%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-49-plus-4-21/
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6/49 + 4/21 = 46/147

Simplified Fraction

46/147

Mixed Number

Proper (46/147)

Decimal Value

0.312925

Percentage

31.2925%

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Step-by-Step Solution: 6/49 + 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 6/49 by 3, and multiply the numerator and denominator of 4/21 by 7 so both fractions share the common base 147.

6 × 3/49 × 3 = 18/147 and 4 × 7/21 × 7 = 28/147

Step 3

Add the Numerators

Now add the numerators (18 + 28 = 46) and keep the common denominator 147 unchanged.

18 + 28/147 = 46/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 46 and 147 is 1, confirming that 46/147 cannot be reduced further—it is already in its simplest irreducible form.

46/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 46 by denominator 147 produces a repeating decimal (approximately 0.312925, or 31.2925%).

46 ÷ 147 = 0.312925 (31.2925%)

Visual Representation

The diagram below illustrates 6/49 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`46/147`
Mixed Number Form	`46/147`
Decimal Form	`0.312925`
Percentage	`31.2925%`

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Frequently Asked Questions

What is 6/49 plus 4/21 as a fraction?

6/49 + 4/21 in simplest fraction form is 46/147.

What is 6/49 plus 4/21 as a decimal?

6/49 + 4/21 converted to a decimal is 0.312925.

What is 6/49 plus 4/21 as a percentage?

6/49 + 4/21 expressed as a percentage is 31.2925%.

Does 6/49 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.312925...) because the denominator contains prime factors other than 2 and 5.