What is 4/21 plus 10/49? (Answer: 58/147)

Exact Answer

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Problem: What is 4/21 plus 10/49?
Formula / Expression: 4/21 + 10/49
Final Answer: 58/147
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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 4/21 by 7, and multiply the numerator and denominator of 10/49 by 3 so both fractions share the common base 147.
Working: 4 × 7/21 × 7 = 28/147 and 10 × 3/49 × 3 = 30/147

Step 3: Add the Numerators
Now add the numerators (28 + 30 = 58) and keep the common denominator 147 unchanged.
Working: 28 + 30/147 = 58/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 58 and 147 is 1, confirming that 58/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 58/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 58 by denominator 147 produces a repeating decimal (approximately 0.394558, or 39.4558%).
Working: 58 ÷ 147 = 0.394558 (39.4558%)

Key Values:
- Simplified Fraction: 58/147
- Mixed Number Form: 58/147
- Decimal Value: 0.394558
- Percentage: 39.4558%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-21-plus-10-49/
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4/21 + 10/49 = 58/147

Simplified Fraction

58/147

Mixed Number

Proper (58/147)

Decimal Value

0.394558

Percentage

39.4558%

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Step-by-Step Solution: 4/21 + 10/49

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 4/21 by 7, and multiply the numerator and denominator of 10/49 by 3 so both fractions share the common base 147.

4 × 7/21 × 7 = 28/147 and 10 × 3/49 × 3 = 30/147

Step 3

Add the Numerators

Now add the numerators (28 + 30 = 58) and keep the common denominator 147 unchanged.

28 + 30/147 = 58/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 58 and 147 is 1, confirming that 58/147 cannot be reduced further—it is already in its simplest irreducible form.

58/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 58 by denominator 147 produces a repeating decimal (approximately 0.394558, or 39.4558%).

58 ÷ 147 = 0.394558 (39.4558%)

Visual Representation

The diagram below illustrates 4/21 plus 10/49 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`58/147`
Mixed Number Form	`58/147`
Decimal Form	`0.394558`
Percentage	`39.4558%`

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Frequently Asked Questions

What is 4/21 plus 10/49 as a fraction?

4/21 + 10/49 in simplest fraction form is 58/147.

What is 4/21 plus 10/49 as a decimal?

4/21 + 10/49 converted to a decimal is 0.394558.

What is 4/21 plus 10/49 as a percentage?

4/21 + 10/49 expressed as a percentage is 39.4558%.

Does 4/21 plus 10/49 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.394558...) because the denominator contains prime factors other than 2 and 5.