What is 12/49 plus 10/21? (Answer: 106/147)

Exact Answer

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Problem: What is 12/49 plus 10/21?
Formula / Expression: 12/49 + 10/21
Final Answer: 106/147
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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 12/49 by 3, and multiply the numerator and denominator of 10/21 by 7 so both fractions share the common base 147.
Working: 12 × 3/49 × 3 = 36/147 and 10 × 7/21 × 7 = 70/147

Step 3: Add the Numerators
Now add the numerators (36 + 70 = 106) and keep the common denominator 147 unchanged.
Working: 36 + 70/147 = 106/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 106 and 147 is 1, confirming that 106/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 106/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 106 by denominator 147 produces a repeating decimal (approximately 0.721088, or 72.1088%).
Working: 106 ÷ 147 = 0.721088 (72.1088%)

Key Values:
- Simplified Fraction: 106/147
- Mixed Number Form: 106/147
- Decimal Value: 0.721088
- Percentage: 72.1088%

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12/49 + 10/21 = 106/147

Simplified Fraction

106/147

Mixed Number

Proper (106/147)

Decimal Value

0.721088

Percentage

72.1088%

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Step-by-Step Solution: 12/49 + 10/21

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 12/49 by 3, and multiply the numerator and denominator of 10/21 by 7 so both fractions share the common base 147.

12 × 3/49 × 3 = 36/147 and 10 × 7/21 × 7 = 70/147

Step 3

Add the Numerators

Now add the numerators (36 + 70 = 106) and keep the common denominator 147 unchanged.

36 + 70/147 = 106/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 106 and 147 is 1, confirming that 106/147 cannot be reduced further—it is already in its simplest irreducible form.

106/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 106 by denominator 147 produces a repeating decimal (approximately 0.721088, or 72.1088%).

106 ÷ 147 = 0.721088 (72.1088%)

Visual Representation

The diagram below illustrates 12/49 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`106/147`
Mixed Number Form	`106/147`
Decimal Form	`0.721088`
Percentage	`72.1088%`

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Frequently Asked Questions

What is 12/49 plus 10/21 as a fraction?

12/49 + 10/21 in simplest fraction form is 106/147.

What is 12/49 plus 10/21 as a decimal?

12/49 + 10/21 converted to a decimal is 0.721088.

What is 12/49 plus 10/21 as a percentage?

12/49 + 10/21 expressed as a percentage is 72.1088%.

Does 12/49 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.721088...) because the denominator contains prime factors other than 2 and 5.