What is 7/21 plus 12/35? (Answer: 71/105)

Exact Answer

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Problem: What is 7/21 plus 12/35?
Formula / Expression: 7/21 + 12/35
Final Answer: 71/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 35 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 21 × 35 = 735, keeping the calculation simpler).
Working: LCD(21, 35) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 7/21 by 5, and multiply the numerator and denominator of 12/35 by 3 so both fractions share the common base 105.
Working: 7 × 5/21 × 5 = 35/105 and 12 × 3/35 × 3 = 36/105

Step 3: Add the Numerators
Now add the numerators (35 + 36 = 71) and keep the common denominator 105 unchanged.
Working: 35 + 36/105 = 71/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 105 is 1, confirming that 71/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 105 produces a repeating decimal (approximately 0.67619, or 67.619%).
Working: 71 ÷ 105 = 0.67619 (67.619%)

Key Values:
- Simplified Fraction: 71/105
- Mixed Number Form: 71/105
- Decimal Value: 0.67619
- Percentage: 67.619%

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Solved with FractionsCalc:
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7/21 + 12/35 = 71/105

Simplified Fraction

71/105

Mixed Number

Proper (71/105)

Decimal Value

0.67619

Percentage

67.619%

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Step-by-Step Solution: 7/21 + 12/35

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 35 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 21 × 35 = 735, keeping the calculation simpler).

LCD(21, 35) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 7/21 by 5, and multiply the numerator and denominator of 12/35 by 3 so both fractions share the common base 105.

7 × 5/21 × 5 = 35/105 and 12 × 3/35 × 3 = 36/105

Step 3

Add the Numerators

Now add the numerators (35 + 36 = 71) and keep the common denominator 105 unchanged.

35 + 36/105 = 71/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 105 is 1, confirming that 71/105 cannot be reduced further—it is already in its simplest irreducible form.

71/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 105 produces a repeating decimal (approximately 0.67619, or 67.619%).

71 ÷ 105 = 0.67619 (67.619%)

Visual Representation

The diagram below illustrates 7/21 plus 12/35 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/105`
Mixed Number Form	`71/105`
Decimal Form	`0.67619`
Percentage	`67.619%`

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Frequently Asked Questions

What is 7/21 plus 12/35 as a fraction?

7/21 + 12/35 in simplest fraction form is 71/105.

What is 7/21 plus 12/35 as a decimal?

7/21 + 12/35 converted to a decimal is 0.67619.

What is 7/21 plus 12/35 as a percentage?

7/21 + 12/35 expressed as a percentage is 67.619%.

Does 7/21 plus 12/35 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.67619...) because the denominator contains prime factors other than 2 and 5.