What is 13/35 plus 10/21? (Answer: 89/105)

Exact Answer

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Problem: What is 13/35 plus 10/21?
Formula / Expression: 13/35 + 10/21
Final Answer: 89/105
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 13/35 by 3, and multiply the numerator and denominator of 10/21 by 5 so both fractions share the common base 105.
Working: 13 × 3/35 × 3 = 39/105 and 10 × 5/21 × 5 = 50/105

Step 3: Add the Numerators
Now add the numerators (39 + 50 = 89) and keep the common denominator 105 unchanged.
Working: 39 + 50/105 = 89/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 105 is 1, confirming that 89/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 89/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 105 produces a repeating decimal (approximately 0.847619, or 84.7619%).
Working: 89 ÷ 105 = 0.847619 (84.7619%)

Key Values:
- Simplified Fraction: 89/105
- Mixed Number Form: 89/105
- Decimal Value: 0.847619
- Percentage: 84.7619%

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Solved with FractionsCalc:
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13/35 + 10/21 = 89/105

Simplified Fraction

89/105

Mixed Number

Proper (89/105)

Decimal Value

0.847619

Percentage

84.7619%

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Step-by-Step Solution: 13/35 + 10/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(35, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 13/35 by 3, and multiply the numerator and denominator of 10/21 by 5 so both fractions share the common base 105.

13 × 3/35 × 3 = 39/105 and 10 × 5/21 × 5 = 50/105

Step 3

Add the Numerators

Now add the numerators (39 + 50 = 89) and keep the common denominator 105 unchanged.

39 + 50/105 = 89/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 89 and 105 is 1, confirming that 89/105 cannot be reduced further—it is already in its simplest irreducible form.

89/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 105 produces a repeating decimal (approximately 0.847619, or 84.7619%).

89 ÷ 105 = 0.847619 (84.7619%)

Visual Representation

The diagram below illustrates 13/35 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/105`
Mixed Number Form	`89/105`
Decimal Form	`0.847619`
Percentage	`84.7619%`

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Frequently Asked Questions

What is 13/35 plus 10/21 as a fraction?

13/35 + 10/21 in simplest fraction form is 89/105.

What is 13/35 plus 10/21 as a decimal?

13/35 + 10/21 converted to a decimal is 0.847619.

What is 13/35 plus 10/21 as a percentage?

13/35 + 10/21 expressed as a percentage is 84.7619%.

Does 13/35 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.847619...) because the denominator contains prime factors other than 2 and 5.