What is 13/35 plus 15/21? (Answer: 38/35)

Exact Answer

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Problem: What is 13/35 plus 15/21?
Formula / Expression: 13/35 + 15/21
Final Answer: 1 3/35 (38/35)
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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 15/21 by 5 so both fractions share the common base 105.
Working: 13 × 3/35 × 3 = 39/105 and 15 × 5/21 × 5 = 75/105

Step 3: Add the Numerators
Now add the numerators (39 + 75 = 114) and keep the common denominator 105 unchanged.
Working: 39 + 75/105 = 114/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 114 and 105, which is 3. Divide both the numerator and denominator by 3.
Working: 114 ÷ 3/105 ÷ 3 = 38/35

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (38) is greater than the denominator (35), divide 38 by 35: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/35.
Working: 38/35 = 1 3/35

Step 6: Decimal & Percentage Representation
Dividing the numerator 38 by denominator 35 produces a repeating decimal (approximately 1.085714, or 108.5714%).
Working: 38 ÷ 35 = 1.085714 (108.5714%)

Key Values:
- Simplified Fraction: 38/35
- Mixed Number Form: 1 3/35
- Decimal Value: 1.085714
- Percentage: 108.5714%

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13/35 + 15/21 = 38/35

Simplified Fraction

38/35

Mixed Number

1 3/35

Decimal Value

1.085714

Percentage

108.5714%

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Step-by-Step Solution: 13/35 + 15/21

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 15/21 by 5 so both fractions share the common base 105.

13 × 3/35 × 3 = 39/105 and 15 × 5/21 × 5 = 75/105

Step 3

Add the Numerators

Now add the numerators (39 + 75 = 114) and keep the common denominator 105 unchanged.

39 + 75/105 = 114/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 114 and 105, which is 3. Divide both the numerator and denominator by 3.

114 ÷ 3/105 ÷ 3 = 38/35

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (38) is greater than the denominator (35), divide 38 by 35: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/35.

38/35 = 13/35

Step 6

Decimal & Percentage Representation

Dividing the numerator 38 by denominator 35 produces a repeating decimal (approximately 1.085714, or 108.5714%).

38 ÷ 35 = 1.085714 (108.5714%)

Visual Representation

The diagram below illustrates 13/35 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`38/35`
Mixed Number Form	`1 3/35`
Decimal Form	`1.085714`
Percentage	`108.5714%`

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Frequently Asked Questions

What is 13/35 plus 15/21 as a fraction?

13/35 + 15/21 in simplest fraction form is 38/35 (or 1 3/35 as a mixed number).

What is 13/35 plus 15/21 as a decimal?

13/35 + 15/21 converted to a decimal is 1.085714.

What is 13/35 plus 15/21 as a percentage?

13/35 + 15/21 expressed as a percentage is 108.5714%.

How do you write 13/35 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 38/35 can be written as the mixed number 1 3/35.

Does 13/35 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.085714...) because the denominator contains prime factors other than 2 and 5.