What is 15/21 plus 25/35? (Answer: 10/7)

Exact Answer

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Problem: What is 15/21 plus 25/35?
Formula / Expression: 15/21 + 25/35
Final Answer: 1 3/7 (10/7)
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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 15/21 by 5, and multiply the numerator and denominator of 25/35 by 3 so both fractions share the common base 105.
Working: 15 × 5/21 × 5 = 75/105 and 25 × 3/35 × 3 = 75/105

Step 3: Add the Numerators
Now add the numerators (75 + 75 = 150) and keep the common denominator 105 unchanged.
Working: 75 + 75/105 = 150/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 150 and 105, which is 15. Divide both the numerator and denominator by 15.
Working: 150 ÷ 15/105 ÷ 15 = 10/7

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (10) is greater than the denominator (7), divide 10 by 7: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/7.
Working: 10/7 = 1 3/7

Step 6: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 7 produces a repeating decimal (approximately 1.428571, or 142.8571%).
Working: 10 ÷ 7 = 1.428571 (142.8571%)

Key Values:
- Simplified Fraction: 10/7
- Mixed Number Form: 1 3/7
- Decimal Value: 1.428571
- Percentage: 142.8571%

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15/21 + 25/35 = 10/7

Simplified Fraction

10/7

Mixed Number

1 3/7

Decimal Value

1.428571

Percentage

142.8571%

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Step-by-Step Solution: 15/21 + 25/35

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 15/21 by 5, and multiply the numerator and denominator of 25/35 by 3 so both fractions share the common base 105.

15 × 5/21 × 5 = 75/105 and 25 × 3/35 × 3 = 75/105

Step 3

Add the Numerators

Now add the numerators (75 + 75 = 150) and keep the common denominator 105 unchanged.

75 + 75/105 = 150/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 150 and 105, which is 15. Divide both the numerator and denominator by 15.

150 ÷ 15/105 ÷ 15 = 10/7

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (10) is greater than the denominator (7), divide 10 by 7: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/7.

10/7 = 13/7

Step 6

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 7 produces a repeating decimal (approximately 1.428571, or 142.8571%).

10 ÷ 7 = 1.428571 (142.8571%)

Visual Representation

The diagram below illustrates 15/21 plus 25/35 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/7`
Mixed Number Form	`1 3/7`
Decimal Form	`1.428571`
Percentage	`142.8571%`

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Frequently Asked Questions

What is 15/21 plus 25/35 as a fraction?

15/21 + 25/35 in simplest fraction form is 10/7 (or 1 3/7 as a mixed number).

What is 15/21 plus 25/35 as a decimal?

15/21 + 25/35 converted to a decimal is 1.428571.

What is 15/21 plus 25/35 as a percentage?

15/21 + 25/35 expressed as a percentage is 142.8571%.

How do you write 15/21 plus 25/35 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 10/7 can be written as the mixed number 1 3/7.

Does 15/21 plus 25/35 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.428571...) because the denominator contains prime factors other than 2 and 5.