What is 10/15 plus 15/21? (Answer: 29/21)

Exact Answer

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Problem: What is 10/15 plus 15/21?
Formula / Expression: 10/15 + 15/21
Final Answer: 1 8/21 (29/21)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 15 × 21 = 315, keeping the calculation simpler).
Working: LCD(15, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 10/15 by 7, and multiply the numerator and denominator of 15/21 by 5 so both fractions share the common base 105.
Working: 10 × 7/15 × 7 = 70/105 and 15 × 5/21 × 5 = 75/105

Step 3: Add the Numerators
Now add the numerators (70 + 75 = 145) and keep the common denominator 105 unchanged.
Working: 70 + 75/105 = 145/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 145 and 105, which is 5. Divide both the numerator and denominator by 5.
Working: 145 ÷ 5/105 ÷ 5 = 29/21

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (29) is greater than the denominator (21), divide 29 by 21: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/21.
Working: 29/21 = 1 8/21

Step 6: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 21 produces a repeating decimal (approximately 1.380952, or 138.0952%).
Working: 29 ÷ 21 = 1.380952 (138.0952%)

Key Values:
- Simplified Fraction: 29/21
- Mixed Number Form: 1 8/21
- Decimal Value: 1.380952
- Percentage: 138.0952%

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10/15 + 15/21 = 29/21

Simplified Fraction

29/21

Mixed Number

1 8/21

Decimal Value

1.380952

Percentage

138.0952%

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Step-by-Step Solution: 10/15 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 15 × 21 = 315, keeping the calculation simpler).

LCD(15, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 10/15 by 7, and multiply the numerator and denominator of 15/21 by 5 so both fractions share the common base 105.

10 × 7/15 × 7 = 70/105 and 15 × 5/21 × 5 = 75/105

Step 3

Add the Numerators

Now add the numerators (70 + 75 = 145) and keep the common denominator 105 unchanged.

70 + 75/105 = 145/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 145 and 105, which is 5. Divide both the numerator and denominator by 5.

145 ÷ 5/105 ÷ 5 = 29/21

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (29) is greater than the denominator (21), divide 29 by 21: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/21.

29/21 = 18/21

Step 6

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 21 produces a repeating decimal (approximately 1.380952, or 138.0952%).

29 ÷ 21 = 1.380952 (138.0952%)

Visual Representation

The diagram below illustrates 10/15 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/21`
Mixed Number Form	`1 8/21`
Decimal Form	`1.380952`
Percentage	`138.0952%`

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Frequently Asked Questions

What is 10/15 plus 15/21 as a fraction?

10/15 + 15/21 in simplest fraction form is 29/21 (or 1 8/21 as a mixed number).

What is 10/15 plus 15/21 as a decimal?

10/15 + 15/21 converted to a decimal is 1.380952.

What is 10/15 plus 15/21 as a percentage?

10/15 + 15/21 expressed as a percentage is 138.0952%.

How do you write 10/15 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 29/21 can be written as the mixed number 1 8/21.

Does 10/15 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.380952...) because the denominator contains prime factors other than 2 and 5.