What is 15/35 plus 10/21? (Answer: 19/21)

Exact Answer

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Problem: What is 15/35 plus 10/21?
Formula / Expression: 15/35 + 10/21
Final Answer: 19/21
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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 15/35 by 3, and multiply the numerator and denominator of 10/21 by 5 so both fractions share the common base 105.
Working: 15 × 3/35 × 3 = 45/105 and 10 × 5/21 × 5 = 50/105

Step 3: Add the Numerators
Now add the numerators (45 + 50 = 95) and keep the common denominator 105 unchanged.
Working: 45 + 50/105 = 95/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 95 and 105, which is 5. Divide both the numerator and denominator by 5.
Working: 95 ÷ 5/105 ÷ 5 = 19/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 21 produces a repeating decimal (approximately 0.904762, or 90.4762%).
Working: 19 ÷ 21 = 0.904762 (90.4762%)

Key Values:
- Simplified Fraction: 19/21
- Mixed Number Form: 19/21
- Decimal Value: 0.904762
- Percentage: 90.4762%

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Solved with FractionsCalc:
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15/35 + 10/21 = 19/21

Simplified Fraction

19/21

Mixed Number

Proper (19/21)

Decimal Value

0.904762

Percentage

90.4762%

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Step-by-Step Solution: 15/35 + 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 15/35 by 3, and multiply the numerator and denominator of 10/21 by 5 so both fractions share the common base 105.

15 × 3/35 × 3 = 45/105 and 10 × 5/21 × 5 = 50/105

Step 3

Add the Numerators

Now add the numerators (45 + 50 = 95) and keep the common denominator 105 unchanged.

45 + 50/105 = 95/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 95 and 105, which is 5. Divide both the numerator and denominator by 5.

95 ÷ 5/105 ÷ 5 = 19/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 21 produces a repeating decimal (approximately 0.904762, or 90.4762%).

19 ÷ 21 = 0.904762 (90.4762%)

Visual Representation

The diagram below illustrates 15/35 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/21`
Mixed Number Form	`19/21`
Decimal Form	`0.904762`
Percentage	`90.4762%`

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Frequently Asked Questions

What is 15/35 plus 10/21 as a fraction?

15/35 + 10/21 in simplest fraction form is 19/21.

What is 15/35 plus 10/21 as a decimal?

15/35 + 10/21 converted to a decimal is 0.904762.

What is 15/35 plus 10/21 as a percentage?

15/35 + 10/21 expressed as a percentage is 90.4762%.

Does 15/35 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.904762...) because the denominator contains prime factors other than 2 and 5.