What is 16/35 plus 10/21? (Answer: 14/15)

Exact Answer

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Problem: What is 16/35 plus 10/21?
Formula / Expression: 16/35 + 10/21
Final Answer: 14/15
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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 16/35 by 3, and multiply the numerator and denominator of 10/21 by 5 so both fractions share the common base 105.
Working: 16 × 3/35 × 3 = 48/105 and 10 × 5/21 × 5 = 50/105

Step 3: Add the Numerators
Now add the numerators (48 + 50 = 98) and keep the common denominator 105 unchanged.
Working: 48 + 50/105 = 98/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 98 and 105, which is 7. Divide both the numerator and denominator by 7.
Working: 98 ÷ 7/105 ÷ 7 = 14/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 14 by denominator 15 produces a repeating decimal (approximately 0.933333, or 93.3333%).
Working: 14 ÷ 15 = 0.933333 (93.3333%)

Key Values:
- Simplified Fraction: 14/15
- Mixed Number Form: 14/15
- Decimal Value: 0.933333
- Percentage: 93.3333%

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Solved with FractionsCalc:
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16/35 + 10/21 = 14/15

Simplified Fraction

14/15

Mixed Number

Proper (14/15)

Decimal Value

0.933333

Percentage

93.3333%

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Step-by-Step Solution: 16/35 + 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 16/35 by 3, and multiply the numerator and denominator of 10/21 by 5 so both fractions share the common base 105.

16 × 3/35 × 3 = 48/105 and 10 × 5/21 × 5 = 50/105

Step 3

Add the Numerators

Now add the numerators (48 + 50 = 98) and keep the common denominator 105 unchanged.

48 + 50/105 = 98/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 98 and 105, which is 7. Divide both the numerator and denominator by 7.

98 ÷ 7/105 ÷ 7 = 14/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 14 by denominator 15 produces a repeating decimal (approximately 0.933333, or 93.3333%).

14 ÷ 15 = 0.933333 (93.3333%)

Visual Representation

The diagram below illustrates 16/35 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`14/15`
Mixed Number Form	`14/15`
Decimal Form	`0.933333`
Percentage	`93.3333%`

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Frequently Asked Questions

What is 16/35 plus 10/21 as a fraction?

16/35 + 10/21 in simplest fraction form is 14/15.

What is 16/35 plus 10/21 as a decimal?

16/35 + 10/21 converted to a decimal is 0.933333.

What is 16/35 plus 10/21 as a percentage?

16/35 + 10/21 expressed as a percentage is 93.3333%.

Does 16/35 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.933333...) because the denominator contains prime factors other than 2 and 5.