What is 10/35 plus 8/21? (Answer: 2/3)

Exact Answer

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Problem: What is 10/35 plus 8/21?
Formula / Expression: 10/35 + 8/21
Final Answer: 2/3
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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 10/35 by 3, and multiply the numerator and denominator of 8/21 by 5 so both fractions share the common base 105.
Working: 10 × 3/35 × 3 = 30/105 and 8 × 5/21 × 5 = 40/105

Step 3: Add the Numerators
Now add the numerators (30 + 40 = 70) and keep the common denominator 105 unchanged.
Working: 30 + 40/105 = 70/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 70 and 105, which is 35. Divide both the numerator and denominator by 35.
Working: 70 ÷ 35/105 ÷ 35 = 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-35-plus-8-21/
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10/35 + 8/21 = 2/3

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

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Step-by-Step Solution: 10/35 + 8/21

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 10/35 by 3, and multiply the numerator and denominator of 8/21 by 5 so both fractions share the common base 105.

10 × 3/35 × 3 = 30/105 and 8 × 5/21 × 5 = 40/105

Step 3

Add the Numerators

Now add the numerators (30 + 40 = 70) and keep the common denominator 105 unchanged.

30 + 40/105 = 70/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 70 and 105, which is 35. Divide both the numerator and denominator by 35.

70 ÷ 35/105 ÷ 35 = 2/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

The diagram below illustrates 10/35 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

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Frequently Asked Questions

What is 10/35 plus 8/21 as a fraction?

10/35 + 8/21 in simplest fraction form is 2/3.

What is 10/35 plus 8/21 as a decimal?

10/35 + 8/21 converted to a decimal is 0.666667.

What is 10/35 plus 8/21 as a percentage?

10/35 + 8/21 expressed as a percentage is 66.6667%.

Does 10/35 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.