What is 4/15 plus 10/21? (Answer: 26/35)

Exact Answer

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Problem: What is 4/15 plus 10/21?
Formula / Expression: 4/15 + 10/21
Final Answer: 26/35
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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 4/15 by 7, and multiply the numerator and denominator of 10/21 by 5 so both fractions share the common base 105.
Working: 4 × 7/15 × 7 = 28/105 and 10 × 5/21 × 5 = 50/105

Step 3: Add the Numerators
Now add the numerators (28 + 50 = 78) and keep the common denominator 105 unchanged.
Working: 28 + 50/105 = 78/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 105, which is 3. Divide both the numerator and denominator by 3.
Working: 78 ÷ 3/105 ÷ 3 = 26/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 26 by denominator 35 produces a repeating decimal (approximately 0.742857, or 74.2857%).
Working: 26 ÷ 35 = 0.742857 (74.2857%)

Key Values:
- Simplified Fraction: 26/35
- Mixed Number Form: 26/35
- Decimal Value: 0.742857
- Percentage: 74.2857%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-15-plus-10-21/
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4/15 + 10/21 = 26/35

Simplified Fraction

26/35

Mixed Number

Proper (26/35)

Decimal Value

0.742857

Percentage

74.2857%

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Step-by-Step Solution: 4/15 + 10/21

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 4/15 by 7, and multiply the numerator and denominator of 10/21 by 5 so both fractions share the common base 105.

4 × 7/15 × 7 = 28/105 and 10 × 5/21 × 5 = 50/105

Step 3

Add the Numerators

Now add the numerators (28 + 50 = 78) and keep the common denominator 105 unchanged.

28 + 50/105 = 78/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 105, which is 3. Divide both the numerator and denominator by 3.

78 ÷ 3/105 ÷ 3 = 26/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 26 by denominator 35 produces a repeating decimal (approximately 0.742857, or 74.2857%).

26 ÷ 35 = 0.742857 (74.2857%)

Visual Representation

The diagram below illustrates 4/15 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`26/35`
Mixed Number Form	`26/35`
Decimal Form	`0.742857`
Percentage	`74.2857%`

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Frequently Asked Questions

What is 4/15 plus 10/21 as a fraction?

4/15 + 10/21 in simplest fraction form is 26/35.

What is 4/15 plus 10/21 as a decimal?

4/15 + 10/21 converted to a decimal is 0.742857.

What is 4/15 plus 10/21 as a percentage?

4/15 + 10/21 expressed as a percentage is 74.2857%.

Does 4/15 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.742857...) because the denominator contains prime factors other than 2 and 5.