What is 5/12 plus 10/21? (Answer: 25/28)

Exact Answer

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Problem: What is 5/12 plus 10/21?
Formula / Expression: 5/12 + 10/21
Final Answer: 25/28
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 12 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 12 × 21 = 252, keeping the calculation simpler).
Working: LCD(12, 21) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 5/12 by 7, and multiply the numerator and denominator of 10/21 by 4 so both fractions share the common base 84.
Working: 5 × 7/12 × 7 = 35/84 and 10 × 4/21 × 4 = 40/84

Step 3: Add the Numerators
Now add the numerators (35 + 40 = 75) and keep the common denominator 84 unchanged.
Working: 35 + 40/84 = 75/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 75 and 84, which is 3. Divide both the numerator and denominator by 3.
Working: 75 ÷ 3/84 ÷ 3 = 25/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 28 produces a repeating decimal (approximately 0.892857, or 89.2857%).
Working: 25 ÷ 28 = 0.892857 (89.2857%)

Key Values:
- Simplified Fraction: 25/28
- Mixed Number Form: 25/28
- Decimal Value: 0.892857
- Percentage: 89.2857%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-12-plus-10-21/
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5/12 + 10/21 = 25/28

Simplified Fraction

25/28

Mixed Number

Proper (25/28)

Decimal Value

0.892857

Percentage

89.2857%

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Step-by-Step Solution: 5/12 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 12 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 12 × 21 = 252, keeping the calculation simpler).

LCD(12, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 5/12 by 7, and multiply the numerator and denominator of 10/21 by 4 so both fractions share the common base 84.

5 × 7/12 × 7 = 35/84 and 10 × 4/21 × 4 = 40/84

Step 3

Add the Numerators

Now add the numerators (35 + 40 = 75) and keep the common denominator 84 unchanged.

35 + 40/84 = 75/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 75 and 84, which is 3. Divide both the numerator and denominator by 3.

75 ÷ 3/84 ÷ 3 = 25/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 28 produces a repeating decimal (approximately 0.892857, or 89.2857%).

25 ÷ 28 = 0.892857 (89.2857%)

Visual Representation

The diagram below illustrates 5/12 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/28`
Mixed Number Form	`25/28`
Decimal Form	`0.892857`
Percentage	`89.2857%`

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Frequently Asked Questions

What is 5/12 plus 10/21 as a fraction?

5/12 + 10/21 in simplest fraction form is 25/28.

What is 5/12 plus 10/21 as a decimal?

5/12 + 10/21 converted to a decimal is 0.892857.

What is 5/12 plus 10/21 as a percentage?

5/12 + 10/21 expressed as a percentage is 89.2857%.

Does 5/12 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.892857...) because the denominator contains prime factors other than 2 and 5.