What is 13/28 plus 10/21? (Answer: 79/84)

Exact Answer

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Problem: What is 13/28 plus 10/21?
Formula / Expression: 13/28 + 10/21
Final Answer: 79/84
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 28 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 28 × 21 = 588, keeping the calculation simpler).
Working: LCD(28, 21) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 13/28 by 3, and multiply the numerator and denominator of 10/21 by 4 so both fractions share the common base 84.
Working: 13 × 3/28 × 3 = 39/84 and 10 × 4/21 × 4 = 40/84

Step 3: Add the Numerators
Now add the numerators (39 + 40 = 79) and keep the common denominator 84 unchanged.
Working: 39 + 40/84 = 79/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 79 and 84 is 1, confirming that 79/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 79/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 84 produces a repeating decimal (approximately 0.940476, or 94.0476%).
Working: 79 ÷ 84 = 0.940476 (94.0476%)

Key Values:
- Simplified Fraction: 79/84
- Mixed Number Form: 79/84
- Decimal Value: 0.940476
- Percentage: 94.0476%

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Solved with FractionsCalc:
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13/28 + 10/21 = 79/84

Simplified Fraction

79/84

Mixed Number

Proper (79/84)

Decimal Value

0.940476

Percentage

94.0476%

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Step-by-Step Solution: 13/28 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 28 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 28 × 21 = 588, keeping the calculation simpler).

LCD(28, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 13/28 by 3, and multiply the numerator and denominator of 10/21 by 4 so both fractions share the common base 84.

13 × 3/28 × 3 = 39/84 and 10 × 4/21 × 4 = 40/84

Step 3

Add the Numerators

Now add the numerators (39 + 40 = 79) and keep the common denominator 84 unchanged.

39 + 40/84 = 79/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 79 and 84 is 1, confirming that 79/84 cannot be reduced further—it is already in its simplest irreducible form.

79/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 84 produces a repeating decimal (approximately 0.940476, or 94.0476%).

79 ÷ 84 = 0.940476 (94.0476%)

Visual Representation

The diagram below illustrates 13/28 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/84`
Mixed Number Form	`79/84`
Decimal Form	`0.940476`
Percentage	`94.0476%`

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Frequently Asked Questions

What is 13/28 plus 10/21 as a fraction?

13/28 + 10/21 in simplest fraction form is 79/84.

What is 13/28 plus 10/21 as a decimal?

13/28 + 10/21 converted to a decimal is 0.940476.

What is 13/28 plus 10/21 as a percentage?

13/28 + 10/21 expressed as a percentage is 94.0476%.

Does 13/28 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.940476...) because the denominator contains prime factors other than 2 and 5.