What is 15/21 plus 20/28? (Answer: 10/7)

Exact Answer

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Problem: What is 15/21 plus 20/28?
Formula / Expression: 15/21 + 20/28
Final Answer: 1 3/7 (10/7)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 15/21 by 4, and multiply the numerator and denominator of 20/28 by 3 so both fractions share the common base 84.
Working: 15 × 4/21 × 4 = 60/84 and 20 × 3/28 × 3 = 60/84

Step 3: Add the Numerators
Now add the numerators (60 + 60 = 120) and keep the common denominator 84 unchanged.
Working: 60 + 60/84 = 120/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 120 and 84, which is 12. Divide both the numerator and denominator by 12.
Working: 120 ÷ 12/84 ÷ 12 = 10/7

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (10) is greater than the denominator (7), divide 10 by 7: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/7.
Working: 10/7 = 1 3/7

Step 6: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 7 produces a repeating decimal (approximately 1.428571, or 142.8571%).
Working: 10 ÷ 7 = 1.428571 (142.8571%)

Key Values:
- Simplified Fraction: 10/7
- Mixed Number Form: 1 3/7
- Decimal Value: 1.428571
- Percentage: 142.8571%

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15/21 + 20/28 = 10/7

Simplified Fraction

10/7

Mixed Number

1 3/7

Decimal Value

1.428571

Percentage

142.8571%

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Step-by-Step Solution: 15/21 + 20/28

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 28) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 15/21 by 4, and multiply the numerator and denominator of 20/28 by 3 so both fractions share the common base 84.

15 × 4/21 × 4 = 60/84 and 20 × 3/28 × 3 = 60/84

Step 3

Add the Numerators

Now add the numerators (60 + 60 = 120) and keep the common denominator 84 unchanged.

60 + 60/84 = 120/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 120 and 84, which is 12. Divide both the numerator and denominator by 12.

120 ÷ 12/84 ÷ 12 = 10/7

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (10) is greater than the denominator (7), divide 10 by 7: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/7.

10/7 = 13/7

Step 6

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 7 produces a repeating decimal (approximately 1.428571, or 142.8571%).

10 ÷ 7 = 1.428571 (142.8571%)

Visual Representation

The diagram below illustrates 15/21 plus 20/28 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/7`
Mixed Number Form	`1 3/7`
Decimal Form	`1.428571`
Percentage	`142.8571%`

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Frequently Asked Questions

What is 15/21 plus 20/28 as a fraction?

15/21 + 20/28 in simplest fraction form is 10/7 (or 1 3/7 as a mixed number).

What is 15/21 plus 20/28 as a decimal?

15/21 + 20/28 converted to a decimal is 1.428571.

What is 15/21 plus 20/28 as a percentage?

15/21 + 20/28 expressed as a percentage is 142.8571%.

How do you write 15/21 plus 20/28 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 10/7 can be written as the mixed number 1 3/7.

Does 15/21 plus 20/28 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.428571...) because the denominator contains prime factors other than 2 and 5.