What is 14/20 plus 15/21? (Answer: 99/70)

Exact Answer

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Problem: What is 14/20 plus 15/21?
Formula / Expression: 14/20 + 15/21
Final Answer: 1 29/70 (99/70)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 21 = 420.
Working: LCD(20, 21) = 420

Step 2: Convert to Equivalent Fractions with Common Denominator 420
Multiply the numerator and denominator of 14/20 by 21, and multiply the numerator and denominator of 15/21 by 20 so both fractions share the common base 420.
Working: 14 × 21/20 × 21 = 294/420 and 15 × 20/21 × 20 = 300/420

Step 3: Add the Numerators
Now add the numerators (294 + 300 = 594) and keep the common denominator 420 unchanged.
Working: 294 + 300/420 = 594/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 594 and 420, which is 6. Divide both the numerator and denominator by 6.
Working: 594 ÷ 6/420 ÷ 6 = 99/70

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (99) is greater than the denominator (70), divide 99 by 70: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/70.
Working: 99/70 = 1 29/70

Step 6: Decimal & Percentage Representation
Dividing the numerator 99 by denominator 70 produces a repeating decimal (approximately 1.414286, or 141.4286%).
Working: 99 ÷ 70 = 1.414286 (141.4286%)

Key Values:
- Simplified Fraction: 99/70
- Mixed Number Form: 1 29/70
- Decimal Value: 1.414286
- Percentage: 141.4286%

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14/20 + 15/21 = 99/70

Simplified Fraction

99/70

Mixed Number

1 29/70

Decimal Value

1.414286

Percentage

141.4286%

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Step-by-Step Solution: 14/20 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 21 = 420.

LCD(20, 21) = 420

Step 2

Convert to Equivalent Fractions with Common Denominator 420

Multiply the numerator and denominator of 14/20 by 21, and multiply the numerator and denominator of 15/21 by 20 so both fractions share the common base 420.

14 × 21/20 × 21 = 294/420 and 15 × 20/21 × 20 = 300/420

Step 3

Add the Numerators

Now add the numerators (294 + 300 = 594) and keep the common denominator 420 unchanged.

294 + 300/420 = 594/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 594 and 420, which is 6. Divide both the numerator and denominator by 6.

594 ÷ 6/420 ÷ 6 = 99/70

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (99) is greater than the denominator (70), divide 99 by 70: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/70.

99/70 = 129/70

Step 6

Decimal & Percentage Representation

Dividing the numerator 99 by denominator 70 produces a repeating decimal (approximately 1.414286, or 141.4286%).

99 ÷ 70 = 1.414286 (141.4286%)

Visual Representation

The diagram below illustrates 14/20 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`99/70`
Mixed Number Form	`1 29/70`
Decimal Form	`1.414286`
Percentage	`141.4286%`

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Frequently Asked Questions

What is 14/20 plus 15/21 as a fraction?

14/20 + 15/21 in simplest fraction form is 99/70 (or 1 29/70 as a mixed number).

What is 14/20 plus 15/21 as a decimal?

14/20 + 15/21 converted to a decimal is 1.414286.

What is 14/20 plus 15/21 as a percentage?

14/20 + 15/21 expressed as a percentage is 141.4286%.

How do you write 14/20 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 99/70 can be written as the mixed number 1 29/70.

Does 14/20 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.414286...) because the denominator contains prime factors other than 2 and 5.