What is 16/28 plus 15/21? (Answer: 9/7)

Exact Answer

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Problem: What is 16/28 plus 15/21?
Formula / Expression: 16/28 + 15/21
Final Answer: 1 2/7 (9/7)
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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 16/28 by 3, and multiply the numerator and denominator of 15/21 by 4 so both fractions share the common base 84.
Working: 16 × 3/28 × 3 = 48/84 and 15 × 4/21 × 4 = 60/84

Step 3: Add the Numerators
Now add the numerators (48 + 60 = 108) and keep the common denominator 84 unchanged.
Working: 48 + 60/84 = 108/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 108 and 84, which is 12. Divide both the numerator and denominator by 12.
Working: 108 ÷ 12/84 ÷ 12 = 9/7

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (9) is greater than the denominator (7), divide 9 by 7: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/7.
Working: 9/7 = 1 2/7

Step 6: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 7 produces a repeating decimal (approximately 1.285714, or 128.5714%).
Working: 9 ÷ 7 = 1.285714 (128.5714%)

Key Values:
- Simplified Fraction: 9/7
- Mixed Number Form: 1 2/7
- Decimal Value: 1.285714
- Percentage: 128.5714%

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16/28 + 15/21 = 9/7

Simplified Fraction

9/7

Mixed Number

1 2/7

Decimal Value

1.285714

Percentage

128.5714%

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Step-by-Step Solution: 16/28 + 15/21

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 16/28 by 3, and multiply the numerator and denominator of 15/21 by 4 so both fractions share the common base 84.

16 × 3/28 × 3 = 48/84 and 15 × 4/21 × 4 = 60/84

Step 3

Add the Numerators

Now add the numerators (48 + 60 = 108) and keep the common denominator 84 unchanged.

48 + 60/84 = 108/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 108 and 84, which is 12. Divide both the numerator and denominator by 12.

108 ÷ 12/84 ÷ 12 = 9/7

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (9) is greater than the denominator (7), divide 9 by 7: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/7.

9/7 = 12/7

Step 6

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 7 produces a repeating decimal (approximately 1.285714, or 128.5714%).

9 ÷ 7 = 1.285714 (128.5714%)

Visual Representation

The diagram below illustrates 16/28 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/7`
Mixed Number Form	`1 2/7`
Decimal Form	`1.285714`
Percentage	`128.5714%`

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Frequently Asked Questions

What is 16/28 plus 15/21 as a fraction?

16/28 + 15/21 in simplest fraction form is 9/7 (or 1 2/7 as a mixed number).

What is 16/28 plus 15/21 as a decimal?

16/28 + 15/21 converted to a decimal is 1.285714.

What is 16/28 plus 15/21 as a percentage?

16/28 + 15/21 expressed as a percentage is 128.5714%.

How do you write 16/28 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 9/7 can be written as the mixed number 1 2/7.

Does 16/28 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.285714...) because the denominator contains prime factors other than 2 and 5.