What is 11/16 plus 15/21? (Answer: 157/112)

Exact Answer

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Problem: What is 11/16 plus 15/21?
Formula / Expression: 11/16 + 15/21
Final Answer: 1 45/112 (157/112)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 21 = 336.
Working: LCD(16, 21) = 336

Step 2: Convert to Equivalent Fractions with Common Denominator 336
Multiply the numerator and denominator of 11/16 by 21, and multiply the numerator and denominator of 15/21 by 16 so both fractions share the common base 336.
Working: 11 × 21/16 × 21 = 231/336 and 15 × 16/21 × 16 = 240/336

Step 3: Add the Numerators
Now add the numerators (231 + 240 = 471) and keep the common denominator 336 unchanged.
Working: 231 + 240/336 = 471/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 471 and 336, which is 3. Divide both the numerator and denominator by 3.
Working: 471 ÷ 3/336 ÷ 3 = 157/112

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (157) is greater than the denominator (112), divide 157 by 112: it goes in 1 whole time(s) with a remainder of 45, giving the mixed number 1 45/112.
Working: 157/112 = 1 45/112

Step 6: Decimal & Percentage Representation
Dividing the numerator 157 by denominator 112 produces a repeating decimal (approximately 1.401786, or 140.1786%).
Working: 157 ÷ 112 = 1.401786 (140.1786%)

Key Values:
- Simplified Fraction: 157/112
- Mixed Number Form: 1 45/112
- Decimal Value: 1.401786
- Percentage: 140.1786%

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11/16 + 15/21 = 157/112

Simplified Fraction

157/112

Mixed Number

1 45/112

Decimal Value

1.401786

Percentage

140.1786%

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Step-by-Step Solution: 11/16 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 21 = 336.

LCD(16, 21) = 336

Step 2

Convert to Equivalent Fractions with Common Denominator 336

Multiply the numerator and denominator of 11/16 by 21, and multiply the numerator and denominator of 15/21 by 16 so both fractions share the common base 336.

11 × 21/16 × 21 = 231/336 and 15 × 16/21 × 16 = 240/336

Step 3

Add the Numerators

Now add the numerators (231 + 240 = 471) and keep the common denominator 336 unchanged.

231 + 240/336 = 471/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 471 and 336, which is 3. Divide both the numerator and denominator by 3.

471 ÷ 3/336 ÷ 3 = 157/112

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (157) is greater than the denominator (112), divide 157 by 112: it goes in 1 whole time(s) with a remainder of 45, giving the mixed number 1 45/112.

157/112 = 145/112

Step 6

Decimal & Percentage Representation

Dividing the numerator 157 by denominator 112 produces a repeating decimal (approximately 1.401786, or 140.1786%).

157 ÷ 112 = 1.401786 (140.1786%)

Visual Representation

The diagram below illustrates 11/16 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`157/112`
Mixed Number Form	`1 45/112`
Decimal Form	`1.401786`
Percentage	`140.1786%`

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Frequently Asked Questions

What is 11/16 plus 15/21 as a fraction?

11/16 + 15/21 in simplest fraction form is 157/112 (or 1 45/112 as a mixed number).

What is 11/16 plus 15/21 as a decimal?

11/16 + 15/21 converted to a decimal is 1.401786.

What is 11/16 plus 15/21 as a percentage?

11/16 + 15/21 expressed as a percentage is 140.1786%.

How do you write 11/16 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 157/112 can be written as the mixed number 1 45/112.

Does 11/16 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.401786...) because the denominator contains prime factors other than 2 and 5.