What is 15/33 plus 15/21? (Answer: 90/77)

Exact Answer

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Problem: What is 15/33 plus 15/21?
Formula / Expression: 15/33 + 15/21
Final Answer: 1 13/77 (90/77)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 33 × 21 = 693, keeping the calculation simpler).
Working: LCD(33, 21) = 231

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 15/33 by 7, and multiply the numerator and denominator of 15/21 by 11 so both fractions share the common base 231.
Working: 15 × 7/33 × 7 = 105/231 and 15 × 11/21 × 11 = 165/231

Step 3: Add the Numerators
Now add the numerators (105 + 165 = 270) and keep the common denominator 231 unchanged.
Working: 105 + 165/231 = 270/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 270 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 270 ÷ 3/231 ÷ 3 = 90/77

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (90) is greater than the denominator (77), divide 90 by 77: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/77.
Working: 90/77 = 1 13/77

Step 6: Decimal & Percentage Representation
Dividing the numerator 90 by denominator 77 produces a repeating decimal (approximately 1.168831, or 116.8831%).
Working: 90 ÷ 77 = 1.168831 (116.8831%)

Key Values:
- Simplified Fraction: 90/77
- Mixed Number Form: 1 13/77
- Decimal Value: 1.168831
- Percentage: 116.8831%

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Solved with FractionsCalc:
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15/33 + 15/21 = 90/77

Simplified Fraction

90/77

Mixed Number

1 13/77

Decimal Value

1.168831

Percentage

116.8831%

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Step-by-Step Solution: 15/33 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 33 × 21 = 693, keeping the calculation simpler).

LCD(33, 21) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 15/33 by 7, and multiply the numerator and denominator of 15/21 by 11 so both fractions share the common base 231.

15 × 7/33 × 7 = 105/231 and 15 × 11/21 × 11 = 165/231

Step 3

Add the Numerators

Now add the numerators (105 + 165 = 270) and keep the common denominator 231 unchanged.

105 + 165/231 = 270/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 270 and 231, which is 3. Divide both the numerator and denominator by 3.

270 ÷ 3/231 ÷ 3 = 90/77

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (90) is greater than the denominator (77), divide 90 by 77: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/77.

90/77 = 113/77

Step 6

Decimal & Percentage Representation

Dividing the numerator 90 by denominator 77 produces a repeating decimal (approximately 1.168831, or 116.8831%).

90 ÷ 77 = 1.168831 (116.8831%)

Visual Representation

The diagram below illustrates 15/33 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`90/77`
Mixed Number Form	`1 13/77`
Decimal Form	`1.168831`
Percentage	`116.8831%`

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Frequently Asked Questions

What is 15/33 plus 15/21 as a fraction?

15/33 + 15/21 in simplest fraction form is 90/77 (or 1 13/77 as a mixed number).

What is 15/33 plus 15/21 as a decimal?

15/33 + 15/21 converted to a decimal is 1.168831.

What is 15/33 plus 15/21 as a percentage?

15/33 + 15/21 expressed as a percentage is 116.8831%.

How do you write 15/33 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 90/77 can be written as the mixed number 1 13/77.

Does 15/33 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.168831...) because the denominator contains prime factors other than 2 and 5.