What is 21/30 plus 15/21? (Answer: 99/70)

Exact Answer

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Problem: What is 21/30 plus 15/21?
Formula / Expression: 21/30 + 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 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).
Working: LCD(30, 21) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 21/30 by 7, and multiply the numerator and denominator of 15/21 by 10 so both fractions share the common base 210.
Working: 21 × 7/30 × 7 = 147/210 and 15 × 10/21 × 10 = 150/210

Step 3: Add the Numerators
Now add the numerators (147 + 150 = 297) and keep the common denominator 210 unchanged.
Working: 147 + 150/210 = 297/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 297 and 210, which is 3. Divide both the numerator and denominator by 3.
Working: 297 ÷ 3/210 ÷ 3 = 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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21/30 + 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: 21/30 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).

LCD(30, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 21/30 by 7, and multiply the numerator and denominator of 15/21 by 10 so both fractions share the common base 210.

21 × 7/30 × 7 = 147/210 and 15 × 10/21 × 10 = 150/210

Step 3

Add the Numerators

Now add the numerators (147 + 150 = 297) and keep the common denominator 210 unchanged.

147 + 150/210 = 297/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 297 and 210, which is 3. Divide both the numerator and denominator by 3.

297 ÷ 3/210 ÷ 3 = 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 21/30 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 21/30 plus 15/21 as a fraction?

21/30 + 15/21 in simplest fraction form is 99/70 (or 1 29/70 as a mixed number).

What is 21/30 plus 15/21 as a decimal?

21/30 + 15/21 converted to a decimal is 1.414286.

What is 21/30 plus 15/21 as a percentage?

21/30 + 15/21 expressed as a percentage is 141.4286%.

How do you write 21/30 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 21/30 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.