What is 17/35 plus 15/21? (Answer: 6/5)

Exact Answer

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Problem: What is 17/35 plus 15/21?
Formula / Expression: 17/35 + 15/21
Final Answer: 1 1/5 (6/5)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).
Working: LCD(35, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 17/35 by 3, and multiply the numerator and denominator of 15/21 by 5 so both fractions share the common base 105.
Working: 17 × 3/35 × 3 = 51/105 and 15 × 5/21 × 5 = 75/105

Step 3: Add the Numerators
Now add the numerators (51 + 75 = 126) and keep the common denominator 105 unchanged.
Working: 51 + 75/105 = 126/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 126 and 105, which is 21. Divide both the numerator and denominator by 21.
Working: 126 ÷ 21/105 ÷ 21 = 6/5

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (6) is greater than the denominator (5), divide 6 by 5: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/5.
Working: 6/5 = 1 1/5

Step 6: Decimal & Percentage Representation
Dividing the numerator 6 by denominator 5 yields an exact terminating decimal of 1.2 (or 120%).
Working: 6 ÷ 5 = 1.2 (120%)

Key Values:
- Simplified Fraction: 6/5
- Mixed Number Form: 1 1/5
- Decimal Value: 1.2
- Percentage: 120%

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17/35 + 15/21 = 6/5

Simplified Fraction

6/5

Mixed Number

1 1/5

Decimal Value

1.2

Percentage

120%

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Step-by-Step Solution: 17/35 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).

LCD(35, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 17/35 by 3, and multiply the numerator and denominator of 15/21 by 5 so both fractions share the common base 105.

17 × 3/35 × 3 = 51/105 and 15 × 5/21 × 5 = 75/105

Step 3

Add the Numerators

Now add the numerators (51 + 75 = 126) and keep the common denominator 105 unchanged.

51 + 75/105 = 126/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 126 and 105, which is 21. Divide both the numerator and denominator by 21.

126 ÷ 21/105 ÷ 21 = 6/5

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (6) is greater than the denominator (5), divide 6 by 5: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/5.

6/5 = 11/5

Step 6

Decimal & Percentage Representation

Dividing the numerator 6 by denominator 5 yields an exact terminating decimal of 1.2 (or 120%).

6 ÷ 5 = 1.2 (120%)

Visual Representation

The diagram below illustrates 17/35 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`6/5`
Mixed Number Form	`1 1/5`
Decimal Form	`1.2`
Percentage	`120%`

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Frequently Asked Questions

What is 17/35 plus 15/21 as a fraction?

17/35 + 15/21 in simplest fraction form is 6/5 (or 1 1/5 as a mixed number).

What is 17/35 plus 15/21 as a decimal?

17/35 + 15/21 converted to a decimal is 1.2.

What is 17/35 plus 15/21 as a percentage?

17/35 + 15/21 expressed as a percentage is 120%.

How do you write 17/35 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 6/5 can be written as the mixed number 1 1/5.

Does 17/35 plus 15/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.2) because the denominator in simplest terms contains only prime factors 2 and/or 5.