What is 5/35 plus 4/21? (Answer: 1/3)

Exact Answer

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Problem: What is 5/35 plus 4/21?
Formula / Expression: 5/35 + 4/21
Final Answer: 1/3
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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 5/35 by 3, and multiply the numerator and denominator of 4/21 by 5 so both fractions share the common base 105.
Working: 5 × 3/35 × 3 = 15/105 and 4 × 5/21 × 5 = 20/105

Step 3: Add the Numerators
Now add the numerators (15 + 20 = 35) and keep the common denominator 105 unchanged.
Working: 15 + 20/105 = 35/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 35 and 105, which is 35. Divide both the numerator and denominator by 35.
Working: 35 ÷ 35/105 ÷ 35 = 1/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 3 produces a repeating decimal (approximately 0.333333, or 33.3333%).
Working: 1 ÷ 3 = 0.333333 (33.3333%)

Key Values:
- Simplified Fraction: 1/3
- Mixed Number Form: 1/3
- Decimal Value: 0.333333
- Percentage: 33.3333%

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Solved with FractionsCalc:
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5/35 + 4/21 = 1/3

Simplified Fraction

1/3

Mixed Number

Proper (1/3)

Decimal Value

0.333333

Percentage

33.3333%

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Step-by-Step Solution: 5/35 + 4/21

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 5/35 by 3, and multiply the numerator and denominator of 4/21 by 5 so both fractions share the common base 105.

5 × 3/35 × 3 = 15/105 and 4 × 5/21 × 5 = 20/105

Step 3

Add the Numerators

Now add the numerators (15 + 20 = 35) and keep the common denominator 105 unchanged.

15 + 20/105 = 35/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 35 and 105, which is 35. Divide both the numerator and denominator by 35.

35 ÷ 35/105 ÷ 35 = 1/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 3 produces a repeating decimal (approximately 0.333333, or 33.3333%).

1 ÷ 3 = 0.333333 (33.3333%)

Visual Representation

The diagram below illustrates 5/35 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/3`
Mixed Number Form	`1/3`
Decimal Form	`0.333333`
Percentage	`33.3333%`

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Frequently Asked Questions

What is 5/35 plus 4/21 as a fraction?

5/35 + 4/21 in simplest fraction form is 1/3.

What is 5/35 plus 4/21 as a decimal?

5/35 + 4/21 converted to a decimal is 0.333333.

What is 5/35 plus 4/21 as a percentage?

5/35 + 4/21 expressed as a percentage is 33.3333%.

Does 5/35 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.333333...) because the denominator contains prime factors other than 2 and 5.