What is 4/42 plus 5/21? (Answer: 1/3)

Exact Answer

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Problem: What is 4/42 plus 5/21?
Formula / Expression: 4/42 + 5/21
Final Answer: 1/3
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 42 is an exact multiple of 21 (21 × 2 = 42). The Least Common Denominator (LCD) is simply 42, meaning we only need to scale one fraction.
Working: LCD(42, 21) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 4/42 by 1, and multiply the numerator and denominator of 5/21 by 2 so both fractions share the common base 42.
Working: 4 × 1/42 × 1 = 4/42 and 5 × 2/21 × 2 = 10/42

Step 3: Add the Numerators
Now add the numerators (4 + 10 = 14) and keep the common denominator 42 unchanged.
Working: 4 + 10/42 = 14/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 14 and 42, which is 14. Divide both the numerator and denominator by 14.
Working: 14 ÷ 14/42 ÷ 14 = 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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4/42 + 5/21 = 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: 4/42 + 5/21

Step 1

Find the Least Common Denominator (LCD)

Notice that 42 is an exact multiple of 21 (21 × 2 = 42). The Least Common Denominator (LCD) is simply 42, meaning we only need to scale one fraction.

LCD(42, 21) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 4/42 by 1, and multiply the numerator and denominator of 5/21 by 2 so both fractions share the common base 42.

4 × 1/42 × 1 = 4/42 and 5 × 2/21 × 2 = 10/42

Step 3

Add the Numerators

Now add the numerators (4 + 10 = 14) and keep the common denominator 42 unchanged.

4 + 10/42 = 14/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 14 and 42, which is 14. Divide both the numerator and denominator by 14.

14 ÷ 14/42 ÷ 14 = 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 4/42 plus 5/21 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 4/42 plus 5/21 as a fraction?

4/42 + 5/21 in simplest fraction form is 1/3.

What is 4/42 plus 5/21 as a decimal?

4/42 + 5/21 converted to a decimal is 0.333333.

What is 4/42 plus 5/21 as a percentage?

4/42 + 5/21 expressed as a percentage is 33.3333%.

Does 4/42 plus 5/21 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.