What is 4/60 plus 5/21? (Answer: 32/105)

Exact Answer

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Problem: What is 4/60 plus 5/21?
Formula / Expression: 4/60 + 5/21
Final Answer: 32/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 60 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 420 (which is smaller than their product 60 × 21 = 1260, keeping the calculation simpler).
Working: LCD(60, 21) = 420

Step 2: Convert to Equivalent Fractions with Common Denominator 420
Multiply the numerator and denominator of 4/60 by 7, and multiply the numerator and denominator of 5/21 by 20 so both fractions share the common base 420.
Working: 4 × 7/60 × 7 = 28/420 and 5 × 20/21 × 20 = 100/420

Step 3: Add the Numerators
Now add the numerators (28 + 100 = 128) and keep the common denominator 420 unchanged.
Working: 28 + 100/420 = 128/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 128 and 420, which is 4. Divide both the numerator and denominator by 4.
Working: 128 ÷ 4/420 ÷ 4 = 32/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 105 produces a repeating decimal (approximately 0.304762, or 30.4762%).
Working: 32 ÷ 105 = 0.304762 (30.4762%)

Key Values:
- Simplified Fraction: 32/105
- Mixed Number Form: 32/105
- Decimal Value: 0.304762
- Percentage: 30.4762%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-60-plus-5-21/
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4/60 + 5/21 = 32/105

Simplified Fraction

32/105

Mixed Number

Proper (32/105)

Decimal Value

0.304762

Percentage

30.4762%

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Step-by-Step Solution: 4/60 + 5/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 60 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 420 (which is smaller than their product 60 × 21 = 1260, keeping the calculation simpler).

LCD(60, 21) = 420

Step 2

Convert to Equivalent Fractions with Common Denominator 420

Multiply the numerator and denominator of 4/60 by 7, and multiply the numerator and denominator of 5/21 by 20 so both fractions share the common base 420.

4 × 7/60 × 7 = 28/420 and 5 × 20/21 × 20 = 100/420

Step 3

Add the Numerators

Now add the numerators (28 + 100 = 128) and keep the common denominator 420 unchanged.

28 + 100/420 = 128/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 128 and 420, which is 4. Divide both the numerator and denominator by 4.

128 ÷ 4/420 ÷ 4 = 32/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 105 produces a repeating decimal (approximately 0.304762, or 30.4762%).

32 ÷ 105 = 0.304762 (30.4762%)

Visual Representation

The diagram below illustrates 4/60 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/105`
Mixed Number Form	`32/105`
Decimal Form	`0.304762`
Percentage	`30.4762%`

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Frequently Asked Questions

What is 4/60 plus 5/21 as a fraction?

4/60 + 5/21 in simplest fraction form is 32/105.

What is 4/60 plus 5/21 as a decimal?

4/60 + 5/21 converted to a decimal is 0.304762.

What is 4/60 plus 5/21 as a percentage?

4/60 + 5/21 expressed as a percentage is 30.4762%.

Does 4/60 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.304762...) because the denominator contains prime factors other than 2 and 5.