What is 7/60 plus 4/21? (Answer: 43/140)

Exact Answer

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Problem: What is 7/60 plus 4/21?
Formula / Expression: 7/60 + 4/21
Final Answer: 43/140
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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 7/60 by 7, and multiply the numerator and denominator of 4/21 by 20 so both fractions share the common base 420.
Working: 7 × 7/60 × 7 = 49/420 and 4 × 20/21 × 20 = 80/420

Step 3: Add the Numerators
Now add the numerators (49 + 80 = 129) and keep the common denominator 420 unchanged.
Working: 49 + 80/420 = 129/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 129 and 420, which is 3. Divide both the numerator and denominator by 3.
Working: 129 ÷ 3/420 ÷ 3 = 43/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 140 produces a repeating decimal (approximately 0.307143, or 30.7143%).
Working: 43 ÷ 140 = 0.307143 (30.7143%)

Key Values:
- Simplified Fraction: 43/140
- Mixed Number Form: 43/140
- Decimal Value: 0.307143
- Percentage: 30.7143%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-60-plus-4-21/
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7/60 + 4/21 = 43/140

Simplified Fraction

43/140

Mixed Number

Proper (43/140)

Decimal Value

0.307143

Percentage

30.7143%

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Step-by-Step Solution: 7/60 + 4/21

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

7 × 7/60 × 7 = 49/420 and 4 × 20/21 × 20 = 80/420

Step 3

Add the Numerators

Now add the numerators (49 + 80 = 129) and keep the common denominator 420 unchanged.

49 + 80/420 = 129/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 129 and 420, which is 3. Divide both the numerator and denominator by 3.

129 ÷ 3/420 ÷ 3 = 43/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 140 produces a repeating decimal (approximately 0.307143, or 30.7143%).

43 ÷ 140 = 0.307143 (30.7143%)

Visual Representation

The diagram below illustrates 7/60 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/140`
Mixed Number Form	`43/140`
Decimal Form	`0.307143`
Percentage	`30.7143%`

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Frequently Asked Questions

What is 7/60 plus 4/21 as a fraction?

7/60 + 4/21 in simplest fraction form is 43/140.

What is 7/60 plus 4/21 as a decimal?

7/60 + 4/21 converted to a decimal is 0.307143.

What is 7/60 plus 4/21 as a percentage?

7/60 + 4/21 expressed as a percentage is 30.7143%.

Does 7/60 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.307143...) because the denominator contains prime factors other than 2 and 5.