What is 4/35 plus 12/21? (Answer: 24/35)

Exact Answer

==================================================
Problem: What is 4/35 plus 12/21?
Formula / Expression: 4/35 + 12/21
Final Answer: 24/35
==================================================

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 4/35 by 3, and multiply the numerator and denominator of 12/21 by 5 so both fractions share the common base 105.
Working: 4 × 3/35 × 3 = 12/105 and 12 × 5/21 × 5 = 60/105

Step 3: Add the Numerators
Now add the numerators (12 + 60 = 72) and keep the common denominator 105 unchanged.
Working: 12 + 60/105 = 72/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 72 and 105, which is 3. Divide both the numerator and denominator by 3.
Working: 72 ÷ 3/105 ÷ 3 = 24/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 24 by denominator 35 produces a repeating decimal (approximately 0.685714, or 68.5714%).
Working: 24 ÷ 35 = 0.685714 (68.5714%)

Key Values:
- Simplified Fraction: 24/35
- Mixed Number Form: 24/35
- Decimal Value: 0.685714
- Percentage: 68.5714%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-35-plus-12-21/
==================================================

4/35 + 12/21 = 24/35

Simplified Fraction

24/35

Mixed Number

Proper (24/35)

Decimal Value

0.685714

Percentage

68.5714%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 4/35 + 12/21

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 4/35 by 3, and multiply the numerator and denominator of 12/21 by 5 so both fractions share the common base 105.

4 × 3/35 × 3 = 12/105 and 12 × 5/21 × 5 = 60/105

Step 3

Add the Numerators

Now add the numerators (12 + 60 = 72) and keep the common denominator 105 unchanged.

12 + 60/105 = 72/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 72 and 105, which is 3. Divide both the numerator and denominator by 3.

72 ÷ 3/105 ÷ 3 = 24/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 24 by denominator 35 produces a repeating decimal (approximately 0.685714, or 68.5714%).

24 ÷ 35 = 0.685714 (68.5714%)

Visual Representation

The diagram below illustrates 4/35 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`24/35`
Mixed Number Form	`24/35`
Decimal Form	`0.685714`
Percentage	`68.5714%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 4/35 plus 12/21 as a fraction?

4/35 + 12/21 in simplest fraction form is 24/35.

What is 4/35 plus 12/21 as a decimal?

4/35 + 12/21 converted to a decimal is 0.685714.

What is 4/35 plus 12/21 as a percentage?

4/35 + 12/21 expressed as a percentage is 68.5714%.

Does 4/35 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.685714...) because the denominator contains prime factors other than 2 and 5.