What is 7/35 plus 2/9? (Answer: 19/45)

Exact Answer

==================================================
Problem: What is 7/35 plus 2/9?
Formula / Expression: 7/35 + 2/9
Final Answer: 19/45
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 9 = 315.
Working: LCD(35, 9) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 7/35 by 9, and multiply the numerator and denominator of 2/9 by 35 so both fractions share the common base 315.
Working: 7 × 9/35 × 9 = 63/315 and 2 × 35/9 × 35 = 70/315

Step 3: Add the Numerators
Now add the numerators (63 + 70 = 133) and keep the common denominator 315 unchanged.
Working: 63 + 70/315 = 133/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 133 and 315, which is 7. Divide both the numerator and denominator by 7.
Working: 133 ÷ 7/315 ÷ 7 = 19/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 45 produces a repeating decimal (approximately 0.422222, or 42.2222%).
Working: 19 ÷ 45 = 0.422222 (42.2222%)

Key Values:
- Simplified Fraction: 19/45
- Mixed Number Form: 19/45
- Decimal Value: 0.422222
- Percentage: 42.2222%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-35-plus-2-9/
==================================================

7/35 + 2/9 = 19/45

Simplified Fraction

19/45

Mixed Number

Proper (19/45)

Decimal Value

0.422222

Percentage

42.2222%

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: 7/35 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 9 = 315.

LCD(35, 9) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 7/35 by 9, and multiply the numerator and denominator of 2/9 by 35 so both fractions share the common base 315.

7 × 9/35 × 9 = 63/315 and 2 × 35/9 × 35 = 70/315

Step 3

Add the Numerators

Now add the numerators (63 + 70 = 133) and keep the common denominator 315 unchanged.

63 + 70/315 = 133/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 133 and 315, which is 7. Divide both the numerator and denominator by 7.

133 ÷ 7/315 ÷ 7 = 19/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 45 produces a repeating decimal (approximately 0.422222, or 42.2222%).

19 ÷ 45 = 0.422222 (42.2222%)

Visual Representation

The diagram below illustrates 7/35 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/45`
Mixed Number Form	`19/45`
Decimal Form	`0.422222`
Percentage	`42.2222%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 7/35 plus 2/9 as a fraction?

7/35 + 2/9 in simplest fraction form is 19/45.

What is 7/35 plus 2/9 as a decimal?

7/35 + 2/9 converted to a decimal is 0.422222.

What is 7/35 plus 2/9 as a percentage?

7/35 + 2/9 expressed as a percentage is 42.2222%.

Does 7/35 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.422222...) because the denominator contains prime factors other than 2 and 5.