What is 3/7 plus 7/16? (Answer: 97/112)

Exact Answer

==================================================
Problem: What is 3/7 plus 7/16?
Formula / Expression: 3/7 + 7/16
Final Answer: 97/112
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 16 = 112.
Working: LCD(7, 16) = 112

Step 2: Convert to Equivalent Fractions with Common Denominator 112
Multiply the numerator and denominator of 3/7 by 16, and multiply the numerator and denominator of 7/16 by 7 so both fractions share the common base 112.
Working: 3 × 16/7 × 16 = 48/112 and 7 × 7/16 × 7 = 49/112

Step 3: Add the Numerators
Now add the numerators (48 + 49 = 97) and keep the common denominator 112 unchanged.
Working: 48 + 49/112 = 97/112

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 112 is 1, confirming that 97/112 cannot be reduced further—it is already in its simplest irreducible form.
Working: 97/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 112 produces a repeating decimal (approximately 0.866071, or 86.6071%).
Working: 97 ÷ 112 = 0.866071 (86.6071%)

Key Values:
- Simplified Fraction: 97/112
- Mixed Number Form: 97/112
- Decimal Value: 0.866071
- Percentage: 86.6071%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-7-plus-7-16/
==================================================

3/7 + 7/16 = 97/112

Simplified Fraction

97/112

Mixed Number

Proper (97/112)

Decimal Value

0.866071

Percentage

86.6071%

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: 3/7 + 7/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 16 = 112.

LCD(7, 16) = 112

Step 2

Convert to Equivalent Fractions with Common Denominator 112

Multiply the numerator and denominator of 3/7 by 16, and multiply the numerator and denominator of 7/16 by 7 so both fractions share the common base 112.

3 × 16/7 × 16 = 48/112 and 7 × 7/16 × 7 = 49/112

Step 3

Add the Numerators

Now add the numerators (48 + 49 = 97) and keep the common denominator 112 unchanged.

48 + 49/112 = 97/112

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 97 and 112 is 1, confirming that 97/112 cannot be reduced further—it is already in its simplest irreducible form.

97/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 112 produces a repeating decimal (approximately 0.866071, or 86.6071%).

97 ÷ 112 = 0.866071 (86.6071%)

Visual Representation

The diagram below illustrates 3/7 plus 7/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/112`
Mixed Number Form	`97/112`
Decimal Form	`0.866071`
Percentage	`86.6071%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/7 plus 7/16 as a fraction?

3/7 + 7/16 in simplest fraction form is 97/112.

What is 3/7 plus 7/16 as a decimal?

3/7 + 7/16 converted to a decimal is 0.866071.

What is 3/7 plus 7/16 as a percentage?

3/7 + 7/16 expressed as a percentage is 86.6071%.

Does 3/7 plus 7/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.866071...) because the denominator contains prime factors other than 2 and 5.