What is 10/35 plus 15/21? (Answer: 1)

Exact Answer

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Problem: What is 10/35 plus 15/21?
Formula / Expression: 10/35 + 15/21
Final Answer: 1
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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 10/35 by 3, and multiply the numerator and denominator of 15/21 by 5 so both fractions share the common base 105.
Working: 10 × 3/35 × 3 = 30/105 and 15 × 5/21 × 5 = 75/105

Step 3: Add the Numerators
Now add the numerators (30 + 75 = 105) and keep the common denominator 105 unchanged.
Working: 30 + 75/105 = 105/105

Step 4: Simplify to an Exact Whole Number
Notice that the numerator (105) is completely divisible by the denominator (105). Dividing 105 by 105 yields the whole number 1 with zero remainder.
Working: 105/105 = 1

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 1 yields an exact terminating decimal of 1 (or 100%).
Working: 1 ÷ 1 = 1 (100%)

Key Values:
- Simplified Fraction: 1
- Mixed Number Form: 1
- Decimal Value: 1
- Percentage: 100%

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Solved with FractionsCalc:
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10/35 + 15/21 = 1

Simplified Fraction

Mixed Number

Decimal Value

Percentage

100%

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Step-by-Step Solution: 10/35 + 15/21

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 10/35 by 3, and multiply the numerator and denominator of 15/21 by 5 so both fractions share the common base 105.

10 × 3/35 × 3 = 30/105 and 15 × 5/21 × 5 = 75/105

Step 3

Add the Numerators

Now add the numerators (30 + 75 = 105) and keep the common denominator 105 unchanged.

30 + 75/105 = 105/105

Step 4

Simplify to an Exact Whole Number

Notice that the numerator (105) is completely divisible by the denominator (105). Dividing 105 by 105 yields the whole number 1 with zero remainder.

105/105 = 1

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 1 yields an exact terminating decimal of 1 (or 100%).

1 ÷ 1 = 1 (100%)

Visual Representation

The diagram below illustrates 10/35 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1`
Mixed Number Form	`1`
Decimal Form	`1`
Percentage	`100%`

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Frequently Asked Questions

What is 10/35 plus 15/21 as a fraction?

10/35 + 15/21 in simplest fraction form is 1.

What is 10/35 plus 15/21 as a decimal?

10/35 + 15/21 converted to a decimal is 1.

What is 10/35 plus 15/21 as a percentage?

10/35 + 15/21 expressed as a percentage is 100%.

Is the answer to 10/35 plus 15/21 a whole number?

Yes, 10/35 + 15/21 simplifies completely to the whole number 1 with no remaining fractional part.