What is 24/35 plus 15/21? (Answer: 7/5)

Exact Answer

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Problem: What is 24/35 plus 15/21?
Formula / Expression: 24/35 + 15/21
Final Answer: 1 2/5 (7/5)
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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 24/35 by 3, and multiply the numerator and denominator of 15/21 by 5 so both fractions share the common base 105.
Working: 24 × 3/35 × 3 = 72/105 and 15 × 5/21 × 5 = 75/105

Step 3: Add the Numerators
Now add the numerators (72 + 75 = 147) and keep the common denominator 105 unchanged.
Working: 72 + 75/105 = 147/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 147 and 105, which is 21. Divide both the numerator and denominator by 21.
Working: 147 ÷ 21/105 ÷ 21 = 7/5

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (7) is greater than the denominator (5), divide 7 by 5: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/5.
Working: 7/5 = 1 2/5

Step 6: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 5 yields an exact terminating decimal of 1.4 (or 140%).
Working: 7 ÷ 5 = 1.4 (140%)

Key Values:
- Simplified Fraction: 7/5
- Mixed Number Form: 1 2/5
- Decimal Value: 1.4
- Percentage: 140%

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Solved with FractionsCalc:
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24/35 + 15/21 = 7/5

Simplified Fraction

7/5

Mixed Number

1 2/5

Decimal Value

1.4

Percentage

140%

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Step-by-Step Solution: 24/35 + 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 24/35 by 3, and multiply the numerator and denominator of 15/21 by 5 so both fractions share the common base 105.

24 × 3/35 × 3 = 72/105 and 15 × 5/21 × 5 = 75/105

Step 3

Add the Numerators

Now add the numerators (72 + 75 = 147) and keep the common denominator 105 unchanged.

72 + 75/105 = 147/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 147 and 105, which is 21. Divide both the numerator and denominator by 21.

147 ÷ 21/105 ÷ 21 = 7/5

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (7) is greater than the denominator (5), divide 7 by 5: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/5.

7/5 = 12/5

Step 6

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 5 yields an exact terminating decimal of 1.4 (or 140%).

7 ÷ 5 = 1.4 (140%)

Visual Representation

The diagram below illustrates 24/35 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/5`
Mixed Number Form	`1 2/5`
Decimal Form	`1.4`
Percentage	`140%`

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Frequently Asked Questions

What is 24/35 plus 15/21 as a fraction?

24/35 + 15/21 in simplest fraction form is 7/5 (or 1 2/5 as a mixed number).

What is 24/35 plus 15/21 as a decimal?

24/35 + 15/21 converted to a decimal is 1.4.

What is 24/35 plus 15/21 as a percentage?

24/35 + 15/21 expressed as a percentage is 140%.

How do you write 24/35 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 7/5 can be written as the mixed number 1 2/5.

Does 24/35 plus 15/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.4) because the denominator in simplest terms contains only prime factors 2 and/or 5.