Solve the Fraction: Finding the Value of 18/(18+36)

Fraction Simplification with Common Factor Division

Solve the following problem:

1818+36= \frac{18}{18+36}=

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Step-by-step written solution

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1

Understand the problem

Solve the following problem:

1818+36= \frac{18}{18+36}=

2

Step-by-step solution

First, let's solve the addition problem that appears in the denominator:

18+36=54 18+36=54

Note that in the resulting fraction (18:54), we can reduce both the numerator and denominator by 18.

18:18=1 18:18=1

54:18=3 54:18=3

Therefore, the result we get is: 13 \frac{1}{3}

3

Final Answer

13 \frac{1}{3}

Key Points to Remember

Essential concepts to master this topic
  • Order: Always calculate denominator operations before simplifying fraction
  • Technique: Divide both 18 and 54 by GCF of 18
  • Check: Verify 13 \frac{1}{3} cannot be reduced further ✓

Common Mistakes

Avoid these frequent errors
  • Simplifying before calculating the denominator
    Don't try to simplify 1818+36 \frac{18}{18+36} as 11+2 \frac{1}{1+2} = wrong answer! This violates order of operations by simplifying before completing addition. Always calculate 18+36=54 first, then simplify 1854 \frac{18}{54} .

Practice Quiz

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\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why can't I simplify the 18 in numerator and denominator separately?

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You can only simplify when you have multiplication or division, not addition! The expression 1818+36 \frac{18}{18+36} means 18 divided by the sum of 18+36, so you must add first.

How do I find the greatest common factor of 18 and 54?

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List factors of both numbers: 18 has factors 1,2,3,6,9,18 and 54 has factors 1,2,3,6,9,18,27,54. The largest common factor is 18, so divide both by 18.

What if I get confused about order of operations?

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Remember PEMDAS! Parentheses first, then calculate what's in the denominator (18+36=54) before doing the division 1854 \frac{18}{54} .

How can I double-check my simplified fraction?

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Convert back to decimals: 13 \frac{1}{3} = 0.333... and 1854 \frac{18}{54} = 18÷54 = 0.333... Same result means correct!

Is there a shortcut for this type of problem?

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Yes! When you see addition in the denominator, factor out common terms: 18+36 = 18(1+2) = 18×3 = 54, so 1854=13 \frac{18}{54} = \frac{1}{3} .

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