Adding Fractions and Common Denominators

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the least common denominator (LCD) of the fractions $\frac{2}{3}$ and $\frac{5}{12}$?

  • 12
  • 6
  • 24 (correct)
  • 36

When adding the fractions $\frac{3}{4}$ and $\frac{1}{6}$, which value should be used as the greatest common denominator (GCD) to simplify the result?

  • 2 (correct)
  • 12
  • 3
  • 24

How do you add the fractions $\frac{1}{8}$ and $\frac{1}{4}$?

  • Convert both to eighths and add: $\frac{1}{8} + \frac{2}{8} = \frac{3}{8}$ (correct)
  • Add directly since the denominators are the same.
  • Convert both to fourths and add: $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$
  • Convert to sixteenths first: $\frac{2}{16} + \frac{4}{16} = \frac{6}{16}$

Which method correctly determines the least common multiple (LCM) needed to find the least common denominator for the fractions $\frac{2}{5}$ and $\frac{3}{10}$?

<p>Identify the multiples of each and select the smallest: 10 is LCM. (A)</p> Signup and view all the answers

What is the sum of the fractions $\frac{7}{12}$ and $\frac{1}{4}$ when correctly added using the least common denominator?

<p>$\frac{11}{12}$ (D)</p> Signup and view all the answers

What is the primary purpose of finding the least common denominator when adding fractions?

<p>To ensure fractions can be added directly without simplification (B)</p> Signup and view all the answers

Which of these fractions has the greatest common denominator with $ rac{4}{5}$?

<p>$ rac{8}{10}$ (B)</p> Signup and view all the answers

When adding two fractions with different denominators, which step is essential?

<p>Convert both fractions to have a common denominator (D)</p> Signup and view all the answers

What happens if you add fractions without finding a common denominator first?

<p>The result may be incorrect (A)</p> Signup and view all the answers

Which term describes the largest number that divides two or more numbers evenly?

<p>Greatest common divisor (GCD) (B)</p> Signup and view all the answers

Flashcards are hidden until you start studying

Study Notes

Least Common Denominator (LCD)

  • The LCD of the fractions (\frac{2}{3}) and (\frac{5}{12}) is 12, as it is the smallest multiple of both denominators (3 and 12) that they can both divide into without a remainder.

Greatest Common Denominator (GCD)

  • When adding (\frac{3}{4}) and (\frac{1}{6}), use the GCD of the numerators (3 and 1) if simplifying afterwards. The GCD is 1 in this case, meaning the fractions will not simplify further post addition.

Adding Fractions

  • To add (\frac{1}{8}) and (\frac{1}{4}), first convert (\frac{1}{4}) to eighths: (\frac{1}{4} = \frac{2}{8}).
  • Then, add the numerators: (\frac{1}{8} + \frac{2}{8} = \frac{3}{8}).

Least Common Multiple (LCM) for LCD

  • To determine the LCD for the fractions (\frac{2}{5}) and (\frac{3}{10}), find the LCM of the denominators (5 and 10).
  • The LCM is 10, as it is the smallest number that both denominators can divide into evenly.

Sum of Fractions

  • To add (\frac{7}{12}) and (\frac{1}{4}), find the LCD, which is 12.
  • Convert (\frac{1}{4}) to twelfths: (\frac{1}{4} = \frac{3}{12}).
  • Add the fractions: (\frac{7}{12} + \frac{3}{12} = \frac{10}{12}).
  • Simplifying gives (\frac{5}{6}).

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

More Like This

Use Quizgecko on...
Browser
Browser