Understanding Least Common Denominator

• 12

• 24

• 6

• 8

Answer explanation

To find the least common denominator (LCD) of \(\frac{1}{4}\) and \(\frac{1}{6}\), we determine the least common multiple (LCM) of the denominators 4 and 6. The LCM of 4 and 6 is 12, making it the least common denominator.

Which of the following is a fraction?

• 3.5

• 7

• 0.75

Answer explanation

A fraction is a number that represents a part of a whole, expressed as 'a/b'. Among the options, \(\frac{3}{5}\) is the only one in this form, making it the correct answer.

Tags

CCSS.3.NF.A.1

CCSS.3.NF.A.2B

• 9

• 18

• 27

• 6

Answer explanation

To find the least common denominator (LCD) of \(\frac{2}{3}\) and \(\frac{5}{9}\), identify the denominators 3 and 9. The LCD is the smallest multiple of both, which is 18.

• They are equal

• Cannot be determined

Answer explanation

To compare \(\frac{3}{8}\) and \(\frac{5}{12}\), convert them to a common denominator (24). \(\frac{3}{8} = \frac{9}{24}\) and \(\frac{5}{12} = \frac{10}{24}\). Since \(10 > 9\), \(\frac{5}{12}\) is larger.

Tags

CCSS.4.NF.A.2

Answer explanation

To simplify \( \frac{8}{12} \), divide both the numerator and denominator by their greatest common divisor, which is 4. This gives \( \frac{8 \div 4}{12 \div 4} = \frac{2}{3} \). Thus, the correct answer is \( \frac{2}{3} \).

Answer explanation

To convert the mixed number 2 \frac{1}{4} to an improper fraction, multiply the whole number (2) by the denominator (4) and add the numerator (1): 2 \times 4 + 1 = 9. Thus, the improper fraction is \frac{9}{4}.

• 10

• 5

• 15

• 20

Answer explanation

The least common denominator (LCD) of fractions is the smallest multiple of their denominators. The denominators here are 5 and 10. The smallest multiple of both is 10, making it the least common denominator.

Identify the fraction from the following options.

• 0.25

• 25%

• 1:4

Answer explanation

The correct fraction is \(\frac{1}{4}\), which is equivalent to 0.25 and 25%. However, \(\frac{1}{4}\) is the explicit fractional representation, making it the most accurate choice.

• 35

• 12

• 70

• 14

Answer explanation

To find the least common denominator (LCD) of \( \frac{3}{7} \) and \( \frac{2}{5} \), we determine the least common multiple (LCM) of the denominators 7 and 5. The LCM of 7 and 5 is 35, but since we need to include both fractions, the LCD is 70.

• They are equal

• Cannot be determined

Answer explanation

To compare \(\frac{7}{10}\) and \(\frac{3}{4}\), convert \(\frac{3}{4}\) to a fraction with a denominator of 10: \(\frac{3}{4} = \frac{7.5}{10}\). Since \(\frac{7}{10} < \frac{7.5}{10}\), \(\frac{7}{10}\) is smaller.