Fractions, improper fractions, and mixed numbers

Answer explanation

To convert the mixed number 3 \frac{2}{5} to an improper fraction, multiply the whole number (3) by the denominator (5) to get 15, then add the numerator (2) to get 17. Thus, the improper fraction is \frac{17}{5}.

Answer explanation

To convert the improper fraction \(\frac{9}{4}\) to a mixed number, divide 9 by 4. The quotient is 2 and the remainder is 1. Thus, \(\frac{9}{4} = 2 \frac{1}{4}\), making \(2 \frac{1}{4}\) the correct answer.

Answer explanation

The fraction \( \frac{3}{6} \) simplifies to \( \frac{1}{2} \) by dividing both the numerator and denominator by their greatest common divisor, which is 3. Thus, \( \frac{1}{2} \) is the equivalent fraction.

Tags

CCSS.3.NF.A.3A

CCSS.3.NF.A.3B

CCSS.4.NF.A.1

Answer explanation

To add \( \frac{2}{3} \) and \( \frac{1}{6} \), first find a common denominator, which is 6. Convert \( \frac{2}{3} \) to \( \frac{4}{6} \). Now add: \( \frac{4}{6} + \frac{1}{6} = \frac{5}{6} \). Thus, the correct answer is \( \frac{5}{6} \).

Tags

CCSS.5.NF.A.1

CCSS.5.NF.A.2

Answer explanation

To subtract \( \frac{5}{8} \) from \( \frac{3}{4} \), first convert \( \frac{3}{4} \) to eighths: \( \frac{3}{4} = \frac{6}{8} \). Then, \( \frac{6}{8} - \frac{5}{8} = \frac{1}{8} \). Thus, the answer is \( \frac{1}{8} \).

Tags

CCSS.5.NF.A.1

CCSS.5.NF.A.2

Answer explanation

To multiply the fractions \(\frac{2}{5}\) and \(\frac{3}{4}\), multiply the numerators: \(2 \times 3 = 6\), and the denominators: \(5 \times 4 = 20\). This gives \(\frac{6}{20}\), which is the correct answer.

Tags

CCSS.5.NF.B.6

Answer explanation

To divide fractions, multiply by the reciprocal. Thus, \( \frac{7}{8} \div \frac{1}{2} = \frac{7}{8} \times \frac{2}{1} = \frac{14}{8} = \frac{7}{4} \). The correct answer is \( \frac{7}{4} \).

Tags

CCSS.6.NS.A.1

Answer explanation

To simplify \( \frac{12}{16} \), divide both the numerator and denominator by their greatest common divisor, which is 4. This gives \( \frac{12 \div 4}{16 \div 4} = \frac{3}{4} \). Thus, the simplest form is \( \frac{3}{4} \).

Answer explanation

To find the sum of 1 1/2 and 2 2/3, convert to improper fractions: 1 1/2 = 3/2 and 2 2/3 = 8/3. Then, find a common denominator (6): 3/2 = 9/6 and 8/3 = 16/6. Adding gives 25/6, which is 4 1/3.

Tags

CCSS.5.NF.A.1

CCSS.5.NF.A.2

Answer explanation

To convert the mixed number 5 \frac{3}{7} to an improper fraction, multiply the whole number (5) by the denominator (7) and add the numerator (3): 5 \times 7 + 3 = 35 + 3 = 38. Thus, the improper fraction is \frac{38}{7}.