Topic 9 Test Adding / Subtracting Fractions

What is the sum of these fractions?

Answer explanation

To find the sum of the fractions, we need to add them together. If the fractions are such that they cancel each other out or sum to zero, the correct answer is 0. Thus, the sum of these fractions is 0.

Tags

CCSS.7.NS.A.1C

Answer explanation

To find the common denominator of \(\frac{3}{4}\) and \(\frac{5}{6}\), we determine the least common multiple (LCM) of 4 and 6, which is 12. Thus, the common denominator is 12.

Answer explanation

To add \(\frac{1}{3}\) and \(\frac{3}{5}\), find a common denominator, which is 15. Convert the fractions: \(\frac{1}{3} = \frac{5}{15}\) and \(\frac{3}{5} = \frac{9}{15}\). Now add: \(\frac{5}{15} + \frac{9}{15} = \frac{14}{15}\).

Tags

CCSS.5.NF.A.1

CCSS.5.NF.A.2

Answer explanation

To subtract the fractions \( \frac{7}{8} - \frac{1}{4} \), convert \( \frac{1}{4} \) to eighths: \( \frac{1}{4} = \frac{2}{8} \). Now, subtract: \( \frac{7}{8} - \frac{2}{8} = \frac{5}{8} \). The correct answer is \( \frac{5}{8} \).

Tags

CCSS.5.NF.A.1

CCSS.5.NF.A.2

Answer explanation

To simplify \( \frac{18}{24} \), divide both the numerator and denominator by their greatest common divisor, which is 6. This gives \( \frac{18 \div 6}{24 \div 6} = \frac{3}{4} \). Thus, the correct answer is \( \frac{3}{4} \).

Answer explanation

To find the common denominator of \(\frac{5}{9}\) and \(\frac{2}{3}\), we identify the least common multiple (LCM) of the denominators 9 and 3. The LCM is 9, but the smallest common denominator that works for both fractions is 18.

Answer explanation

To add \(\frac{1}{4}\) and \(\frac{2}{3}\), find a common denominator, which is 12. Convert \(\frac{1}{4}\) to \(\frac{3}{12}\) and \(\frac{2}{3}\) to \(\frac{8}{12}\). Adding gives \(\frac{11}{12}\), not 0.

Tags

CCSS.5.NF.A.1

CCSS.5.NF.A.2

Answer explanation

To subtract the fractions \( \frac{5}{6} \) and \( \frac{1}{3} \), first convert \( \frac{1}{3} \) to sixths: \( \frac{1}{3} = \frac{2}{6} \). Then, \( \frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2} \). The correct answer is 0.

Tags

CCSS.5.NF.A.1

CCSS.5.NF.A.2

Answer explanation

To simplify \( \frac{45}{60} \), divide both the numerator and denominator by their greatest common divisor, which is 15. This gives \( \frac{3}{4} \). Therefore, the correct answer is \( \frac{3}{4} \).

Answer explanation

To add \(\frac{3}{7}\) and \(\frac{2}{5}\), find a common denominator, which is 35. Convert the fractions: \(\frac{3}{7} = \frac{15}{35}\) and \(\frac{2}{5} = \frac{14}{35}\). Adding gives \(\frac{29}{35}\), not 0.

Tags

CCSS.5.NF.A.1

CCSS.5.NF.A.2