Question

1. circle the correct answer.

a. \\(\frac{1}{2} + \frac{5}{12}\\) greater than 1 less than 1
b. \\(2\frac{7}{8} - 1\frac{7}{9}\\) greater than 1 less than 1
c. \\(1\frac{1}{12} - \frac{7}{10}\\) greater than \\(\frac{1}{2}\\) less than \\(\frac{1}{2}\\)
d. \\(\frac{3}{7} + \frac{1}{8}\\) greater than \\(\frac{1}{2}\\) less than \\(\frac{1}{2}\\)

1. use >, <, or = to make the following statement true.

\\(4\frac{4}{5} + 3\frac{2}{3}\\) \\(\bigcirc\\) \\(8\frac{1}{2}\\)

Explanation:

Step1: Compute sum for part a

$\frac{1}{2} + \frac{5}{12} = \frac{6}{12} + \frac{5}{12} = \frac{11}{12}$

Step2: Compare result to 1 (part a)

$\frac{11}{12} < 1$

Step3: Compute difference for part b

$2\frac{7}{8} - 1\frac{7}{9} = \frac{23}{8} - \frac{16}{9} = \frac{207}{72} - \frac{128}{72} = \frac{79}{72}$

Step4: Compare result to 1 (part b)

$\frac{79}{72} > 1$

Step5: Compute difference for part c

$1\frac{1}{12} - \frac{7}{10} = \frac{13}{12} - \frac{7}{10} = \frac{65}{60} - \frac{42}{60} = \frac{23}{60}$

Step6: Compare result to $\frac{1}{2}$ (part c)

$\frac{23}{60} < \frac{30}{60} = \frac{1}{2}$

Step7: Compute sum for part d

$\frac{3}{7} + \frac{1}{8} = \frac{24}{56} + \frac{7}{56} = \frac{31}{56}$

Step8: Compare result to $\frac{1}{2}$ (part d)

$\frac{31}{56} > \frac{28}{56} = \frac{1}{2}$

Step9: Compute left-hand sum for Q2

$4\frac{4}{5} + 3\frac{2}{3} = \frac{24}{5} + \frac{11}{3} = \frac{72}{15} + \frac{55}{15} = \frac{127}{15} \approx 8.467$

Step10: Convert right-hand value for Q2

$8\frac{1}{2} = \frac{17}{2} = 8.5$

Step11: Compare values for Q2

$\frac{127}{15} < \frac{17}{2}$

Answer:

1. a. less than 1

b. greater than 1
c. less than $\frac{1}{2}$
d. greater than $\frac{1}{2}$

1. $<$