Question

start
start
in 3-8, without multiplying, decide which symbol belongs in
the box: <, >, or =.

1. $5\frac{1}{3} \times 2\frac{3}{4} \square 5\frac{1}{3}$
2. $10\frac{3}{4} \times \frac{2}{2} \square 10\frac{3}{4}$
3. $\frac{1}{12} \times 1\frac{6}{7} \square 1\frac{6}{7}$
4. $5\frac{1}{5} \times 5\frac{1}{10} \square 5\frac{1}{10}$
5. $\frac{1}{4} \times 4\frac{1}{2} \square 4\frac{1}{2}$
6. $3\frac{9}{10} \times 1\frac{2}{3} \square 1\frac{2}{3}$

in 9 and 10, without multiplying, order the following products
from least to greatest.

1. $\frac{5}{6} \times 1\frac{8}{9}$ $\frac{5}{6} \times \frac{1}{4}$ $\frac{5}{6} \times 10\frac{1}{12}$ $\frac{5}{6} \times \frac{6}{6}$
2. $\frac{1}{12} \times \frac{1}{4}$ $3\frac{1}{4} \times \frac{1}{4}$ $4\frac{1}{3} \times \frac{1}{4}$ $\frac{1}{10} \times \frac{1}{4}$

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topic 8 | lesson 8-8

Explanation:

Step1: Compare factor to 1

$2\frac{3}{4} > 1$, so $5\frac{1}{3} \times 2\frac{3}{4} > 5\frac{1}{3}$

Step2: Compare factor to 1

$\frac{2}{2}=1$, so $10\frac{3}{4} \times \frac{2}{2} = 10\frac{3}{4}$

Step3: Compare factor to 1

$\frac{1}{12} < 1$, so $\frac{1}{12} \times 1\frac{6}{7} < 1\frac{6}{7}$

Step4: Compare factor to 1

$5\frac{1}{5} > 1$, so $5\frac{1}{5} \times 5\frac{1}{10} > 5\frac{1}{10}$

Step5: Compare factor to 1

$\frac{1}{4} < 1$, so $\frac{1}{4} \times 4\frac{1}{2} < 4\frac{1}{2}$

Step6: Compare factor to 1

$3\frac{9}{10} > 1$, so $3\frac{9}{10} \times 1\frac{2}{3} > 1\frac{2}{3}$

Step7: Order second factors

$\frac{1}{4} < \frac{6}{6} < 1\frac{8}{9} < 10\frac{1}{12}$. Multiply by $\frac{5}{6}$ (positive, order stays):
$\frac{5}{6} \times \frac{1}{4} < \frac{5}{6} \times \frac{6}{6} < \frac{5}{6} \times 1\frac{8}{9} < \frac{5}{6} \times 10\frac{1}{12}$

Step8: Order first factors

$\frac{1}{12} < \frac{1}{10} < 3\frac{1}{4} < 4\frac{1}{3}$. Multiply by $\frac{1}{4}$ (positive, order stays):
$\frac{1}{12} \times \frac{1}{4} < \frac{1}{10} \times \frac{1}{4} < 3\frac{1}{4} \times \frac{1}{4} < 4\frac{1}{3} \times \frac{1}{4}$

Answer:

1. $>$
2. $=$
3. $<$
4. $>$
5. $<$
6. $>$
7. $\frac{5}{6} \times \frac{1}{4}, \frac{5}{6} \times \frac{6}{6}, \frac{5}{6} \times 1\frac{8}{9}, \frac{5}{6} \times 10\frac{1}{12}$
8. $\frac{1}{12} \times \frac{1}{4}, \frac{1}{10} \times \frac{1}{4}, 3\frac{1}{4} \times \frac{1}{4}, 4\frac{1}{3} \times \frac{1}{4}$