Using the appropriate properties of operations of rational numbers, evaluate the following:
3/134/5-7/5-4/55/13

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Solution

$\frac{3}{13} \times \frac{4}{5} - \frac{7}{5} - \frac{4}{5} \times \frac{5}{13} = \frac{12}{65} - \frac{7}{5} - \frac{20}{65} = \frac{12 - 91 - 20}{65} = \frac{- 99}{65 \frac{}{}}$

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Q. Using the appropriate properties of operations of rational numbers, evaluate the following:

\frac{3}{13} \times \frac{4}{5} \times \frac{7}{5} \times \frac{4}{13} \times \frac{5}{13}

Q. Using the appropriate properties of operations of rational numbers, evaluate the following:

\frac{5}{7} \times \frac{2}{11} \times \frac{- 8}{7} \times \frac{6}{11}

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

(i) $\frac{2}{5} + \frac{7}{3} + \frac{- 4}{5} + \frac{- 1}{3}$

(ii) $\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}$

(iii) $\frac{2}{5} + \frac{8}{3} + \frac{- 11}{15} + \frac{4}{5} + \frac{- 2}{3}$

(iv) $\frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}$

Evaluate each of the following: $(i) \frac{2}{3} - \frac{3}{5} (i i) \frac{- 4}{7} - \frac{2}{- 3} (i i i) \frac{4}{7} - \frac{- 5}{- 7} (i v) - 2 - \frac{5}{9} (v) \frac{- 3}{- 8} - \frac{- 2}{7} (v i) \frac{- 4}{13} - \frac{- 5}{26} (v i i) \frac{- 5}{14} - \frac{- 2}{7} (v i i i) \frac{13}{15} - \frac{12}{25} (i x) \frac{- 6}{13} - \frac{- 7}{13} (x) \frac{7}{24} - \frac{19}{36} (x i) \frac{5}{63} - \frac{- 8}{21}$

Q. Simplify. Use the correct properties of operations every time.

(1) −28 × 1
(2) 4 + 0
(3) 0 × (−10)
(4) (−5) − 0
(5) 13 − (−3)
(6) 29 + 99 + 1
(7) 593 × 25 × 4
(8) 95 + 741 + 5
(9) 5 × 379 × 2
(10) 87 × 95 + 87 × 5

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Using the appropriate properties of operations of rational numbers, evaluate the following: 3/13*4/5-7/5-4/5*5/13

313×45-75-45×513=1265-75-2065=12-91-2065=-9965

Using the appropriate properties of operations of rational numbers, evaluate the following:
3/134/5-7/5-4/55/13

$\frac{3}{13} \times \frac{4}{5} - \frac{7}{5} - \frac{4}{5} \times \frac{5}{13} = \frac{12}{65} - \frac{7}{5} - \frac{20}{65} = \frac{12 - 91 - 20}{65} = \frac{- 99}{65 \frac{}{}}$