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Properties of Addition and Subtraction of Integers

-1 / 2+[-4 / ...

Question

-1/2+ [(-4/3)+3/7] and [(-1/2)+3/7]+(-4/3)

are there same

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Solution

They are same.

Because of
Associative property of addition and substraction.

(a+b)+c = a+(b+c)

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Question 22

Which of the following is an example of distributive property of multiplication over addition for rational numbers.
(a) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = [- \frac{1}{4} \times \frac{2}{3}] + [- \frac{1}{4} \times (\frac{- 4}{7})]$
(b) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = [\frac{1}{4} \times \frac{2}{3}] - (\frac{- 4}{7})$
(c) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = \frac{2}{3} + (- \frac{1}{4}) \times \frac{- 4}{7}$
(d) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = {\frac{2}{3} + (\frac{- 4}{7})} - \frac{1}{4}$

Q. How many 7's are there in the following number sequence which are not immediately preceded by 4 but immediately followed by 2?
3 4 7 2 8 7 2 9 4 7 1 3 5 7 2 9 9 7 7 2 5 1 4 7 2 3

\frac{2}{3} + \frac{1}{7}

\frac{3}{10} + \frac{7}{15}

\frac{4}{9} + \frac{2}{7}

\frac{5}{7} + \frac{1}{3}

\frac{4}{5} + \frac{2}{3}

\frac{3}{4} - \frac{1}{3}

\frac{5}{6} - \frac{1}{3}

If |Z-2+1| ≤2, the greatest and least values of |z + 4| are

Solve

(a) (b)

(c) (d)

(e) (f)

(g) (h)

(i) (j)

(k) (l)

(m) (n)

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