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Verify the property x × (y + z) = x × y + x × z of rational numbers by taking. (a) x = -1/2, y = 3/4, z = 1/4 (b) x = -1/2, y = 2/3, z = 3/4 (c) x = -2/3, y = -4/6, z = -7/9 (d) x = -1/5, y = 2/15, z = -3/10

Solution (a) x = -1/2, y = 3/4, z = 1/4 Solution:- According to the given data we have to verify the property x × (y + z) = x × y... View Article

Verify the property x × (y × z) = (x × y) × z of rational numbers by using (a) x = 1, y = -1/2 and z = 1/4 (b) x = 2/3, y = -3/7 and z = 1/2 (c) x = -2/7, y = -5/6 and z = 1/4

Solution (a) x = 1, y = -1/2 and z = 1/4 Solution:- As per the given data, we have to verify the property x × (y × z) = (x ×... View Article

Verify the property x × y = y × z of rational numbers by using (a) x = 7 and y = 1/2 (b) x = 2/3 and y = 9/4 (c) x = -5/7 and y = 14/15 (d) x = -3/8 and y = -4/9

Solution (a) x = 7 and y = 1/2 Answer As per the given data, we have to verify the property = x × y = y × x Here, the values are, x =... View Article

Tell which property allows you to compute (1/5) × [(5/6) × (7/9)] as [(1/5) × (5/6)] × (7/9)

Solution (1/5) × [(5/6) × (7/9)] as [(1/5) × (5/6)] × (7/9) The given set of rational numbers is according to the rule... View Article

Simplify each of the following by using suitable property. Also name the property. (a) [(1/2) × (1/4)] + [(1/2) × 6] (b) [(1/5) × (2/15)] – [(1/5) × (2/5)] (c) (-3/5) × {(3/7) + (-5/6)}

Solution (a) [(½) × (¼)] + [(½) × 6] Solution:- The given set of rational numbers is according to the rule of... View Article

Verify the property x + y = y + x of rational numbers by taking (a) x = 1/2, y = 1/2 (b) x = -2/3, y = -5/6 (c) x = -3/7, y = 20/21 (d) x = -2/5, y = – 9/10

Solution (a) x = 1/2, y = 1/2 Answer As per the given data, we have to verify the property = x + y = y + x Here the values are, x = 1/2, y = 1/2... View Article

Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer.

Solution According to the properties of rational numbers: Rational numbers are closed under addition, subtraction, and multiplication. Closure... View Article

Verify – (-x) = x for (i) x = 3/5 (ii) x = -7/9 (iii) x = 13/-15

Solution (i) x = 3/5 Answer We have to verify – (-x) = x – x = -3/5 – (-x) = – (-3/5) X = 3/5 (ii) x = -7/9... View Article

Using suitable rearrangement and find the sum: (a) (4/7) + (-4/9) + (3/7) + (-13/9) (b) -5 + (7/10) + (3/7) + (-3) + (5/45) + (-4/5)

Solution (a) (4/7) + (-4/9) + (3/7) + (-13/9) Answer On rearrangeing the rational numbers then adding the numbers with same denominator we... View Article

Select those which can be written as a rational number with denominator 4 in their lowest form: (7/8), (64/16), (36/-12), (-16/17), (5/-4), (140/28)

Solution Rational number with denominator 4 from the given set of numbers in their lowest form are listed below 64/16 = 16/4 36/-12 = 12/-4... View Article

Solve the following: Select the rational numbers from the list which are also the integers. 9/4, 8/4, 7/4, 6/4, 9/3, 8/3, 7/3, 6/3, 5/2, 4/2, 3/1, 3/2, 1/1, 0/1, -1/1, -2/1, -3/2, -4/2, -5/2, -6/2

Solution The rational number from the given list which are also the integers are listed below 8/4 = 2 9/3 = 3 6/3 = 2 4/2 = 2 3/1 = 3 1/1... View Article

Rational numbers can be added (or multiplied) in any order State whether the statement is true (T) or false (F).

The given statement is True Explanation The commutative property or commutative law, when two numbers are added or multiplied... View Article

The rational numbers 1/2 and -5/2 are on the opposite sides of 0 on the number line. State whether the statement is true (T) or false (F).

The given statement is True Explanation A number line is a pictorial representation of numbers on a straight line. It’s a reference... View Article

0 is whole number but it is not a rational number. State whether the statement is true (T) or false (F).

The given statement is False Explanation The whole number is a set of numbers that include all counting numbers (1, 2, 3,4,5,6... View Article

Every whole number is a rational number. State whether the statement is true (T) or false (F).

The given statement is True Explanation A rational number can be defined as any number which can be represented in the form of p/q where q... View Article

Every whole number is an integer. State whether the statement is true (T) or false (F).

The given statement is True Explanation An integer is a number which can be positive or negative or zero. The types of numbers could be... View Article

0 is the smallest rational number State whether the statement is true (T) or false (F).

The given statement is False Explanation Negative rational number below 0 is infinite. So, the smallest rational number does not exist.... View Article

If x and y are two rational numbers such that x > y, then x – y is always a positive rational number. State whether the statement is true (T) or false (F).

The given statement is True Explanation Let us assume that x = 9, y = 5 Then, = x – y = 9 – 5 = 4 So if x and y are two... View Article

The negative of a negative rational number is a positive rational number. State whether the statement is true (T) or false (F).

The given statement is True Explanation Let y be a positive rational number. Then, The negative of y is = – (- y) = y Let... View Article

The rational numbers can be represented on the number line. State whether the statement is true (T) or false (F).

The given statement is True Explanation A number line is a pictorial representation of numbers on a straight line. It’s a reference... View Article

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