Test for history - Multiplication and Division of Rational Numbers, Rational Numbers, Class 7 Math

Introduction:
History is the study of past events and developments, which helps us understand the present and shape the future. It allows us to explore the actions, decisions, and consequences of individuals, societies, and civilizations. This test aims to assess your knowledge of the topics related to multiplication and division of rational numbers and rational numbers in Class 7 Math.

Test Questions:

1. Explain what rational numbers are and provide examples.
2. How do you represent rational numbers on the number line?
3. Perform the following operations and simplify the answer:
a) (-5/6) × (4/5)
b) (2/3) ÷ (-4/5)
4. Simplify the following expression:
(-3/4) × [8/9 - (3/5 × 5/8)]
5. Determine the rational number that should replace the question mark in each equation:
a) 3/4 = ?/12
b) 5/? = 1/8
6. Convert the following recurring decimals into rational numbers:
a) 0.333...
b) 0.8181...
7. Solve the equation for the unknown variable:
(2/3) × x = 8/9

Answers:

1. Rational numbers:
Rational numbers are numbers that can be expressed in the form of p/q, where p and q are integers and q is not equal to zero. Examples of rational numbers include:
- 1/2
- 3/4
- -2/5
- 0 (since it can be written as 0/1)

2. Representation on the number line:
Rational numbers can be represented on the number line by marking the point corresponding to their values. For example, the rational number 3/4 would be represented by locating the point between 0 and 1, dividing that segment into 4 equal parts, and then marking the point that corresponds to 3 parts.

3. Operations:
a) (-5/6) × (4/5) = (-5 × 4) / (6 × 5) = -20/30 = -2/3
b) (2/3) ÷ (-4/5) = (2/3) × (-5/4) = (-2 × 5) / (3 × 4) = -10/12 = -5/6

4. Simplification:
(-3/4) × [8/9 - (3/5 × 5/8)] = (-3/4) × [8/9 - (15/40)] = (-3/4) × [8/9 - 3/8] = (-3/4) × [64/72 - 27/72] = (-3/4) × 37/72 = -111/288

5. Equations:
a) 3/4 = ?/12
Cross multiplying, we get: 4 × ? = 3 × 12
? =

Assosiative