Mathematics · 2nd preparatory · First Term

Numbers and Their Operations — Operations on Real Numbers

About this lesson

This unit focuses on operations on real numbers, including addition, subtraction, multiplication, and division. It introduces the concept of like radical terms (terms with the same index and radicand) and demonstrates how to add, subtract, and multiply them. The unit also covers rationalizing denominators to express numbers with integer denominators, and it presents the properties of operations on real numbers: closure, commutativity, associativity, distribution, identity, and inverse. Students learn to find additive and multiplicative inverses of expressions involving radicals. Real-life applications include calculating areas and perimeters of shapes (e.g., carpets, tanks, flower beds) and solving problems involving volumes of cuboids and cubes.

Main topics in this lesson

  • Operations on real numbers
  • Like and unlike radical terms
  • Rationalizing denominators
  • Properties of addition and multiplication
  • Additive and multiplicative inverses
  • Applications to geometry and real-life problems

Key terms and vocabulary

  • Closure
  • Commutative
  • Associative
  • Additive identity
  • Multiplicative identity
  • Additive inverse
  • Multiplicative inverse
  • Radical term
  • Like radical terms
  • Radicand
  • Index

Questions and answers on Numbers and Their Operations — Operations on Real Numbers - practice and revision

Multiple choice questions on this lesson in Mathematics for 2nd preparatory, First Term, with practice exercises for revision and exam preparation.

1

ما ناتج تبسيط 6/√2 بضرب البسط والمقام في √2؟

  • 1 3√2
  • 2 6√2
  • 3 3
  • 4 √2/3
2

ما ناتج 2√3 × 5√3؟

  • 1 30
  • 2 10√3
  • 3 10√9
  • 4 30√3
3

ما ناتج (√5)²؟

  • 1 5
  • 2 25
  • 3 √5
  • 4 10
4

ما العدد الذي إذا أضفناه إلى 5√2 كان الناتج صفراً؟

  • 1 −5√2
  • 2 5√2
  • 3 1/(5√2)
  • 4 √2/10
5

ما ناتج 4√3 + 2√3 − √3؟

  • 1 5√3
  • 2 6√3
  • 3 5√9
  • 4 7√3
6

عند تبسيط المقدار 1/√3 بضرب البسط والمقام في √3 يكون الناتج:

  • 1 √3/3
  • 2 1/3
  • 3 √3
  • 4 3/√3

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