Simplifying Expressions with Fractions
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Questions and Answers

What is the sum of the numerators in fraction (i)?

  • 6
  • 10
  • 14 (correct)
  • 16

    • What is the sum of the denominators in fraction (iii)?

  • 40
  • 37
  • 43
  • 41 (correct)

    • What is the sum of the numerators in fraction (v)?

  • 6
  • 11
  • 13
  • 8 (correct)

    • What is the sum of the denominators in fraction (vii)?

    <p>13</p> Signup and view all the answers

    What is the result of the operation in part (ii)?

    <p>3</p> Signup and view all the answers

    What is the result of the operation in part (iv)?

    <p>11</p> Signup and view all the answers

    What is the value of the expression 24 ÷ (– 4)?

    <p>6</p> Signup and view all the answers

    What is the value of the expression (– 16) ÷ (– 4)?

    <p>4</p> Signup and view all the answers

    What is the general term of the triangular number pattern starting from 1?

    <p>n(n + 1) / 2</p> Signup and view all the answers

    What is the first term of the triangular number pattern?

    <p>1/2</p> Signup and view all the answers

    What is the 20th term of the triangular number pattern?

    <p>210</p> Signup and view all the answers

    What is the perimeter of the square design?

    <p>32 cm</p> Signup and view all the answers

    What is the perimeter of the isosceles triangular design?

    <p>22 cm</p> Signup and view all the answers

    What is the perimeter of the composite figure?

    <p>48 cm</p> Signup and view all the answers

    What is the measure of angle A in triangle ABC?

    <p>30o</p> Signup and view all the answers

    What is the measure of angle P in triangle MPQ?

    <p>30o</p> Signup and view all the answers

    What is the measure of angle C in triangle ABC?

    <p>60o</p> Signup and view all the answers

    What is the measure of angle K in triangle KLR?

    <p>60o</p> Signup and view all the answers

    What is the measure of angle ao in triangle AQR?

    <p>30o</p> Signup and view all the answers

    What is the measure of angle xo in triangle MPQ?

    <p>30o</p> Signup and view all the answers

    What is the measure of angle 3x in triangle ABC?

    <p>90o</p> Signup and view all the answers

    What is the measure of angle 2xo in triangle KLR?

    <p>60o</p> Signup and view all the answers

    What is the total measure of the interior angles of a quadrilateral?

    <p>360°</p> Signup and view all the answers

    What is the relationship between the sum of the interior angles of triangles ABC and ADC?

    <p>They are equal</p> Signup and view all the answers

    What is the purpose of joining the vertices A and C in the figure?

    <p>To create two triangles</p> Signup and view all the answers

    What is the value of a + b + c in triangle ADC?

    <p>180°</p> Signup and view all the answers

    What is the relationship between the sum of the interior angles of quadrilateral ABCD and the sum of the interior angles of triangles ABC and ADC?

    <p>They are equal</p> Signup and view all the answers

    What is the purpose of finding the sum of the interior angles of triangle ABC and triangle ADC?

    <p>To find the sum of the interior angles of a quadrilateral</p> Signup and view all the answers

    What is the condition for a plane figure to be bilaterally symmetrical?

    <p>The figure can be folded along a line to get two identical parts that coincide with each other</p> Signup and view all the answers

    What is the relationship between the number of axes of bilateral symmetry and the order of rotational symmetry of a bilaterally symmetrical plane figure?

    <p>The number of axes of bilateral symmetry is always twice the order of rotational symmetry</p> Signup and view all the answers

    What is the difference between an axis of symmetry and a line of symmetry?

    <p>An axis of symmetry is a line that divides the figure into two identical parts that coincide with each other, while a line of symmetry is a line that divides the figure into two equal parts in area and shape but does not coincide with each other</p> Signup and view all the answers

    What is the minimum number of axes of bilateral symmetry a plane figure can have?

    <p>1</p> Signup and view all the answers

    What is the order of rotational symmetry of a plane figure that has bilateral symmetry?

    <p>2</p> Signup and view all the answers

    What is the condition for a line to be an axis of symmetry of a plane figure?

    <p>The line divides the figure into two identical parts that coincide with each other</p> Signup and view all the answers

    What is the relationship between the rotational symmetry of a plane figure and its bilateral symmetry?

    <p>A plane figure with bilateral symmetry always has rotational symmetry</p> Signup and view all the answers

    What is the main difference between rotational symmetry and bilateral symmetry?

    <p>Rotational symmetry is about rotating the figure, while bilateral symmetry is about dividing the figure into two parts</p> Signup and view all the answers

    Study Notes

    Simplification of Expressions

    • Simplify expressions by combining like terms
    • Example: 2 + 1 = 3 (i), 5 + 1 = 6 (ii), 3 + 1 = 4 (iii), and 7 + 1 = 8 (iv)
    • Simplify expressions with fractions: 1/5 + 1 = 1.2 (v), 3/2 + 2 = 5 (vi), and 1/3 + 4 = 4.33 (vii)

    Division

    • Division is the inverse operation of multiplication
    • Example: 24 ÷ (-4) = -6 (i), (-16) ÷ (-4) = 4 (ii), and 32 ÷ (-4) = -8 (iii)

    Triangular Number Pattern

    • The general term of the triangular number pattern is n(n + 1)/2
    • The first term of the triangular number pattern is 1
    • The 19th and 20th terms of the triangular number pattern are 190 and 210, respectively
    • The sum of the 19th and 20th terms of the triangular number pattern is equal to the 20th term of the square number pattern

    Perimeter of Shapes

    • The perimeter of a square is 4 times the length of one side
    • The perimeter of an isosceles triangle is the sum of the lengths of all three sides
    • The perimeter of a composite figure is the sum of the perimeters of the individual shapes

    Rotational Symmetry

    • A plane figure has rotational symmetry if it looks the same after a rotation of 360°/n, where n is an integer
    • The order of rotational symmetry is the smallest integer n for which the figure looks the same after a rotation of 360°/n
    • A figure with bilateral symmetry has a line of symmetry, which divides the figure into two identical parts

    Angles in Triangles

    • The sum of the interior angles of a triangle is 180°
    • The sum of the interior angles of a quadrilateral is 360°
    • The sum of the angles in a triangle is equal to the sum of the angles in another triangle, if they have the same shape and size

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    Practice simplifying expressions involving fractions and basic arithmetic operations. Test your skills with these problems and improve your math abilities.

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