Topics
Basic Concepts in Geometry
Angles
Integers
Operations on Fractions
Decimal Fractions
Bar Graphs
Symmetry
Divisibility
HCF-LCM
Equations
Ratio and Proportion
Percentage
Profit –Loss
Banks and Simple Interest
Triangles and Their Properties
Quadrilaterals
Geometrical Constructions
- Perpendicular Lines
- Drawing a Perpendicular to a Line at a Point on the Line
- Drawing a perpendicular to a line from a point outside the line
- The Perpendicular Bisector
- Drawing the perpendicular bisector of a segment using a compass.
- Carl Gauss’s Clever Trick
Three Dimensional Shapes
Conversion Between Improper Fractions and Mixed Numbers
1. Conversion of an Improper Fraction into a Mixed Number:
Example: If 7 apples are divided equally between 2 people, how many will each one get?
`"7"/"2"` = 7 ÷ 2
3
`2")"overline( 7 )`
– 6
1
(Where , 2 = Divisor, 7 = Dividend, 3 = Quotient, 1 = Remainder)
`"7"/"2"` =3`"1"/"2"`
Each will get 3 full apples and `"1"/"2"` an apple.
2. Conversion of a Mixed Number into an Improper Fraction:
Example: 3 `"2"/"5"` is a mixed number. Convert this into an improper fraction.
3 `"2"/"5"` = 3 + `"2"/"5"` = `"3"/"1"` + `"2"/"5"` = `"3 × 5"/"1 × 5"` + `"2"/"5"`=`"3 × 5 + 2" / "5"` = `"15+ 2 "/"5" ` = `"17"/"5"`
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