Fractions
ICSE Class 6 · Mathematics · Chapter 14
What this chapter covers
- A fraction as part of a whole
- Showing fractions in pictures and on the number line
- A fraction as division
- Proper, improper and mixed fractions
- Equivalent fractions
- Comparing fractions
- Operations on fractions
Key points
- A fraction shows how many equal parts of a whole are taken; the parts must be equal.
- The denominator tells how many equal parts make the whole; the numerator tells how many are taken.
- A fraction can be shown as a shaded picture or as a point on the number line.
- A fraction is also a division: (a)/(b) means a ÷ b, and the denominator is never 0.
- A proper fraction is less than 1; an improper fraction is 1 or more; a mixed fraction is a whole number with a proper fraction.
- Multiplying or dividing the numerator and denominator by the same non-zero number gives an equivalent fraction.
- Dividing the numerator and denominator by their HCF gives the simplest form.
- To compare or to add and subtract unlike fractions, first make the denominators equal using their LCM.
- To multiply two fractions, multiply the numerators together and the denominators together; "of" means multiply.
Questions answered
In the fraction (4)/(9), which number is the numerator and which is the denominator? What does each one tell you?
4 is the numerator and 9 is the denominator. The whole has 9 equal parts, and 4 of them are taken.
A cricket team has 11 players and 4 of them are bowlers. What fraction of the team are bowlers?
(4)/(11).
Write 6 ÷ 7 as a fraction.
(6)/(7).
Say whether each fraction is proper or improper: (8)/(3), (3)/(8), (5)/(5).
(8)/(3) is improper, (3)/(8) is proper, and (5)/(5) is improper (it equals 1).
Change (17)/(5) into a mixed fraction, and 2(3)/(8) into an improper fraction.
(17)/(5) = 3(2)/(5) and 2(3)/(8) = (19)/(8).
Reduce (24)/(40) to its simplest form.
The HCF of 24 and 40 is 8, so (24)/(40) = (3)/(5).
Which is greater, (2)/(3) or (3)/(5)?
(2)/(3) = (10)/(15) and (3)/(5) = (9)/(15), so (2)/(3) is greater.
Work out (5)/(8) - (1)/(4) and (3)/(4) × (2)/(9).
(5)/(8) - (2)/(8) = (3)/(8), and (3)/(4) × (2)/(9) = (6)/(36) = (1)/(6).