Rational Numbers
ICSE Class 7 · Mathematics · Chapter 2
What this chapter covers
- Why we need rational numbers
- Equivalent rational numbers and standard form
- Rational numbers on the number line
- Adding and subtracting rational numbers
- Multiplying rational numbers
- Reciprocals and dividing rational numbers
- Decimal representation of rational numbers
- Word problems on rational numbers
Key points
- A rational number can be written as (p)/(q) with p and q integers and q ≠ 0.
- Every integer and every fraction is a rational number.
- A rational number is positive when its numerator and denominator have the same sign, and negative when the signs differ.
- Multiplying or dividing the numerator and denominator by the same non-zero integer gives an equivalent rational number.
- The standard form has a positive denominator and no common factor other than 1.
- Every rational number has a point on the number line; the number further right is greater.
- To add or subtract, use a common denominator; subtracting a number means adding its negative.
- To multiply, multiply numerators and denominators; like signs give a positive answer.
- To divide, multiply by the reciprocal of the divisor; 0 has no reciprocal.
- Every rational number is a terminating or a recurring decimal, and every terminating decimal can be written as a rational number.
Questions answered
Which of these are rational numbers: (0)/(5), (4)/(0), -7, (-3)/(-8)?
(0)/(5), -7 and (-3)/(-8) are rational numbers. (4)/(0) is not, because its denominator is zero.
Write (-45)/(-60) and (28)/(-35) in standard form.
(-45)/(-60) = (45)/(60) = (3)/(4), and (28)/(-35) = (-28)/(35) = (-4)/(5).
Between which two consecutive integers does (-11)/(4) lie on the number line?
(-11)/(4) = -2(3)/(4), so it lies between -3 and -2.
Which is greater, (-5)/(6) or (-7)/(9)? Give a reason.
With denominator 18 they are (-15)/(18) and (-14)/(18). Since -14 > -15, (-7)/(9) is greater.
Find (-7)/(12) + (5)/(8).
(-14)/(24) + (15)/(24) = (1)/(24).
Find (-3)/(10) - (2)/(15).
(-9)/(30) - (4)/(30) = (-13)/(30).
Find (-8)/(15) × (-5)/(12).
Cancel to get (2 × 1)/(3 × 3) = (2)/(9). The product is positive because both factors are negative.
Find (-7)/(8) ÷ (21)/(-16).
(-7)/(8) × (-16)/(21) = (2)/(3).