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प्रश्न
Find a rational number exactly halfway between:
`1/6` and `1/9`
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उत्तर
We know that, a rational number, which is halfway between two rational number i.e. a and b = `(a + b)/2`
Given rational numbers are `1/6` and `1/9`
Here, a = `1/6` and b = `1/9`
∴ `(a + b)/2 = (1/6 + 1/9)/2`
= `((1 xx 3)/(6 xx 3) + (1 xx 2)/(9 xx 2))/2` ...[∵ LCM of 6 and 9 = 18]
= `(3/18 + 2/18)/2`
= `((3 + 2)/18)/2`
= `(5/18)/2`
= `5/(18 xx 2)`
= `5/36`
Hence, the exactly halfway between `1/6` and `1/9` is `5/36`.
APPEARS IN
संबंधित प्रश्न
Observe the number line and answer the questions.
- Which number is indicated by point B?
- Which point indicates the number `1 3/4`?
- State whether the statement ‘the point D denotes the number `5/2`’ is true or false.
The number `sqrt2` is shown on a number line. Steps are given to show `sqrt3` on the number line using `sqrt2`. Fill in the boxes properly and complete the activity.
Activity :
- The point Q on the number line shows the number ______.
- A line perpendicular to the number line is drawn through the point Q. Point R is at unit distance from Q on the line.
- Right angled ∆ORQ is obtained by drawing seg OR.
`l ("OQ") = sqrt2` , `l("QR") = 1`
`therefore` by Pythagoras theorem,
`[l("OR")]^2 = [l("OQ")]^2 + [l("QR")]^2 `
= `square^2`+ `square^2` = `square` + `square`
= `square`
∴ l(OR) = `square`
Draw an arc with centre O and radius OR. Mark the point of intersection of the line and the arc as C. The point C shows the number `sqrt3`.
Evaluate:
`4/(-9) + 1`
The points S, Y, N, C, R, A, T, I and O on the number line are such that CN = NY = YS and RA = AT = TI = IO. Find the rational numbers represented by the letters Y, N, A, T and I
Draw a number line and represent the following rational numbers on it
`(-8)/3`
`-3/4` is smaller than –2.
The rational numbers can be represented on the number line.
The rational numbers `1/2` and `- 5/2` are on the opposite sides of 0 on the number line.
Arrange the numbers `1/4, 13/16, 5/8` in the descending order.
Represent the following rational numbers on a number line:
`3/8, (-7)/3, 22/(-6)`
