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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`.
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संबंधित प्रश्न
Show the following numbers on a number line. Draw a separate number line for the example.
`3/2 , 5/2 , -3/2`
Show the following numbers on a number line. Draw a separate number line for the example.
`(-5)/8 , 11/8`
Show the following numbers on a number line. Draw a separate number line for the example.
`13/10 , (-17)/10`
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 + 3/(-5)`
Evaluate:
`2 + (-3)/5`
`-3/4` is smaller than –2.
Write the following rational numbers in the descending order.
`8/7, (-9)/8, (-3)/2, 0, 2/5`
The rational numbers `(-12)/(-5)` and `(-7)/17` are on the opposite sides of zero on the number line.
Find a rational number exactly halfway between:
`5/(-13)` and `(-7)/9`
