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Question
Find a rational number exactly halfway between:
`5/(-13)` and `(-7)/9`
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Solution
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 `5/(-13)` and `(-7)/9`
Here, a = `-5/13` and b = `-7/9`
∴ `(a + b)/2 = ((-5)/13 + (-7/9))/2`
= `((-5)/13 - 7/9)/2`
= `((-5 xx 9)/(13 xx 9) - (7 xx 13)/(9 xx 13))/2`
= `((-45)/177 - 91/177)/2`
= `((-45 - 91)/177)/2`
= `(-136)/(117 xx 2)`
= `(-136)/234`
Hence, the exactly of halfway between `5/(-13)` and `(-7)/9` is `-136/234`.
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RELATED QUESTIONS
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`.
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`5/9 + 3/-4`
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Evaluate:
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Find the rational numbers represented by the question marks marked on the following number line
The rational numbers `1/2` and `- 5/2` are on the opposite sides of 0 on the number line.
On a number line, `(-1)/2` is to the ______ of zero (0).
The rational numbers `(-12)/(-5)` and `(-7)/17` are on the opposite sides of zero on the number line.
Represent the following rational numbers on a number line:
`3/8, (-7)/3, 22/(-6)`
Find a rational number exactly halfway between:
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