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प्रश्न
Find a rational number exactly halfway between:
`1/15` and `1/12`
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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 `1/15` and `1/12`
Here, a = `1/15` and b = `1/12`
∴ `(a + b)/2 = (1/15 + 1/12)/2`
= `((1 xx 4)/(15 xx 4) + (1 xx 5)/(12 xx 5))/2` ...[∵ LCM of 15 and 12 = 60]
= `(4/60 + 5/60)/2`
= `((4 + 5)/60)/2`
= `9/(60 xx 2)`
= `9/120`
= `3/40`
Hence, the exactly halfway between `1/15` and `1/12` is `3/40`.
APPEARS IN
संबंधित प्रश्न
Represent `(-2)/11, (-5)/11, (-9)/11` on the number line.
Show the following numbers on a number line. Draw a separate number line for the example.
`(-5)/8 , 11/8`
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:
`5/9 + (-7)/6`
Draw a number line and represent the following rational numbers on it
`9/4`
Draw a number line and represent the following rational numbers on it
`(-8)/3`
Draw a number line and represent the following rational numbers on it
`15/(-4)`
The rational number `(-8)/(-3)` lies neither to the right nor to the left of zero on the number line.
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`
