Question:Find the ratio of `17 1/2` new pence to £`1.12 1/2` as a fraction in its lowest terms. 

`(17 1/2)/(112 1/2)=35/225=7/45.`

Question:Find the ratio of 3.15 m to 27 cm. 

`(3.15 m)/(27 cm) = (315 cm)/(27 cm) = 35/3`
The ratio is 35:3

Question:Express `17 1/2` new pence as a percentage of £2.50. 

`(17 1/2)/250 = 35/500 = 7/100 = 7/100 * 100% = 7%`

Question:Find 15% of 3 meters. 

`15/100 xx 3 m = 45/100 m = 45/100 xx 100 cm = 45 cm.`

Question:Find 8% of £24.18 correct to the nearest new penny. 

`8/100 xx £24.18`

= `(£193.44)/100`

= £1.9344

= £1.93 (correct to nearest new penny).

Question:Find 73% of £24.18 

First method
`73/100 xx £24.18` 

= `(£1765.14)/100`

= £17.6514

= £17.65 (correct to nearest new penny).Second method
73% of £24.18 = £17.6514 = £17.65 (to nearest new penny)

Question:A father leaves a legacy of £5500 to be divided between his three daughters, Ann, Beryl and Caroline in the ratios 2:4:5. Find how much each receives. 

First Method
If legacy is divided so that Ann receives 2 equal parts, Beryl 4 equal parts and Caroline 5 equal parts, the total must be divided into (2+4+5) equal parts, or 11 equal parts:
`1/11` of £5500=£500.
 Ann receives `2xx£500=£1000` .
Beryl receives `4xx£500=£2000` .
Caroline Receives `5xx£500=£2500` .Second method
Suppose that Ann receives £2k, Beryl £4k and Caroline £5k.
Then 2k+4k+5k=5500.
=>11k=5500 or k=500.
Ann receives £1000, Beryl £2000 and Caroline £2500.

Question:The lengths of the sides of the triangles ABC and XYZ are shown in figure. Are the triangles similar? If so, find an angle equal to the angle A.

Figure Triangle: 

XY:XZ:YZ=6:8:10=3:4:5=AB:BC:AC
 Therefore the triangles ABC and YXY are similar (corresponding sides are XY and AB; XZ and BC; YZ and AC).
 The angle A is opposite BC. It therefore equals the angle opposite XZ, i.e. the angle Y.

Question:Find the average of £1.34, £4.16 and £5.81 

£1.34+£4.16+£5.81 = £11.31
The average=`(£11.31)/3`= £3.77

Question:Find the average of x+y, 2x+3y, 2x-2y and 3x-2y 

(x+y)+(2x+3y)+(2x-2y)+(3x-2y) = x+2x+2x+3x+y+3y-2y-2y = 8x
The average = `8x/4`= 2x