By Tony Croft

Origin Maths has been written for college kids taking greater or extra schooling classes, who've now not specialized in arithmetic on post-16 skills and want to take advantage of mathematical instruments of their classes. it's supreme for these learning advertising, enterprise reports, administration, technology, engineering, desktop technology, social technology, geography, mixed reports and layout. it will likely be worthwhile in case you lack self assurance and want cautious, regular counsel in mathematical tools. Even for these whose mathematical services is already demonstrated, the ebook could be a beneficial revision and reference advisor. the fashion of the publication additionally makes it compatible for self-study or distance studying.

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**Example text**

2 3 1 2 Â Â5 1 2 1 9 (b) 3 (d) 3 4 3 4 Â 1 3 Â 11 1 2 6. 5 Division by a fraction To divide one fraction by another fraction, we invert the second fraction and then multiply. When we invert a fraction we interchange the numerator and denominator. 14 Solution Find 6 25 Ä 25: We invert 2 5 to obtain 52: Multiplication is then performed. 5 1. Explain the process of division by a fraction. 5 1. Evaluate (a) (e) 3 4 5 6 (i) 2 Ä Ä 1 4 1 (b) 8 5 12 0 (f ) 3 1 Ä @ Â 2A 4 8 9 4 Ä 3 99 Ä1 100 ( j) 6 1 4 (c) Ä2 4 2 7 (g) 3 5 1 À2 þ5 (k) 6 1 4 1 4 Ä 4 (d) 21 1 Ä1 8 0 Ä @2 9 Ä1 4 0 (h) @ 2 1 2 1 1 4 1 2 Ä 3 4 1 AÂ2 þ 5A Test and assignment exercises 2 1.

2. Divide 930 cm in the ratio 1 : 1 : 3. 3. A 6 m length of wood is cut in the ratio 2 : 3 : 4. Calculate the length of each piece. 6. A mass of 40 kg is divided into three portions in the ratio 3 : 4 : 8. Calculate the mass of each portion. 4. Divide 1200 in the ratio 1 : 2 : 3 : 4. 7. Express the following ratios in their simplest forms: (a) 12 : 24 (b) 3 : 6 (c) 3 : 6 : 12 (d) 13 : 7 5. A sum of £2600 is divided between Alan, Bill and Claire in the ratio of 234 : 112 : 214. Calculate the amount that each receives.

Draw Venn diagrams, shading the following sets. (a) A \ B (b) B [ C (c) B [ ðA \ CÞ (d) C (e) B \ C (f ) A \ B \ C (g) B \ ðA \ CÞ 4. The sets A, B and C are given by A ¼ f1; 2; 3; 4; 5; 6g B ¼ f4; 6g, C ¼ f3; 4; 5; 6; 7; 8; 9g. Illustrate A, B and C on a single Venn diagram. 1 Percentage A percentage is a fraction whose denominator is 100. We use the percent 17 symbol %, to represent a percentage: for example, 100 may be written as 17%. 1 Solution Express 19 100 and 35 100 as percentages. Both of these fractions have a denominator of 100.