Proportional Reasoning-2
NoteWhat This Chapter Covers
This chapter continues our journey through proportional reasoning. We start by reminding ourselves what makes two ratios proportional, then take that idea into unexpected corners: the scale printed on a map, blending chutneys and rangoli colours with ratios of three or more terms, and splitting a whole in a given ratio. We then learn to build a pie chart by sharing 360° in proportion to data, and finally meet a fresh idea, inverse proportion, where one quantity rises exactly as fast as the other falls. On the way you will plan a music rehearsal, run taps and pumps into tanks, and see why two cooks slicing onions side by side beat either one working solo.
Learning Outcomes
By the end of this chapter, you will be able to:
- test whether two ratios are proportional using cross-multiplication;
- read and use the Representative Fraction (RF) scale on a map to turn map distance into ground distance;
- handle ratios of three or more terms to scale recipes, blends and colour mixes;
- share a whole in a given multi-term ratio, including ratios with decimals;
- build a pie chart by dividing 360° in proportion to data;
- spot an inverse proportion, write it as xy=k, and apply x_1y_1 = x_2y_2 to questions about workers, pumps, speed and rations.