Chapter 4
210 Words
Chapter 4: Ratios and Proportions
4.1 Introduction to Ratios
A ratio is a comparison between two numbers or quantities. It tells how many times one value is contained within the other. Ratios can be written in three forms: a:b, a to b, or abfrac{a}{b}ba.
Example: The ratio of 4 to 6 is written as 4:6 or 46frac{4}{6}64, which simplifies to 2:3.
4.2 Simplifying Ratios
To simplify a ratio, divide both terms by their greatest common divisor.
Example: The ratio 8:12 can be simplified by dividing both terms by 4, giving 2:3.
4.3 Proportions
A proportion is an equation that shows two ratios are equivalent.
Example: 23=46frac{2}{3} = frac{4}{6}32=64
4.4 Solving Proportions
To solve a proportion, cross-multiply and solve for the unknown.
Example: 34=x8frac{3}{4} = frac{x}{8}43=8x
Cross-multiply:
3×8=4×x⇒24=4x⇒x=63 times 8 = 4 times x quad Rightarrow quad 24 = 4x quad Rightarrow quad x = 63×8=4×x⇒24=4x⇒x=6Exercises
Exercise 1: Simplify the following ratios:
10:15
18:24
12:16
20:30
30:45
Exercise 2: Solve the following proportions:
25=x15frac{2}{5} = frac{x}{15}52=15x
34=12xfrac{3}{4} = frac{12}{x}43=x12
79=x18frac{7}{9} = frac{x}{18}97=18x
56=25xfrac{5}{6} = frac{25}{x}65=x25
47=8xfrac{4}{7} = frac{8}{x}74=x8
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