In your own words, describe the procedure for solving a proportion. What is the difference between a ratio and a proportion?
Ratios and Proportions
In Mathematics, a proportion is a statement of equality between two ratios. Balances can be solved using various methods, including cross-multiplication and setting up a balance using equivalent fractions (Billstein, Libeskind & Lott, 2013). Cross multiplication refers to multiplying the numerator of one bit by the denominator of the other and vice versa. Additionally, this can be done to create an equation that can be solved for a missing value. First, to set up a proportion using equivalent fractions, find two ratios that are equal to each other. Then, set up an equation using these ratios and solve for the missing value.
Example
2 : x = 3 : 9
This is a proportion because the two ratios are equal to each other. Use cross multiplication to solve for x.
Convert to a fraction form
2/x = 3/9
Multiplication method
- 3 = 2.9
- 3x=18
- x=18/3
- x=6
The difference between a ratio and a proportion is that a proportion is an equality between two ratios, while a ratio is a comparison of two values. Ratios can be expressed as fractions, but not all are ratios (Billstein, Libeskind & Lott, 2013). The bit must compare two deals to be a ratio. For example, the fraction ¾ corresponds to the quantity of three to the amount of four. On the other hand, the fraction ¾ does not express a ratio because it is simply three-fourths in an amount and does not compare two values. Solving proportions is a way to find missing deals in ratios. One can either use cross multiplication or set up equivalent fractions to do this. Cross multiplication involves multiplying the numerator of one bit by the denominator of the other and vice versa.
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References
Billstein, R., Libeskind, S., & Lott, J. (2013). Problem Solving Approach to Mathematics for Elementary School Teachers. Pearson New International Edition PDF eBook. Pearson Higher Ed.