Simplifying ratios is like reducing fractions to their simplest form. A ratio compares two or more quantities. To simplify a ratio, you divide each quantity by their greatest common factor (GCF). This makes the ratio easier to understand and work with. For example, the ratio 6:8 can be simplified to 3:4 by dividing both numbers by 2.
Simplifying ratios helps in various real-life situations, such as scaling recipes, understanding proportions in art, or comparing statistics. Practice makes perfect, so let's dive into the exercises!
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. Ratio | A. The largest number that divides evenly into two or more numbers |
| 2. Simplify | B. A comparison of two or more quantities |
| 3. Greatest Common Factor (GCF) | C. To reduce a fraction or ratio to its lowest terms |
| 4. Proportion | D. A statement that two ratios are equal |
| 5. Equivalent Ratios | E. Ratios that represent the same comparison |
Complete the following paragraph with the correct words:
To __________ a ratio, you need to find the __________ __________ __________ (GCF) of the numbers in the ratio. Then, __________ each number by the GCF. The new ratio will be in its simplest __________. For example, to simplify 12:18, the GCF is __________. Dividing both numbers by 6 gives the simplified ratio of 2:3.
Explain in your own words why simplifying ratios is useful in everyday life. Provide at least two examples.
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