A proportion is a statement that two ratios are equal. Solving proportions involves finding a missing value in one of the ratios. This is often done using cross-multiplication, where you multiply the numerator of one ratio by the denominator of the other ratio, and set the two products equal to each other. Once you have your equation, you can solve for the unknown variable. This is super useful for scaling recipes, converting measurements, and understanding relationships between quantities!
Match the following terms with their correct definitions:
| Term | Definition |
|---|---|
| 1. Ratio | A. A comparison of two quantities using division. |
| 2. Proportion | B. The top number of a fraction. |
| 3. Numerator | C. The bottom number of a fraction. |
| 4. Denominator | D. A statement that two ratios are equal. |
| 5. Cross-Multiplication | E. A method to solve proportions by multiplying diagonally. |
(Answers: 1-A, 2-D, 3-B, 4-C, 5-E)
A ________ is a comparison of two quantities. A ________ is an equation stating that two ratios are equal. To solve a proportion, you can use ________. For example, in the proportion $\frac{a}{b} = \frac{c}{d}$, cross-multiplication gives us $a \times d = b \times$ ________. Solving for the missing variable will give us the solution to the ________.
(Answers: ratio, proportion, cross-multiplication, c, proportion)
Imagine you're baking a cake, and the recipe calls for 2 eggs and 1 cup of flour. If you want to make a bigger cake that uses 6 eggs, how much flour will you need to keep the proportions correct? Explain your reasoning.
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