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Middle SchoolNumber System
Ratios & Proportions
Comparing quantities and scaling
Understand ratios for comparing quantities and proportions for scaling problems.
✓ Ratio a:b means for every a of one thing...✓ Simplify ratios by dividing by HCF✓ Proportion: a/b = c/d → ad = bc
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📖 Understanding Ratios & Proportions
A ratio compares two or more quantities of the same kind. The ratio of 3 to 5 is written as 3:5 or 3/5. Ratios can be simplified just like fractions.
A proportion states that two ratios are equal. If a/b = c/d, then ad = bc (cross multiplication). This is very useful for solving missing value problems.
Direct proportion: as one quantity increases, the other increases at the same rate. Example: more workers, more work done.
Inverse proportion: as one quantity increases, the other decreases. Example: more workers, less time needed.
🔑 Key Points to Remember
- ✓Ratio a:b means for every a of one thing, there are b of another
- ✓Simplify ratios by dividing by HCF
- ✓Proportion: a/b = c/d → ad = bc
- ✓Direct proportion: y = kx (k is constant)
- ✓Inverse proportion: y = k/x
#ratio#proportion#scaling#middle school#direct#inverse
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