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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 HCFProportion: a/b = c/d → ad = bc

📖 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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