Grade 7 Math: Ratios & Proportions: Challenge

# Hard Level Guide Stretch thinking with multi-step problems, application questions, and deeper reasoning. # Understanding Ratios A ratio compares two quantities and can be written with a colon, as a fraction, or with the word 'to.' The order matters: a ratio of boys to girls is not the same as girls to boys. Ratios describe part-to-part or part-to-whole relationships in recipes, maps, and sports statistics. # Equivalent Ratios and Unit Rates Equivalent ratios name the same relationship, like 2:3 and 4:6. Multiply or divide both parts by the same number to find equivalents. A unit rate has a denominator of 1, such as 60 miles per hour. Divide to compare quantities to one unit. # Proportions and Cross-Multiplication A proportion states that two ratios are equal. Cross-multiplication checks whether ratios form a proportion: if a/b = c/d, then ad = bc. Use proportions to scale recipes, convert measurements, and solve percent problems. # Graphs and Tables Ratio tables list pairs of values that share the same ratio. Graphing equivalent ratios produces a straight line through the origin. Constant of proportionality k links y = kx in proportional relationships. Identify whether a graph shows a proportional relationship.