3.1.3 Comparing ratios and fractions

• In the fraction $\frac{2}{5}$, what is the denominator?


  5
• What are the two main components of a fraction that need to be identified when converting to a ratio?

  Numerator and denominator
• Steps to find equivalent ratios and fractions

  1️⃣ Multiply or divide both parts by the same number

  2️⃣ Simplify the ratio or fraction
• Match the original ratio/fraction with its equivalent form:

  2:3 ↔️ 4:6

  $\frac{4}{10}$ ↔️ $\frac{2}{5}$
• What are equivalent ratios and fractions used to represent?

  The same comparison
• What is the purpose of simplifying a ratio or fraction?

  Reduce to simplest form
• What should you always do after finding an equivalent ratio or fraction?

  Simplify to lowest terms
• What are the two numbers in the ratio 3:4?

  3 and 4
• If you have 3 apples and 5 bananas, what is the ratio of apples to bananas?

  3:5
• What is a fraction used to represent?

  A part of a whole
• In the fraction $\frac{2}{5}$, what is the numerator?


  2
• Steps of the cross-multiplication method

  1️⃣ Multiply the numerator of each fraction by the denominator of the other

  2️⃣ Compare the results

  3️⃣ Determine which fraction is larger or smaller
• Steps for applying ratio and fraction comparisons in word problems

  1️⃣ Identify Key Numbers

  2️⃣ Set Up the Comparison

  3️⃣ Solve the Problem
• Match the fraction with its corresponding ratio:

  $\frac{3}{7}$ ↔️ 3:7

  $\frac{1}{4}$ ↔️ 1:4

  $\frac{5}{6}$ ↔️ 5:6
• How do you find the missing quantity in a ratio or fraction comparison?

  Use proportions
• Simplifying fractions or ratios is not necessary for comparison.

  False
• What should you do with fractions and ratios whenever possible?

  Simplify them
• How many eggs are needed for 6 cups of flour in the example?

  4 eggs
• Which fraction is smaller: $\frac{2}{3}$ or $\frac{3}{4}$?


  $\frac{2}{3}$
• How do you compare ratios and fractions with different denominators?

  Make denominators the same
• What does the cross-multiplication method show about $\frac{2}{3}$ and \frac{3}{4}</latex>?


  $\frac{2}{3}$ < $\frac{3}{4}$
• What ratio is equivalent to the fraction $\frac{2}{5}$?


  2:5
• Why should fractions and ratios be simplified when possible?

  To make calculations easier