ACCUPLACER Arithmetic

ACCUPLACER Arithmetic focuses on essential arithmetic skills necessary for success in higher education and various standardized tests.

Whole Numbers and OperationsFractions and DecimalsPercentages
Order of OperationsRatios and ProportionsEstimating and Rounding
Budgeting and Money MathCooking and RecipesShopping and Discounts
Use Scratch Paper for CalculationsCheck Your Reasonableness
Whole Numbers and Op...Fractions and Decima...PercentagesOrder of OperationsRatios and Proportio...Estimating and Round...Budgeting and Money ...Cooking and RecipesShopping and Discoun...Use Scratch Paper fo...Check Your Reasonabl...
Advanced Topics

Ratios and Proportions

Comparing Numbers: Ratios

A ratio shows how two numbers compare. It can be written as 3:2, 3/2, or "3 to 2." Ratios are used to compare quantities, like ingredients in a recipe.

Proportions: Keeping Ratios Equal

A proportion says that two ratios are equal, like \( \frac{a}{b} = \frac{c}{d} \). If you know three numbers, you can solve for the fourth with simple multiplication.

Everyday Uses

Ratios and proportions help with scaling recipes, mixing paint, or converting currency.

How to Solve Proportions

Cross-multiply to find the missing value: \( a \times d = b \times c \).

Examples

  • If 2 apples cost $4, 5 apples cost \( 2/4 = 5/x \Rightarrow x = 10 \) dollars.

  • Recipe calls for 1 cup sugar to 4 cups flour. Double the recipe: 2 cups sugar to 8 cups flour.

In a Nutshell

Ratios and proportions help you compare and solve for unknowns in everyday math.

Key Terms

Ratio
A comparison of two quantities.
Proportion
An equation showing two ratios are equal.
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Estimating and Rounding