ISEE Upper Level Quantitative Reasoning

A comprehensive course to master the mathematical reasoning skills needed for success on the ISEE Upper Level exam.

Numbers, Operations, and Number PropertiesAlgebraic Thinking and ExpressionsFractions, Decimals, and Percents
Ratios, Proportions, and RatesSolving Word Problems and Quantitative ComparisonsGeometry: Shapes, Area, and Volume
Using Math in Everyday LifeInterpreting Data and GraphsBudgeting and Managing Money
Time Management During the TestElimination and Smart Guessing
Numbers, Operations,...Algebraic Thinking a...Fractions, Decimals,...Ratios, Proportions,...Solving Word Problem...Geometry: Shapes, Ar...Using Math in Everyd...Interpreting Data an...Budgeting and Managi...Time Management Duri...Elimination and Smar...
Basic Concepts

Fractions, Decimals, and Percents

Mastering Parts of a Whole

Fractions, decimals, and percents are just different ways of showing parts of something. Mastering how to switch between them is useful for shopping, sports, and more!

Fractions

Fractions show how much of something you have: \( \frac{3}{4} \) of a pizza.

Decimals

Decimals are another way to show parts, like 0.75 instead of \( \frac{3}{4} \).

Percents

Percents mean “out of 100.” So 75% is the same as 0.75 or \( \frac{3}{4} \).

Conversions

  • Fraction to decimal: Divide the top by the bottom.
  • Decimal to percent: Multiply by 100 and add the % sign.
  • Percent to fraction: Write over 100 and simplify.

Why It’s Useful

Discounts, test scores, and recipes all use fractions, decimals, or percents.

Examples

  • Scoring 18 out of 20 on a quiz is \( \frac{18}{20} = 0.9 = 90% \).

  • A 25% off sale means you pay only 75% of the price.

In a Nutshell

Switch easily between fractions, decimals, and percents to solve real-world problems.

Key Terms

Percent
A ratio out of 100, shown with the % symbol.
Decimal
A way to write fractions using place value and a decimal point.
Fraction
A way to show part of a whole, with a numerator and denominator.
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Ratios, Proportions, and Rates