Fractions and Decimals Study Guide

Introduction to Fractions

A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator.

To convert a fraction to a decimal, divide the numerator by the denominator. For example, to convert 3/4 to a decimal, divide 3 by 4: 3 ÷ 4 = 0.75

To convert a decimal to a fraction, write the decimal as a fraction with a denominator of 10, 100, 1000, etc., depending on the number of decimal places. For example, to convert 0.75 to a fraction: 0.75 = 75/100 = 3/4

To add or subtract fractions with the same denominator, simply add or subtract the numerators and keep the denominator the same. For fractions with different denominators, find a common denominator and then perform the operation.

1. Convert the fraction 5/8 to a decimal.
Answer: 5 ÷ 8 = 0.625

2. Convert the decimal 0.4 to a fraction.
Answer: 0.4 = 4/10 = 2/5

3. Add the fractions 1/3 and 2/5.
Answer: 1/3 + 2/5 = 5/15 + 6/15 = 11/15

4. Multiply the fractions 2/3 and 3/4.
Answer: 2/3 * 3/4 = 6/12 = 1/2

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals.

Use models, benchmarks, and equivalent forms to judge the size of fractions.

Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.