Fractions and decimals

前置知识

4 项必需的前置知识（一直追溯到底）

你将学会

• Place fractions on a number line and explain a/b as a copies of 1/b.
• Generate equivalent fractions and use them to compare, add and subtract fractions.
• Convert between decimals with up to three places and fractions with denominators 10, 100 and 1000.
• Multiply a fraction by a whole number.

定义

• For a whole number b > 0, 1/b is the length of each part when the unit interval is cut into b equal parts, and a/b is the length of a such parts.
• a/b and c/d are equivalent (equal as numbers) when ad = bc.
• A decimal such as 0.37 means 37/100.

定理

• a/b = (na)/(nb) for every whole number n > 0.
• a/b + c/d = (ad + bc)/(bd).
• A fraction in lowest terms has a terminating decimal expansion exactly when its denominator has no prime factors other than 2 and 5.

常见误解

• Adding numerators and denominators: 1/2 + 1/3 is not 2/5.
• Thinking a larger denominator means a larger fraction.
• Believing 0.25 > 0.3 because 25 > 3.
• Thinking fractions are only parts of shapes rather than numbers.

通向

可选发现

• Real numbers and irrationality Some numbers, such as √2, cannot be written as fractions at all.
• ← Measuring length and time

学习路径

• Conventional K–12 progression
• Adult beginner pathway

延伸阅读

• Hung-Hsi Wu, Understanding Numbers in Elementary School Mathematics (2011)