Algebraic Notation
Use and interpret algebraic notation including: ab for a × b, 3y for y + y + y, a² for a × a, a/b for a ÷ b, coefficients as fractions, and brackets for grouping; read and write algebraic expressions fluently
What a learner can do afterwards
- Read and interpret expressions using standard algebraic conventions for multiplication, division, and powers
- Write algebraic expressions from word descriptions using correct notation
- Understand that juxtaposition means multiplication and that a/b means a divided by b
1 · Read
Algebra has its own shortcuts for writing things quickly. When a number and a letter sit next to each other, like 3a, or two letters sit together, like ab, it means multiply. You never need a times sign in between.
3y means y + y + y, the same as 3 times y. If y is 4, then 3y = 4 + 4 + 4 = 12.
A small raised 2 means squared, which means times itself. So a² means a × a. If a is 5, then a² = 5 × 5 = 25.
a/b means a ÷ b, just like a fraction. If a is 10 and b is 2, then a/b = 10 ÷ 2 = 5. A fraction like (2/3)x works the same way: it means two thirds of x.
Brackets glue terms into one group. In 3(a + 2), work out what's inside the brackets first, then multiply the whole result by 3.
Letters together mean multiply, a small raised number means repeat that multiplication, and brackets mean treat the group as one thing.
Readings 'Words, terms and symbols', 'Reading a/b as division' and 'What the small 2 and the brackets cover' are original to this dataset. 4 extra questions are original to this dataset. Extra questions x1, x2, x3, x4, x6 and x9 follow English-to-math phrase templates by Carl Yao (Portland Community College), WeBWorK Open Problem Library, licensed CC BY-NC-SA 3.0.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.