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Algebra (all content)

Course: Algebra (all content) > Unit 1

Lesson 3: Substitution and evaluating expressions
Math
Algebra (all content)
Introduction to algebra
Substitution and evaluating expressions
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Evaluating expressions

Google Classroom
Learn to evaluate all sorts of expressions: expressions with one variable, two variables, fractions and decimals, and even expressions in word problems.
Khan Academy video wrapper
Evaluating expressions with two variablesSee video transcript

Try it yourself

Evaluate 2, c, plus, 1 when c, equals, 4.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Let's study another example.

Evaluate 10, minus, start fraction, m, divided by, n, end fraction, plus, n when m, equals, 6 and n, equals, 3.
empty space, 10, minus, start fraction, start color #11accd, m, end color #11accd, divided by, start color #e07d10, n, end color #e07d10, end fraction, plus, start color #e07d10, n, end color #e07d10
equals, 10, minus, start fraction, start color #11accd, 6, end color #11accd, divided by, start color #e07d10, 3, end color #e07d10, end fraction, plus, start color #e07d10, 3, end color #e07d10, space, space, space, space, space, space, space, space, start text, R, e, p, l, a, c, e, space, end text, start color #11accd, m, end color #11accd, start text, space, w, i, t, h, space, end text, start color #11accd, 6, end color #11accd, start text, space, a, n, d, space, end text, start color #e07d10, n, end color #e07d10, start text, space, w, i, t, h, space, end text, start color #e07d10, 3, end color #e07d10
equals, 10, minus, 2, plus, 3
equals, 11

Let's try some practice problems!

Evaluate 10, minus, a when a, equals, 1.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Evaluate 6, b when b, equals, 2.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Evaluate 7, c, minus, 4 when c, equals, 3.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Evaluate start fraction, 8, divided by, d, end fraction, plus, 3 when d, equals, 4.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Evaluate 6, a, ​, ​, plus, 4, b, minus, 6 when a, equals, 1 and b, equals, 3.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Evaluate 5, x, minus, start fraction, x, divided by, y, end fraction when x, equals, 4 and y, equals, 2.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Evaluate start fraction, 3, divided by, 2, end fraction, y, minus, 3, plus, start fraction, 5, divided by, 3, end fraction, z when y, equals, 4 and z, equals, 3.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Evaluate 13, minus, 0, point, 5, w, plus, 6, x when w, equals, 10 and x, equals, start fraction, 1, divided by, 2, end fraction.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Let's try a word problem

The expression 2, m, plus, 10, c gives the amount of money (in dollars) a dessert store makes from selling m muffins and c cakes.
How much money does the dessert store make from selling 3 muffins and 4 cakes?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
dollars

Challenge problem 1

Complete the table to evaluate 2, x at different values of x.
x2, x
12
24
36
4
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
5
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
6
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Challenge problem 2

A flower store uses the expression 2, plus, 5, r to determine the cost (in dollars) of r roses.
Complete the table to find the cost of different numbers of roses.
Number of roses left parenthesis, r, right parenthesisCost left parenthesis, 2, plus, 5, r, right parenthesis
317
6
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
9
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Cam has 32 dollars. How many roses can he afford to buy?
Assume that he wants to buy as many roses as he can.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Extra challenge

Explain to a family member, friend, or classmate why the cost of 6 roses is not double the cost of 3 roses.

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