Simplifying Algebra

Simplifying Algebra

Saying Expression

• Hi there. How are you doing? 

• "Hi, What’s up?" 

Saying Expression

• Good morning! Everyone, please listen. Today, we are going to learn how to simplify algebraic expressions.

• Good morning! Learn us learn about simplifying algebraic expression.

Open Ended

I will give you a minute to think of another expression/statement and tell me if that statement/expression is simpler or not.

In Mathematics, we want to write expressions as simply as possible, but do not want to change their meaning or value.

Simplify the expression

- make the expression simpler to understand or look at without changing the value of the expression. 

Multiple Choice

In the given algebraic expression, what are the variables?

3x + 4y – 5 = 2

• x only

• y only

• x and y

• 2, 3, 4, 5

Multiple Choice

Write an algebraic expression to represent the statement.

There are k marbles in a box at first. 6 marbles are added to the original number of marbles in the box.

• k + 6

• 6k

• k - 6

• 6 - k

Multiple Choice

Write an algebraic expression to represent the statement.

In a football match, the red team scores 3 goals in the first half and in the second half, another y goals. How many goals did the red team score in the game altogether?

• 3 + x

• 3 + y

• y - 3

• 3 - y

Multiple Choice

Write an algebraic expression to represent the statement.

Barney cuts a 16cm length off a p cm length of ribbon. What is the length of the remaining piece of ribbon?

• 16 + p

• p + 16

• 16 - p

• p - 16

Multiple Choice

Write an algebraic expression to represent the statement.

Alexa is y years old. Her brother is 7 years older than her. Write an expression for her brother’s age in terms of y.

• 7 - y

• y - 7

• y + 7

• $\frac{y}{7}$

Multiple Choice

Write an algebraic expression to represent the statement.

There are t people on a train as it draws into Bolton station. At Bolton, m people get on and r people get off. How many people are on the train now?

• t - m - r

• t + m - r

• tm - r

• rm + t

Multiple Choice

Write an algebraic expression to represent the statement.

There are m Wow! choco bars in a multipack. Brian buys 6 multipacks and x separate bars. How many bars does he have?

• 6 + m + x

• 6 + m - x

• 6m + x

• 6m - x

Multiple Choice

Write an algebraic expression to represent the statement.

Pens are sold in packs of 5. A teacher buys p packs. Write an expression for the total number of pens bought.

• 5 + p

• $\frac{p}{5}$
  

• $\frac{5}{p}$

• 5p

Multiple Choice

Write an algebraic expression to represent the statement.

Mrs. Rabbit shares 40 carrots out equally between her babies. She has r babies. How many carrots does each baby get?

• $\frac{r}{40}$
  

• $\frac{40}{r}$

• 40r

• 40 - r

Multiple Choice

Write an algebraic expression to represent the statement.

Jenny has n sweets. She shares her sweets equally among 3 friends. Write an expression for the number of sweets each friend get.

• $\frac{n}{3}$

• 3n

• $\frac{3}{n}$

• n - 3

Multiple Choice

Write an algebraic expression to represent the statement.

The class is raising money for a school trip. They raise $w by washing cars, $b by packing bags in the supermarket and $18 from a cake sale. How much money have they raised altogether?

• w - b + 18

• w + b + 18

• w + b - 18

• w - b - 18

Multiple Choice

Write an algebraic expression to represent the statement.

Buns are sold in packs of 3. Cheese slices are sold in packs of 10. Robert buys b packs of buns and c packs of cheese slices. Write an expression for the total number of buns and cheese slices he buys.

• 3b - 10c

• 3b + 10c

• $\frac{3b}{10c}$
  

• 3 + b + 10 + c

Open Ended

When we say two expressions are equivalent what does that mean??

Open Ended

If two expressions are equivalent, must they always look exactly the same? What makes you think so?

If two expressions are equivalent, must they always look exactly the same?

• 2 + 6 = 6 + 2

If two expressions are equivalent, must they always look exactly the same?

•  $2\cdot3\cdot4$  = $20\ +\ 4$  
  

If two expressions are equivalent, must they always look exactly the same?

•  $3\ \left(4\cdot2\right)\ =\ 8\cdot3$  

Positive and Negative Integers

• 1 and +1 are positive integers.

• All counting numbers are positive numbers.

• +2 and 2 are positive integers.

• These are -1, -2, -3, -4, -5, so and so forth.

Positive and Negative Integers

• Negative numbers have (-) sign.

• These are -1, -2, -3, -4, -5, so and so forth.

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Like and Unlike Terms

• 7x and 2x are like terms because they are both "x".

• 3x² and −2x² are like terms because they are both "x²".

• 7x and 2y are unlike terms because they have different variables

• 3x² and −2x are unlike terms because they have diffent exponents

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Zero Pairs

• a pair of numbers whose sum is zero

• +1 + ( -1)

• 2 + (-2)

• 100 + (-100)

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Poll

Click the zero pair of 3.

• +3

• -3

Poll

What is the zero pair of -6?

• +6

• -6

Poll

Click the zero pair of x.

• x

• -x

Poll

Click the zero pair of -y.

• +y

• -y

Poll

What is the zero pair of 3x?

• 3x

• -3x

Poll

Click the zero pair of 4y.

• 4y

• -4y

Simplifying algebraic expressions

• Collect like terms together

• Group tiles to identify zero pairs

• Simplify the algebraic expression

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Let us try working the hands-on activity on TM 6A PB p. 12

• 5y + y =

• y + 3y + 3 =

• 6y - 6y =

Let us try working the hands-on activity on TM 6A PB p. 12.

• 4y - 7 - 2y

• 5y - 3y + 9 - 8

• 6y - y - 5 + 3y

Turn your Pupil's book to p. 12 and do "Do and Learn" numbers 1 and 2 for the remaining time.

Multiple Select

TM PB p. 12 Do and Learn

1a. What is the missing number or letter?

12 q = 10q + ____

• 2q

• -2q

• q

Multiple Select

TM PB p. 12 Do and Learn

1b. What is the missing number or letter?

4r = ____ x r

• 3r

• 4r

• 4

Multiple Select

TM PB p. 12 Do and Learn

1c. What is the missing number or letter?

10s = 10 x ____

• 10

• s

• 10s

Multiple Select

TM PB p. 12 Do and Learn

2a. Simplify the following algebraic expressions.

f + f + f + f

• 4f

• 3f

• 5f

Multiple Select

TM PB p. 12 Do and Learn

2b. Simplify the following algebraic expressions.

k + k + k - k

• 3k

• 2k

• -2k

Multiple Select

TM PB p. 12 Do and Learn

2d. Simplify the following algebraic expressions.

8m + 11m

• 19m

• -19m

• 3m

Multiple Select

TM PB p. 12 Do and Learn

2d. Simplify the following algebraic expressions.

8m + 11m

• 19m

• -19m

• 3m