Question

A recipe calls for 1 1/2 cups of flour, 3/4 cup of white sugar, and 1/8 cup of brown sugar.

a. How many total cups of ingredients are there? Show your work using a number line.

b. Which of the following mixing bowls can you use to make the recipe: 2-cup, 3-cup, or 4-cup? Justify your answers.​

Answer 1

Answer:

e3

(ii) (a)

  4 5 x

(b)

  4 5 x y

Terms: 4 ,5 x

Terms: 4 ,5 x y

Factors: 4, ; 5 x

Factors: 4, ; 5, x y

(c)

2

5 3 y y 

(d)

2 2

xy x y  2

Terms:

2

5 ,3 y y

Terms:

2 2

xy x y ,2

Factors:

5, ; 3, , y y y

Factors:

x y x x y y , ; 2 , , ,

(e)

pq q 

(f)

1.2 2.4 3.6 ab b a  

Terms:

pq q,

Terms:

1.2 , 2.4 ,3.6 ab b a 

Factors:

p q q , ;

Factors:

1.2, , ; 2.4, ; 3.6, a b b a 

(g)

3 1

4 4

x 

(h)

2 2 0.1 0.2 p q 

Terms:

3 1

,

4 4

x

Terms:

2 2 0.1 ,0.2 p q

Factors:

3 1

, ;

4 4

x

Factors:

0.1, , ; 0.2, , p p q q

Question 3:

Identify the numerical coefficients of terms (other than constants) in the following

expressions:

(i)

2

5 3  t

(ii)

2 3 1   t t t

(iii)

x xy y   2 3

(iv)

100 1000 m n 

(v)

2 2   p q pq 7

(vi)

1.2 0.8 a b 

(vii)

2

3.14r

(viii)

2l b  

(ix)

2

0.1 0.01 y y 

Step-by-step explanation:

3

(vi)

5 7 ,3 4 2,2 3 5 5 7 3 4 2 2 3 5 m n n m m mn m n n m m mn             

=

5 4 2 7 3 3 2 5 m m m n n mn       

=

5 4 2 7 3 3 3        m n mn  

=

3 4 3 3 m n mn   

(vii)

2 2 2 2 2 2 2 2 4 , 3 , 5 ,5 4 ( 3 ) ( 5 ) 5 x y xy xy x y x y xy xy x y        

=

2 2 2 2 4 5 3 5 x y x y xy xy   

=

2 2 9 8 x y xy 

(viii)

2 2 2 2 2 2 3 4 5, 10 ,15 9 7 p q pq p q pq p q     

=

 

2 2 2 2 2 2 3 4 5 10 15 9 7 p q pq p q pq p q       

=

2 2 2 2 2 2 3 10 7 4 9 5 15 p q p q p q pq pq      

=    

2 2 3 10 7 4 9 20       p q pq

=

2 2 0 5 20 p q pq  

=

5 20 pq 

(ix)

ab a b ab a ab ab a b ab a ab          4 ,4 ,4 4 4 4

=

      4 4 4 4 a a b b ab ab

=

0 0 0 0   

(x)

2 2 2 2 2 2

x y y x x y       1, 1 ,1

=

2 2 2 2 2 2

x y y x x y         1 1 1

=

2 2 2 2 2 2

x x x y y y         1 1 1

=

   

2 2 1 1 1 1 1 1 1 1 1          x y

=

2 2

   x y 1

Question 3:

Subtract:

(i)

2

5y

from

2

y

(ii)

6xy

from 12xy

(iii)

a b  

from

a b  

(iv)

a b  5

from

b a 5  

(v)

2

  m mn 5

from

2

4 3 8 m mn  

(vi)

2

   x x 10 5

from

5 10 x 

(vii)

2 2 5 7 5 a ab b  

from

2 2 3 2 2 ab a b  

(viii)

2 2 4 5 3 pq q p   from

2 2 5 3 p q pq  