Answer :
Let's address each part of your query.
E. [tex]\( 1 \frac{1}{9} \div-2 \frac{1}{3} = \frac{-11}{21} \)[/tex]
To determine if this equation is true or false, we can consider the following steps:
1. Convert the mixed numbers to improper fractions:
[tex]\( 1 \frac{1}{9} = \frac{10}{9} \)[/tex]
[tex]\( -2 \frac{1}{3} = -\frac{7}{3} \)[/tex]
2. Recall that dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\( \frac{10}{9} \div -\frac{7}{3} = \frac{10}{9} \times -\frac{3}{7} \)[/tex]
3. Perform the multiplication:
[tex]\( \frac{10 \times -3}{9 \times 7} = \frac{-30}{63} \)[/tex]
4. Simplify the fraction:
[tex]\( \frac{-30}{63} = \frac{-10}{21} \)[/tex] (After dividing the numerator and denominator by 3)
Given the steps above, the right-hand side should be [tex]\( \frac{-10}{21} \)[/tex], not [tex]\( \frac{-11}{21} \)[/tex].
Answer: False
F. [tex]\( -\frac{1}{6} \div -\frac{1}{9} \div \frac{3}{2} = 1 \)[/tex]
Again, we follow the order of operations (division and simplification):
1. Perform the first division:
[tex]\( -\frac{1}{6} \div -\frac{1}{9} = -\frac{1}{6} \times -9 = \frac{9}{6} = \frac{3}{2} \)[/tex]
2. Perform the second division:
[tex]\( \frac{3}{2} \div \frac{3}{2} = \frac{3}{2} \times \frac{2}{3} = 1 \)[/tex]
Given these steps, the equation simplifies to 1, confirming the left-hand side equals the right-hand side.
Answer: True
(5) For problem 4, which equations were you able to identify as false without performing the computation? Explain your answer.
Without performing the complete computations, you could identify equation E as potentially false by:
1. Considering the denominators and numerators of the fractions: The resulting fraction from the division of [tex]\( \frac{10}{9} \)[/tex] by [tex]\( \frac{7}{3} \)[/tex] should logically yield a fraction closer to [tex]\( \frac{10}{21} \)[/tex], not [tex]\( \frac{11}{21} \)[/tex].
2. Comparing it logically to the results from easier fractions – it doesn't fit the pattern of similar division results you know already.
Equations involving simpler comparisons or intuition about the magnitude of results can often be flagged this way.
(6) Select expressions that have a quotient of -3.25. Circle all that apply:
To determine which expressions have a quotient of -3.25, we can either estimate or compute directly:
A. [tex]\( -1.46 \div 0.45 \approx -3.244 \)[/tex]
B. [tex]\( -22.1 \div 6.8 \approx -3.25 \)[/tex]
C. [tex]\( 2.275 \div (-0.7) \approx -3.25 \)[/tex]
D. [tex]\( -33.8 \div 10.4 \approx -3.25 \)[/tex]
E. [tex]\( 8.75 \div (-2.7) \approx -3.24 \)[/tex]
F. [tex]\( 39 \div (-12) = -3.25 \)[/tex]
The matching quotients are:
B, C, D, and F.
Answer: B, C, D, F
(7) Ms. Ambrose paid \[tex]$32.28 for 8.75 gallons of gas. Approximately how much did she pay per gallon? Show or explain your work. To calculate the cost per gallon: 1. Divide the total cost by the total number of gallons: \[ \frac{32.28}{8.75} \approx 3.689142857 \] Therefore, Ms. Ambrose paid approximately $[/tex]3.69 per gallon.
E. [tex]\( 1 \frac{1}{9} \div-2 \frac{1}{3} = \frac{-11}{21} \)[/tex]
To determine if this equation is true or false, we can consider the following steps:
1. Convert the mixed numbers to improper fractions:
[tex]\( 1 \frac{1}{9} = \frac{10}{9} \)[/tex]
[tex]\( -2 \frac{1}{3} = -\frac{7}{3} \)[/tex]
2. Recall that dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\( \frac{10}{9} \div -\frac{7}{3} = \frac{10}{9} \times -\frac{3}{7} \)[/tex]
3. Perform the multiplication:
[tex]\( \frac{10 \times -3}{9 \times 7} = \frac{-30}{63} \)[/tex]
4. Simplify the fraction:
[tex]\( \frac{-30}{63} = \frac{-10}{21} \)[/tex] (After dividing the numerator and denominator by 3)
Given the steps above, the right-hand side should be [tex]\( \frac{-10}{21} \)[/tex], not [tex]\( \frac{-11}{21} \)[/tex].
Answer: False
F. [tex]\( -\frac{1}{6} \div -\frac{1}{9} \div \frac{3}{2} = 1 \)[/tex]
Again, we follow the order of operations (division and simplification):
1. Perform the first division:
[tex]\( -\frac{1}{6} \div -\frac{1}{9} = -\frac{1}{6} \times -9 = \frac{9}{6} = \frac{3}{2} \)[/tex]
2. Perform the second division:
[tex]\( \frac{3}{2} \div \frac{3}{2} = \frac{3}{2} \times \frac{2}{3} = 1 \)[/tex]
Given these steps, the equation simplifies to 1, confirming the left-hand side equals the right-hand side.
Answer: True
(5) For problem 4, which equations were you able to identify as false without performing the computation? Explain your answer.
Without performing the complete computations, you could identify equation E as potentially false by:
1. Considering the denominators and numerators of the fractions: The resulting fraction from the division of [tex]\( \frac{10}{9} \)[/tex] by [tex]\( \frac{7}{3} \)[/tex] should logically yield a fraction closer to [tex]\( \frac{10}{21} \)[/tex], not [tex]\( \frac{11}{21} \)[/tex].
2. Comparing it logically to the results from easier fractions – it doesn't fit the pattern of similar division results you know already.
Equations involving simpler comparisons or intuition about the magnitude of results can often be flagged this way.
(6) Select expressions that have a quotient of -3.25. Circle all that apply:
To determine which expressions have a quotient of -3.25, we can either estimate or compute directly:
A. [tex]\( -1.46 \div 0.45 \approx -3.244 \)[/tex]
B. [tex]\( -22.1 \div 6.8 \approx -3.25 \)[/tex]
C. [tex]\( 2.275 \div (-0.7) \approx -3.25 \)[/tex]
D. [tex]\( -33.8 \div 10.4 \approx -3.25 \)[/tex]
E. [tex]\( 8.75 \div (-2.7) \approx -3.24 \)[/tex]
F. [tex]\( 39 \div (-12) = -3.25 \)[/tex]
The matching quotients are:
B, C, D, and F.
Answer: B, C, D, F
(7) Ms. Ambrose paid \[tex]$32.28 for 8.75 gallons of gas. Approximately how much did she pay per gallon? Show or explain your work. To calculate the cost per gallon: 1. Divide the total cost by the total number of gallons: \[ \frac{32.28}{8.75} \approx 3.689142857 \] Therefore, Ms. Ambrose paid approximately $[/tex]3.69 per gallon.
