Numbers and Algebra - Operations - Quiz 4

Which number is not natural?

0 Natural numbers are whole counting numbers that begin with 1. Zero is not a natural number.

Solve the following equation. Write the solution as a fraction in simplest form. 3(4x - 5) + 8 = 9(2x - 1)

1/3 The first step in solving this equation is to simplify each side completely. The first step of simplification requires distributing into each set of parentheses to get 12x - 15 + 8 = 18x - 9. Next, like terms on each side are combined to the extent possible to get 12x - 7 = 18x - 9. Finally, solving can begin. While several steps would be valid at this point, the smaller variable part is often moved to join the larger and so 12x can be subtracted from each side to get -7 = 6x - 9. Now, the variable can be isolated by adding 9 to each side (2 = 6x) and dividing by the coefficient of x, 6, on each side. The resulting solution, 2/6 = x, should be reduced completely by the common factor of 2 in the numerator and denominator of the fraction, yielding the best answer: 1/3.

Base ten blocks can be used to represent an algorithm. Which expression best represents an algorithm based on the blocks shown?

100 + 36 There are 136 blocks total. Because they are all the same color without symbols, it can be assumed they are added.

Solve: [5(6+5) + 475]/{-3[3+ 7(5)] + 119}

106 [5(6+5) + 475]/{-3[3+ 7(5)] + 119} = (5(11) + 475) / (-3(3 + 35) + 119) = (55 + 475)/(-114 + 119) = 530/5 = 106

A teacher writes the problem shown below on the board for a warm-up. 7x + 4 - 3x + 2 = 127x+4−3x+2=12 She asks students to combine like terms as the first step in solving the problem. Which equation demonstrates an understanding of the first step?

4x+6=12 This correctly combines like terms, which should always be the first step.

Asher makes $240 every pay period plus 15% on all sales. He determines his paycheck using the expression 240 + .15x. Which of the following is equivalent to Asher's expression?

5(48 + .03x) This expression factored (essentially "pulled out") the 5 from both terms. The distributive property proves this true: 5 × 48 = 240 and 5 x .03x = .15x

A third-grade class begins working on a mathematics project at 9:50 a.m. and stops working on the project at 11:10 a.m. How many minutes did the class work on the project?

80 minutes There are 10 minutes from 9:50 to 10:00 and 11:00 to 11:10 and one hour from 10:00 to 11:00. There are 60 minutes in every hour. Between 9:50 a.m. and 11:10 a.m. is one hour and twenty minutes, or 80 minutes.

Jordan was simplifying the expression: 3x^{2}-4+8x-5x^{2}+63x2−4+8x−5x2+6. She simplified it to 8x^{2}+8x+108x2+8x+10, and then raised her hand to have her teacher check her work. Of the following, what is the best response from the teacher to Jordan?

Jordan is not correct. Every term has a sign to the left of it. When she combined 3x^{2}3x2 and -5x^{2}−5x2, she disregarded the sign of the 5x^{2}5x2 term and got 8x^{2}8x2 when she should have simplified it to -2x^{2}−2x2. She made the same mistake when adding the constants. She dropped the negative in front of the 4; -4 and 6 combine to 2. Jordan had a sign errors for the terms that were negative. Every term has a sign to the left of it.

Susan's second-grade class is studying fact families. Each student is purposefully assigned a fact card and asked to find other members of their family. Above are the cards received by 5 students. Students in the same fact family then work in a group to create fact family houses that are displayed at the school's Open House where parents come by to see the classroom and the student's work. Why is this an effective way to group students?

Students are discussing the concept before working on it. They have been studying fact families and this gives them an opportunity to discuss it among themselves as they find their group. This shows mastery of the concept which is then displayed in the project.

Which of the following is not a rational number?

π The value of pi (π) never ends and does not repeat, making it irrational.