Expressions, Equations, and Relationships>Generating Equivalent Numerical Expressions Using Order of Operations and Exponents(TEKS.Math.6.7.A)
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Texas 6th Grade Math › Expressions, Equations, and Relationships>Generating Equivalent Numerical Expressions Using Order of Operations and Exponents(TEKS.Math.6.7.A)
What is the value of this expression? $$3^2 + 5 \times (12 - 8)$$
$29$
$26$
$56$
$61$
Explanation
Use order of operations (PEMDAS). Parentheses: $12-8=4$. Exponents: $3^2=9$. Multiplication: $5\times4=20$. Addition: $9+20=29$. Distractors: $26$ treats $3^2$ as $6$; $56$ adds before multiplying: $(3^2+5)\times4$; $61$ ignores the parentheses: $5\times12-8=60-8=52$, then $52+9=61$.
Which shows the prime factorization of $60$?
$2 \times 30$
$1 \times 2 \times 3 \times 10$
$2^2 \times 3 \times 5$
$3^2 \times 5$
Explanation
Factor $60$: $60=6\times10=(2\times3)\times(2\times5)=2^2\times3\times5$. Choice A is incomplete and includes a composite ($30$). Choice B improperly includes $1$ and a composite ($10$). Choice D is missing a factor of $2$.
What is the value of this expression? $$4 \times (2^3 + 6) - 5^2$$
$-44$
$31$
$23$
$13$
Explanation
PEMDAS: Exponents first: $2^3=8$ and $5^2=25$. Parentheses: $8+6=14$. Multiplication: $4\times14=56$. Subtraction: $56-25=31$. Distractors: $-44$ subtracts before multiplying: $(8+6)-25=-11$, then $4\times(-11)=-44$; $23$ treats $2^3$ as $6$: $4\times(6+6)-25=48-25=23$; $13$ ignores parentheses: $4\times2^3+6-25=32+6-25=13$.
Which expression is equivalent to $$6 \times (4 + 2^3)$$?
$(6 \times 4) + 2^3$
$6 \times (2 + 3)^2$
$6 \times 4 + 2^3$
$6 \times 2^3 + 6 \times 4$
Explanation
Compute the original: $2^3=8$, so $6\times(4+8)=6\times12=72$. Distribute to get an equivalent expression: $6\times4+6\times2^3=24+48=72$ (choice D). Choices A and C do addition after multiplication: $24+8=32$. Choice B changes the operations: $6\times(2+3)^2=6\times25=150$.
Which shows the prime factorization of $84$?
$2^2 \times 3 \times 7$
$1 \times 84$
$2 \times 6 \times 7$
$3 \times 14$
Explanation
Build a factor tree: $84=2\times42=2\times(2\times21)=2^2\times(3\times7)=2^2\times3\times7$. Choice B includes $1$ and the composite $84$. Choice C includes the composite $6$. Choice D is incomplete and uses composites.