Question

6 • m4 • ta • lesson 6

1. insert one set of parentheses into (2^5 + 7 cdot 9 - 1) so that the expression has a value of 88.
2. insert one set of parentheses into (11 cdot 4 - 10 div 2) so that the expression has a value of 17.

remember
for problems 15–17, multiply.

1. (4.72 \times 0.5)
2. (1.25 \times 0.6)
3. (6.65 \times 0.4)
4. which of the following are equivalent to (8^4)? choose all that apply. for every expression is not equivalent to (8^4), explain why it is not equivalent.

a. (8 \times 4)
b. (8 + 8 + 8 + 8)
c. (8 \times 8 \times 8 \times 8)
d. (4 + 8)
e. (4,096)

Explanation:

Problem 13

Step1: Calculate base value of $2^5$

$2^5 = 32$

Step2: Test parenthesis placement

We need a result of 88. Subtract 32 from 88: $88-32=56$. Now find where to place parentheses to make $7 \cdot 9 -1 = 56$. Test $(9-1)$: $7 \cdot (9-1)=7 \cdot 8=56$. Combine with $2^5$: $2^5 + 7 \cdot (9-1)$

Step3: Verify the expression

$2^5 + 7 \cdot (9-1) = 32 + 56 = 88$

Problem 14

Step1: Test parenthesis placement

We need a result of 17. Test $(4-10\div2)$ first: $10\div2=5$, $4-5=-1$, $11 \cdot (-1)=-11$ (incorrect). Test $(11\cdot4 -10)$: $11\cdot4=44$, $44-10=34$, $34\div2=17$. So the expression is $(11 \cdot 4 -10) \div 2$

Step2: Verify the expression

$(11 \cdot 4 -10) \div 2 = (44-10)\div2 = 34\div2=17$

Problem 15

Step1: Multiply decimals directly

$4.72 \times 0.5 = \frac{472}{100} \times \frac{5}{10}$

Step2: Simplify the product

$\frac{472 \times 5}{1000} = \frac{2360}{1000}=2.36$

Problem 16

Step1: Multiply decimals directly

$1.25 \times 0.6 = \frac{125}{100} \times \frac{6}{10}$

Step2: Simplify the product

$\frac{125 \times 6}{1000} = \frac{750}{1000}=0.75$

Problem 17

Step1: Multiply decimals directly

$6.65 \times 0.4 = \frac{665}{100} \times \frac{4}{10}$

Step2: Simplify the product

$\frac{665 \times 4}{1000} = \frac{2660}{1000}=2.66$

Problem 18

Step1: Calculate $8^4$

$8^4 = 8 \times 8 \times 8 \times 8 = 4096$

Step2: Evaluate each option

A. $8 \times 4 = 32
eq 4096$ (multiplication, not exponentiation)
B. $8+8+8+8=32
eq 4096$ (addition, not exponentiation)
C. $8 \times 8 \times 8 \times 8 = 4096 = 8^4$
D. $4+8=12
eq 4096$ (addition, not exponentiation)
E. $4096 = 8^4$

Answer:

1. $2^5 + 7 \cdot (9-1)$
2. $(11 \cdot 4 - 10) \div 2$
3. $2.36$
4. $0.75$
5. $2.66$
6. Equivalent expressions:

C. $8 \times 8 \times 8 \times 8$
E. $4,096$
Non-equivalent explanations:
A. $8 \times 4$ is simple multiplication, not $8$ multiplied 4 times.
B. $8+8+8+8$ is repeated addition, not exponentiation.
D. $4+8$ is a sum, unrelated to $8^4$.