Question

equations and solutions
expressions and number sentences

1. write a number sentence to represent the description. then determine whether the number sentence is true or false. if the number sentence is false, change the number sentence to make it true.

description	number sentence	true or false	true number sentence
one - third of 36 is 12.	\\(\frac{1}{3}\times36 = 12\\)	true
three - eighths of the sum of 11 and 5 is 8.	\\(\frac{3}{8}\times11 + 5 = 8\\)	false
4 more than the product of 9 and 2 squared is 2 less than the product of 7 and 6.

for problems 2–4, write the number in the blank that makes the number sentence true.

1. \\(5 + \underline{7}=18 - 6\\)
2. \\(\frac{1}{4}(40)=\frac{1}{2}(\underline{20})\\)
3. \\(3\cdot12 = 2^{2}\cdot\underline{9}\\)

Explanation:

Step1: Fix third row number sentence

First, calculate the sum of 11 and 5, then multiply by $\frac{3}{8}$.
Number sentence: $\frac{3}{8} \times (11+5) = 8$

Step2: Verify third row truth value

Calculate left side: $\frac{3}{8} \times 16 = 6$. $6
eq 8$, so false.
True number sentence: $\frac{3}{8} \times (11+5) = 6$

Step3: Write fourth row number sentence

Translate description to math: $9 \times 2^2 + 4 = (7 \times 6) - 2$

Step4: Verify fourth row truth value

Calculate left: $9 \times 4 + 4 = 40$. Calculate right: $42 - 2 = 40$. $40=40$, so true.

Step5: Solve problem 2

Simplify right side: $18-6=12$. Find missing number: $12-5=7$

Step6: Solve problem 3

Calculate left side: $\frac{1}{4} \times 40 = 10$. Find missing number: $10 \div \frac{1}{2} = 20$

Step7: Solve problem 4

Calculate left side: $3 \times 12 = 36$. Calculate $2^2=4$. Find missing number: $36 \div 4 = 9$

Answer:

Completed Table:

Description	Number Sentence	True or False	True Number Sentence
One-third of 36 is 12.	$\frac{1}{3} \times 36=12$	True	(no change needed)
Three-eighths of the sum of 11 and 5 is 8.	$\frac{3}{8} \times (11+5)=8$	False	$\frac{3}{8} \times (11+5)=6$
4 more than the product of 9 and 2 squared is 2 less than the product of 7 and 6.	$9 \times 2^2 + 4 = (7 \times 6) - 2$	True	(no change needed)

Problems 2-4:

1. $5 + \boldsymbol{7} = 18 - 6$
2. $\frac{1}{4}(40)=\frac{1}{2}(\boldsymbol{20})$
3. $3 \cdot 12 = 2^2 \cdot \boldsymbol{9}$