Question

1. select all equations that are true.

a ( 835 div 30 = 27\frac{5}{30} )
b ( 604 div 40 = 15\frac{4}{40} )
c ( 724 div 60 = 12\frac{4}{60} )
d ( 542 div 30 = 23\frac{10}{30} )
e ( 220 div 60 = 3\frac{1}{4} )

1. consider the expression ( 12 - 2 \times 4 + 9 ).

part a
use order of operations to evaluate the expression.
bubble sheet image
part b
which placement of the parentheses makes the expression equal 130?
a ( (12 - 2) \times 4 + 9 )
b ( (12 - 2 \times 4) + 9 )
c ( (12 - 2) \times (4 + 9) )
d ( 12 - 2 \times (4 + 9) )

1. what is the product?

( \begin{array}{r}428\\times 42\hlineend{array} )
a 17,865 c 17,976
b 17,876 d 17,986

1. look at the decimal. how is the value of the 5 on the right related to the value of the 5 on the left?

0.554
a the value of the 5 on the right is 10 times the value of the 5 on the left.
b the value of the 5 on the right is ( \frac{1}{10} ) the value of the 5 on the left.
c the value of the 5 on the right is 100 times the value of the 5 on the left.
d the value of the 5 on the right is ( \frac{1}{100} ) the value of the 5 on the left.

1. complete the statement about the equation.

( 6.9 + (15 div 3) = 4 \times 2.6 )
the equation is (\begin{array}{|c|}hline a \text{ true} \\ b \text{ false} \hlineend{array})

1. a 360-ounce bag of rice has a serving size of 7 ounces on its label. how many full servings does the bag contain?

a 49 servings
b 50 servings
c 51 servings
d 52 servings

Explanation:

Step1: Verify each division equation

For A: $835 \div 30$

Calculate $30 \times 27 = 810$, remainder $835-810=25$. So $835\div30=27\frac{25}{30}$, not $27\frac{5}{30}$. False.

For B: $604 \div 40$

Calculate $40 \times 15 = 600$, remainder $604-600=4$. So $604\div40=15\frac{4}{40}$. True.

For C: $724 \div 60$

Calculate $60 \times 12 = 720$, remainder $724-720=4$. So $724\div60=12\frac{4}{60}$. True.

For D: $542 \div 30$

Calculate $30 \times 18 = 540$, remainder $542-540=2$. So $542\div30=18\frac{2}{30}$, not $23\frac{10}{30}$. False.

For E: $220 \div 60$

Calculate $60 \times 3 = 180$, remainder $220-180=40$. So $220\div60=3\frac{40}{60}=3\frac{2}{3}$, not $3\frac{1}{4}$. False.

Step2: Evaluate $12-2\times4+9$ (Part A)

Follow order of operations: multiply first.
$2\times4=8$
Then subtract and add left to right: $12-8=4$, $4+9=13$

Step3: Find correct parentheses (Part B)

For A: $(12-2)\times4+9$

$10\times4+9=40+9=49$

For B: $(12-2\times4)+9$

$(12-8)+9=4+9=13$

For C: $(12-2)\times(4+9)$

$10\times13=130$

For D: $12-2\times(4+9)$

$12-2\times13=12-26=-14$

Step4: Calculate $428\times42$

Break into parts: $428\times40=17120$, $428\times2=856$
Add results: $17120+856=17976$

Step5: Analyze decimal place values

In $0.554$, left 5 is in tenths place ($0.5$), right 5 is in hundredths place ($0.05$).
$0.05 = \frac{1}{10} \times 0.5$

Step6: Verify the equation $6.9+(15\div3)=4\times2.6$

Calculate left side: $15\div3=5$, $6.9+5=11.9$
Calculate right side: $4\times2.6=10.4$
$11.9
eq10.4$, so equation is false.

Step7: Calculate full servings of rice

Divide total ounces by serving size: $360\div7\approx51.428$
Only full servings count, so 51.

Answer:

1. B. $604 \div 40 = 15\frac{4}{40}$, C. $724 \div 60 = 12\frac{4}{60}$
2. Part A: 13

Part B: C. $(12 - 2) \times (4 + 9)$

1. C. 17,976
2. B. The value of the 5 on the right is $\frac{1}{10}$ the value of the 5 on the left.
3. B. false
4. C. 51 servings