practice
use the distributive property to rewrite each expression. then evaluate.
1. 4 + 5(6)
2. 7(13 + 12)
3. 6(5 - 1)
4. (3 + 8)5
5. 14(8 - 5)
6. (9 - 4)9
7. opera anas drama class is planning a field - trip to see mozarts famous opera don giovanni. tickets cost $39 each, and there are 23 students and 2 teachers going on the field trip.
a. write an expression to find the groups total ticket cost.
b. what is the groups total ticket cost?
8. salary in a recent year, the median salary for an engineer in the united states was $52,000 and the median salary for a computer programmer was $55,000.
a. write an expression to estimate the total cost for a business to employ an engineer and a programmer for 5 years.
b. estimate the total cost for a business to employ an engineer and a programmer for 5 years.
9. costumes isabellas ballet class is performing a spring recital for which they need butterfly costumes. each butterfly costume is made from 3 3/5 yards of fabric.
a. write an expression to find the number of yards of fabric needed for 10 costumes.
b. use the distributive property to find the number of yards of fabric needed for 10 costumes. show your work. (hint: a mixed number can be written as the sum of an integer and a fraction.)
10. reasoning letisha and noelle each opened a checking account, a savings account, and a college fund. the chart shows the amounts that they deposit into each account every month.
a. write an expression to find the amount in letishas checking, savings, and college accounts after 12 months.
b. how much is in letishas checking, savings, and college accounts after 12 months?

Question

practice
use the distributive property to rewrite each expression. then evaluate.
1. 4 + 5(6)
2. 7(13 + 12)
3. 6(5 - 1)
4. (3 + 8)5
5. 14(8 - 5)
6. (9 - 4)9
7. opera anas drama class is planning a field - trip to see mozarts famous opera don giovanni. tickets cost $39 each, and there are 23 students and 2 teachers going on the field trip.
  a. write an expression to find the groups total ticket cost.
  b. what is the groups total ticket cost?
8. salary in a recent year, the median salary for an engineer in the united states was $52,000 and the median salary for a computer programmer was $55,000.
  a. write an expression to estimate the total cost for a business to employ an engineer and a programmer for 5 years.
  b. estimate the total cost for a business to employ an engineer and a programmer for 5 years.
9. costumes isabellas ballet class is performing a spring recital for which they need butterfly costumes. each butterfly costume is made from 3 3/5 yards of fabric.
  a. write an expression to find the number of yards of fabric needed for 10 costumes.
  b. use the distributive property to find the number of yards of fabric needed for 10 costumes. show your work. (hint: a mixed number can be written as the sum of an integer and a fraction.)
10. reasoning letisha and noelle each opened a checking account, a savings account, and a college fund. the chart shows the amounts that they deposit into each account every month.
  a. write an expression to find the amount in letishas checking, savings, and college accounts after 12 months.
  b. how much is in letishas checking, savings, and college accounts after 12 months?

Accepted Answer

1. **For the problem "Use the Distributive Property to rewrite each expression. Then evaluate. 7(13 + 12)"**:
   - # Explanation:
     - ## Step1: Apply distributive property
       The distributive property is $a(b + c)=ab+ac$. Here $a = 7$, $b = 13$, and $c = 12$. So $7(13 + 12)=7\times13+7\times12$.
     - ## Step2: Calculate the products
       $7\times13 = 91$ and $7\times12=84$.
     - ## Step3: Add the results
       $91 + 84=175$.
   - # Answer:
     175
2. **For 7 - a (writing an expression for the group's total ticket - cost in the opera field - trip problem)**:
   - # Explanation:
     - ## Step1: Identify the number of people
       There are 23 students and 2 teachers, so the total number of people is $23 + 2$.
     - ## Step2: Write the expression
       Since each ticket costs $39, the expression for the total cost is $39\times(23 + 2)$.
   - # Answer:
     $39\times(23 + 2)$
3. **For 7 - b (finding the group's total ticket - cost in the opera field - trip problem)**:
   - # Explanation:
     - ## Step1: Apply distributive property
       $39\times(23 + 2)=39\times23+39\times2$.
     - ## Step2: Calculate the products
       $39\times23=(40 - 1)\times23=40\times23-1\times23 = 920-23 = 897$, and $39\times2 = 78$.
     - ## Step3: Add the results
       $897+78 = 975$.
   - # Answer:
     975
4. **For 8 - a (writing an expression for the total cost of employing an engineer and a programmer for 5 years)**:
   - # Explanation:
     - ## Step1: Identify the annual salaries
       The median salary of an engineer is $52000 and of a programmer is $55000. The combined annual salary is $52000 + 55000$.
     - ## Step2: Write the 5 - year expression
       The expression for the 5 - year cost is $5\times(52000 + 55000)$.
   - # Answer:
     $5\times(52000 + 55000)$
5. **For 8 - b (estimating the total cost of employing an engineer and a programmer for 5 years)**:
   - # Explanation:
     - ## Step1: Apply distributive property
       $5\times(52000 + 55000)=5\times52000+5\times55000$.
     - ## Step2: Calculate the products
       $5\times52000 = 260000$ and $5\times55000 = 275000$.
     - ## Step3: Add the results
       $260000+275000 = 535000$.
   - # Answer:
     535000
6. **For 9 - a (writing an expression for the fabric needed for 10 costumes)**:
   - # Explanation:
     - ## Step1: Identify the fabric per costume
       Each costume requires $3\frac{3}{5}$ yards of fabric.
     - ## Step2: Write the expression for 10 costumes
       The expression is $10\times3\frac{3}{5}$.
   - # Answer:
     $10\times3\frac{3}{5}$
7. **For 9 - b (using the distributive property to find the fabric needed for 10 costumes)**:
   - # Explanation:
     - ## Step1: Rewrite the mixed - number
       $3\frac{3}{5}=3+\frac{3}{5}$.
     - ## Step2: Apply distributive property
       $10\times3\frac{3}{5}=10\times(3+\frac{3}{5})=10\times3 + 10\times\frac{3}{5}$.
     - ## Step3: Calculate the products
       $10\times3 = 30$ and $10\times\frac{3}{5}=6$.
     - ## Step4: Add the results
       $30 + 6=36$.
   - # Answer:
     36
8. **For 10 - a (writing an expression for the amount in Letisha's accounts after 12 months)**:
   - # Explanation:
     - ## Step1: Identify the monthly deposits
       Letisha deposits $125 in checking, $75 in savings, and $50 in college account per month. The total monthly deposit is $125 + 75+50$.
     - ## Step2: Write the 12 - month expression
       The expression for the 12 - month amount is $12\times(125 + 75+50)$.
   - # Answer:
     $12\times(125 + 75+50)$
9. **For 10 - b (finding the amount in Letisha's accounts after 12 months)**:
   - # Explanation:
     - ## Step1: Apply distributive property
       $12\times(125 + 75+50)=12\times125+12\times75+12\times50$.
     - ## Step2: Calculate the products
       $12\times125 = 1500$, $12\times75=900$, and $12\times50 = 600$.
     - ## Step3: Add the results
       $1500+900 + 600=3000$.
   - # Answer:
     3000

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