문자의 사용과 식의 계산

Jeannette has $\char36 5$ and $\char36 10$ bills in her wallet. The number of fives is three more than six times the number of tens. Let $t$ represent the number of tens. Write an expression for the number of fives.

Car insurance Justin’s car insurance has a $\char36 750$ deductible per incident. This means that he pays $\char36 750$ and his insurance company will pay all costs beyond $\char36 750.$ If Justin files a claim for $\char36 2,100,$ how much will he pay, and how much will his insurance company pay?

Home insurance Pam and Armando’s home insurance has a $\char36 2,500$ deductible per incident. This means that they pay $\char36 2,500$ and their insurance company will pay all costs beyond $\char36 2,500.$ If Pam and Armando file a claim for $\char36 19,400,$ how much will they pay, and how much will their insurance company pay?

Explain why “the sum of x and y” is the same as “the sum of y and x,” but “the difference of x and y” is not the same as “the difference of y and x.” Try substituting two random numbers for $x$ and $y$ to help you explain.

Explain the difference between $\text{``}4$ times the sum of $x$ and $y\text{''}$ and “the sum of $4$ times $x$ and $y.\text{''}$

Simplify: $7y+2+y+13.$

Multiply: $\frac{2}{3}\cdot 18.$

Find the opposite of $15.$

Use the commutative properties to rewrite the following expressions:

1. ⓐ $\,-1+3=\_\_\_\_\_$
2. ⓑ $\,4\cdot 9=\_\_\_\_\_$

Use the commutative properties to rewrite the following: - ⓐ $\,-4+7=\_\_\_\_\_\,$

• ⓑ $\,6\cdot 12=\_\_\_\_\_$

Use the commutative properties to rewrite the following: - ⓐ $\,14+(-2)=\_\_\_\_\_\,$

• ⓑ $\,3(-5)=\_\_\_\_\_$

Use the associative properties to rewrite the following:

1. ⓐ $\,(3+0.6)+0.4=\_\_\_\_\_\_\_\_\_\_$
2. ⓑ $\,\left(-4\cdot \frac{2}{5}\right)\cdot 15=\_\_\_\_\_\_\_\_\_\_$

Use the associative properties to rewrite the following: ⓐ $(1+0.7)+0.3=\_\_\_\_\_\_\_\_\_\_\quad$ ⓑ $\,(-9\cdot 8)\cdot \frac{3}{4}=\_\_\_\_\_\_\_\_\_\_$

Use the associative properties to rewrite the following: ⓐ $(4+0.6)+0.4=\_\_\_\_\_\_\_\_\_\_\quad$ ⓑ $\,(-2\cdot 12)\cdot \frac{5}{6}=\_\_\_\_\_\_\_\_\_\_$

Use the Associative Property of Multiplication to simplify: $6(3x).$

Use the Associative Property of Multiplication to simplify the given expression: $8(4x).$

Use the Associative Property of Multiplication to simplify the given expression: $-9(7y).$

Evaluate each expression when $x=\frac{7}{8}.$

• ⓐ $\,x+0.37+(-x)$
• ⓑ $\,x+(-x)+0.37$

Evaluate each expression when $y=\frac{3}{8}:\,$ⓐ $\,y+0.84+(-y)$ ⓑ $\,y+(-y)+0.84.$

Evaluate each expression when $f=\frac{17}{20}:\,$ⓐ $\,f+0.975+(-f)$ ⓑ $\,f+(-f)+0.975.$