Digits, Grade 7, Volume 1, Homework Helper

### 1-6: TEKS Practice

• 1.

• a. Simplify the expression negative 8 . open . negative , 3 fourths , plus 6 . close by applying the Distributive Property.

• b. Evaluate the expression negative 8 . open . negative , 3 fourths , plus 6 . close . .

• 2.

• a. Apply the Distributive Property to simplify the expression − 8(− 2.5 − 7).

• b. Evaluate the expression − 8(− 2.5 − 7).

• 3. Simplify the expression 4.5(− 6) + 19.

• 4. Use the formula f equals , 9 fifths c plus 32 to convert negative 20 degrees cap c to degrees Fahrenheit.

• 5. Simplify the complex fraction fraction negative , 1 fourth , over negative 12 end fraction . .

• 6. The water level of a lake fell by 1 , and 1 half in. during a 1 , and 2 thirds -week-long dry spell. Simplify the complex fraction fraction negative 1 , and 1 half , over 1 , and 2 thirds end fraction to find the average rate at which the water level changed every week.

• 7.

• a. Writing Simplify the complex fraction fraction 3 fourths , over 2 , and 1 fourth end fraction . .

• b. Explain why, when dividing fractions with the same denominator, you can find the quotient by dividing the numerators. Use the complex fraction as an example.

• 8. Reasoning

• I. negative 4 . open . negative 1 , and 1 half , minus 9 . close

• II. negative 4 . open . open . negative 1 minus , 1 half . close . minus 9 . close

• a. Use the Distributive Property to rewrite expression I. Which expression is correct?

• A. negative 4 . open . negative 1 , and 1 half . close . minus open negative 4 close open 9 close

• B. negative 4 . open . negative 1 , and 1 half . close . minus 4 open 9 close

• C. negative 4 . open . negative 1 , and 1 half . close . minus 9

• b. Evaluate expression I.

• c. Use the Distributive Property to rewrite expression II. Which expression is correct?

• A. negative 4 open negative 1 close minus open negative 4 close . open , 1 half , close . minus open negative 4 close open 9 close

• B. negative 4 open negative 1 close minus open negative 4 close . open , negative , 1 half , close . minus open negative 4 close open negative 9 close

• C. negative 4 open negative 1 close plus open negative 4 close . open , 1 half , close . minus open negative 4 close open 9 close

• d. Evaluate expression II.

• e. Copy expressions I and II. Circle the parts in the two expressions that are different. How do the expressions inside your circles compare? Explain your reasoning.

• 9. Error Analysis In evaluating the expression 9 fourths , open negative 20 close plus 18 comma Jenny found the value to be 63. She thinks that the number is too great, but is not sure what she did wrong.

• a. Evaluate the expression.

• b. What was Jenny's likely error?

• A. She multiplied 9 fourths by 20 instead of − 20.

• B. She multiplied − 20 by 4 ninths instead of 9 fourths .