7th Grade Rational Numbers

7th Grade Rational Numbers

By Mr. Alonzo

Multiple Choice

The temperature at noon was −3°C. By 10 P.M. on the same day the temperature decreased by 5.4°. What was the temperature at 10 P.M.?

• -8.4^oC

• -5.4^oC

• -2.4^oC

• 1.6^oC

The correct answer was -8.4

The temperature at noon was −3°C. By 10 P.M. on the same day the temperature decreased by 5.4°. What was the temperature at 10 P.M.?

Notice that the temperature "decreased" by 5.4°C.
This would mean that the 5.4 is negative and you would set up the following equation.

 $-3-5.4=-8.4$  
Because you have two integers with the same sign you "combine" them and the result in this case would be a "bigger" negative.

Multiple Choice

Derek spends $3 on breakfast and $5.50 on lunch every school day. How much does he spend on breakfast and lunch a school week?

• $38.50

• $42.50

• $49.90

• $59.50

The correct answer was $42.50

Derek spends $3 on breakfast and $5.50 on lunch every school day. How much does he spend on breakfast and lunch a school week?

First you notice that Derek spends $3 and $5.50 on food at school each day. If you add these two together you would get $8.50. Then you would multiply this amount by the number of school days each week which is 5. The equation you should have created for this word problem is

 $5\times\left(3+5.50\right)=42.50$  

Multiple Choice

What is the value of

 $\left(-4.5\right)\left(-8.25\right)$  

• -37.125

• -12.75

• 3.75

• 37.125

The correct answer was 37.125

In an algebraic equation the (parenthesis) symbol means to multiply. If you multiply these two integers together

 $\left(-4.5\right)\left(-8.25\right)$  
You would get 37.125. 

Remember that every two negative signs in an equation cancel each other out when you are multiplying or dividing integers. Since there are two here they cancel each other out and you end up with a positive answer.

Multiple Choice

 An artist is cutting pieces of ribbon to use in a project. Each piece he cuts measures  $\frac{7}{8}$    inch. The artist cuts off 5 pieces. How many total inches of ribbon has he cut off? 

•  $4\frac{1}{8}$  

•  $4\frac{3}{8}$  

•  $5\frac{5}{7}$  

•  $5\frac{7}{8}$  

The correct Answer was  $4\frac{3}{8}$  

 An artist is cutting pieces of ribbon to use in a project. Each piece he cuts measures  $\frac{7}{8}$ inch. The artist cuts off 5 pieces. How many total inches of ribbon has he cut off? 

For this problem you would simply multiply the length of each piece of ribbon which is  $\frac{7}{8}$  of an inch by the number of pieces which is 5. The equation would look like this
 $\frac{7}{8}\times5=\ \frac{7}{8}\times\frac{5}{1}=\frac{35}{8}=4\frac{3}{8}$  

Multiple Choice

An airplane took off and reached an altitude of 10,000 feet in 25 minutes. How many feet per minute, on average, did the airplane climb?

• 400

• 500

• 600

• 2,500

The correct answer was 400

An airplane took off and reached an altitude of 10,000 feet in 25 minutes. How many feet per minute, on average, did the airplane climb? 

We know that the plane ascended to an altitude of 10,000 in 25 minutes but we want to know the amount of feet the plane ascended each minute (unit rate).

If you divide the total feet ascended by the number of minutes you would end up with a unit rate of 400 feet "per" 1 minute

 $10,000\div25=400$  

Multiple Choice

The number of students enrolled at Hill School decreased by 120 students over an 8-year period. What was the average decrease in student enrollment per year?

• 8

• 12

• 15

• 20

The correct answer was 15

The number of students enrolled at Hill School decreased by 120 students over an 8-year period. What was the average decrease in student enrollment per year? 

We know that the enrollment at the school decreased by 120 students total but this was spread across 8 years. To find the average amount of students lost each year you would divide the total by the number of years.

 $120\div8=15$  

Multiple Choice

Alexis sold boxes of homemade granola bars for $8.50 each. It costs her $2.25 to bake and package each box of granola bars. What was her profit from selling each box of granola bars?

• -$6.25

• $5.38

• $6.25

• $10.75

The correct answer was $6.25

Alexis sold boxes of homemade granola bars for $8.50 each. It costs her $2.25 to bake and package each box of granola bars. What was her profit from selling each box of granola bars? 

Alexis made a total amount of $8.50 from each box of granola bars that she sold. However, it costs her $2.25 to create each box of granola bars. Therefore we must subtract her expenses from the total to reach her profit.

 $8.50-2.25=6.25$  

Multiple Choice

Alexandra’s backpack weighs  $7\frac{5}{8}$   pounds. What is the weight of her backpack expressed as a decimal? 

• 7.13

• 7.58

• 7.625

• 7.85

The correct answer was 7.625

Alexandra’s backpack weighs  $7\frac{5}{8}$   pounds. What is the weight of her backpack expressed as a decimal? 

When converting a mixed number to a decimal we can ignore the whole number because we know that it means 7 wholes. We therefore know that the decimal will start with a 7 in the ones place.

To convert  $\frac{5}{8}$  to a decimal you must use long division.  $5\div8=0.625$  
You then combine your number of wholes with the decimal that you get from the fraction and you get 7.625

Multiple Choice

Which number below is in the set of integers but is not in the set of whole numbers?

• -2

• 0

• $5\frac{1}{2}$

• 100

The correct answer was -2

Which number below is in the set of integers but is not in the set of whole numbers?
Both 0 and 100 are whole numbers

 $5\frac{1}{2}$  is not a whole number nor is it an integer either so it is not the correct answer.
Therefore, -2 is the only rational number that is an integer but is also not a whole number.

Multiple Choice

Which of the following fractions is equivalent to a repeating decimal?

• $\frac{1}{5}$

• $\frac{5}{8}$

• $\frac{2}{3}$

• $\frac{3}{4}$

The correct answer was $\frac{2}{3}$  

 $\frac{1}{5}$  as a decimal would equal 0.2

 $\frac{5}{8}$  as a decimal would equal 0.625

 $\frac{3}{4}$  as a decimal would equal 0.75

 $\frac{2}{3}$  as a decimal would equal  $0.\overline{66}$  and therefore the 6's go on forever.

The correct answer was 31 feet

The elevation of New Orleans, Louisiana, is on average 8 feet below sea level. The elevation of El Centro, California, is 39 feet below sea level. What is the difference in elevation between the two cities?

The elevation of New Orleans is 8 feet "below" sea level so this would be -8
The elevation of El Centro is 39 feet "below" sea lever so this would be -39
Since we are finding the "difference" we are subtracting.

 $-8--39=31$  (remember that subtracting a negative turns into a plus)

The correct answer was

 $1\frac{11}{24}$  or  $\frac{35}{24}$  

In this problem you are trying the find the difference between the two amounts so you would be doing subtraction.
 $1\frac{5}{6}-\frac{3}{8}$  
Your steps to solving this problem would be
1. Convert the mixed number to an improper fraction (because you can't do math with mixed numbers  $1\frac{5}{6}=\frac{11}{6}$  so  $\frac{11}{6}-\frac{3}{8}$  
2. Next you must find the least common denominator because you can't subtract fractions unless they have the same denominator.
3. You can simplify to a mixed number.
 $\frac{11}{6}=\frac{44}{24}$        $\frac{3}{8}=\frac{9}{24}$       so      $\frac{44}{24}-\frac{9}{24}=\frac{35}{24}=1\frac{11}{24}$  

The correct answer was  $-8.5$  

The word "product" means multiply.
 $-3.4\times2.5=-8.5$  

The correct answer was $22.50

Fatima wants to purchase a scarf for $45.00 and a sweater for $77.50. If she currently has $100, how much more money does she need to purchase the two items? 

In this problem you are trying to find "how much more money" Fatima needs to buy the stuff she wants.

so you are trying to find the difference which means subtraction.

You are trying to find the difference between what she is buying and how much money she has right now so you must add the cost of the two items she wants to buy first  $\left(45+77.50\right)=122.50$  

Then you subtract  $122.50-100=22.50$  

The correct answer was $140

Arnaud paid $350 for a rug. The price of the rug that Bill purchased was  $\frac{2}{5}$   the price that Arnaud paid. How much did Bill pay for his rug?

*Hint* When you see the word "of" in a math word problem most of the time that means you are supposed to multiply (so remember the word of means to multiply)

1. First you set up the equation $\frac{2}{5}\times350=$  

2. Next you put the whole number over "1"  $\frac{2}{5}\times\frac{350}{1}=$  
3. You multiply straight across  $\frac{2}{5}\times\frac{350}{1}=\frac{700}{5}$  
4. Simplify  $\frac{700}{5}\ is\ the\ same\ thing\ as\ 700\div5\ which\ equals\ 140$  

The correct answer was $74

The Martin family spent $518 on groceries in one week. What is the average amount the family spent on groceries per day? 

The Martin family spend a total amount of 518 dollars per week on groceries so if you divide this number by 7 you can find the average amount of money they spent per day.

 $518\div7=74$  

The correct answer was 0.9

What is the average of −2.5, 5.2, 1.7, and −0.8?

To find the "average" of a set of numbers first you add up all the numbers.

 $-2.5+5.2+1.7+\left(-0.8\right)=3.6$  
Then you divide the sum by the amount of numbers that you added together which in this case is 4.
 $3.6\div4=0.9$  

The correct answer was  $-1.625$  

What is the quotient of  $-5.2\div3.2$  

The word "quotient" means to divide. In this case you must do long division.
          _____
 $3.2$   | $-5.2$  
   ^ You can't divide with a decimal number outside the "house"
(So first you can multiply both numbers by 10 to move the decimal to the right one time)
        _____
 $32$  | $-52$  
Now just do normal long division and put a negative in front of your answer because "one" of the numbers in the problem is negative.

The correct answer was  $\frac{4}{15}$  

Gail read  $\frac{2}{15}$   of a book on Monday and  $\frac{3}{5}$   of the book on Tuesday. What fraction of the book does she have left to read to finish the book?

In this problem you are trying to find the difference between what she as read so far and what she has left to read so you are subtracting.

First you add up the amounts she read so far to find the total amount she read.  $\frac{2}{15}+\frac{3}{5}\$  (find least common denominator)  $\frac{2}{15}+\frac{9}{15}=\frac{11}{15}$  
Then you subtract this amount from "1 whole" because she is reading "1 whole" book.  $1=\frac{15}{15}$                so             $\frac{15}{15}-\frac{11}{15}=\frac{4}{15}$  

The correct answer you could have selected was either 0 or 1

Anna wrote down a whole number that is greater than −2 and less than +2. What is one possible number she could have written down?

The only whole numbers between -2 and 2 are 0 and 1.

-1 is not a whole number because it is negative.

Multiple Choice

Kevin is  $5\frac{1}{2}$   feet tall. Jane is  $5\frac{3}{8}$   feet tall. Who is taller?

• Kevin

• Jane

The correct answer was Kevin

Kevin is  $5\frac{1}{2}$   feet tall. Jane is  $5\frac{3}{8}$   feet tall. Who is taller?

The fastest way to see who is taller is to use the butterfly method. Since they are both 5 feet something you can ignore the 5 and just pay attention to the fraction part of the mixed number.
Using the butterfly method for  $\frac{1}{2}\ \frac{3}{8}$  you will find that  $\frac{1}{2}$  is bigger and therefore Kevin is taller.

The correct answer was $\frac{19}{21}$  

Beatrice built about  $\frac{1}{3}$   of a sandcastle. Linda built  $\frac{4}{7}$  of the same castle. What fraction of the sandcastle did they build together? 

To find the answer you must add the two fractions together.
 $\frac{1}{3}+\frac{4}{7}=$  (When adding fractions you must find the least common denominator first)

  $\frac{1}{3}+\frac{4}{7}=\frac{7}{21}+\frac{12}{21}=\frac{19}{21}$  

The correct answer was 0.66

In Priya’s math class there are 10 boys and 15 girls. What is the ratio of boys to girls in Priya’s math class? Express your answer as a decimal (to the hundredths place).

The ratio of boys to girls is  $\frac{10}{15}$  which reduces to  $\frac{2}{3}$  .

To convert fractions to decimals you use long division.  $2\div3=0.66$  Since the 6's go on forever in this problem the question asked you to stop after the hundredths place.