Understanding Integers
What are integers? Provide an example.
Integers are whole numbers that can be positive, negative, or zero. Example: -2, 0, 3.
What is a rational number? Give an example.
A rational number is a number that can be expressed as a fraction of two integers.
What is the first step when dividing fractions?
The first step is to keep the first fraction as it is.
How do you add the decimals 2.5 and 3.75? Show your work.
2.5 + 3.75 = 6.25.
What is a ratio? Give an example.
A ratio compares two quantities. Example: 3:4.
How do you compare the integers -3 and 2? Use the correct symbol.
-3 < 2 (since -3 is to the left of 2 on the number line).
Place the following rational number on a number line: 3/4.
3/4 is located between 0 and 1, specifically three-quarters of the way to 1.
Solve 1/2 divided by 3/4.
2/3
Subtract 5.6 from 12.3. What is the result?
12.3 - 5.6 = 6.7.
If a car travels 120 miles using 4 gallons of gas, what is the unit rate in miles per gallon?
The unit rate for miles per gallon is 30 mpg (120 miles ÷ 4 gallons).
Order the following integers from least to greatest: 0, -1, 2, -3, 1.
Ordered from least to greatest: -3, -1, 0, 1, 2.
Compare 1/2 and 3/4 using a common denominator.
The common denominator for 1/2 (which converts to 6/12) and 3/4 (which converts to 9/12) shows that 6/12 is less than 9/12.
How would you divide the mixed number 2 1/2 by 1/3? Show your work.
Multiply 3.2 by 4.5 and explain how you place the decimal.
Multiply 3.2 by 4.5: 32×45=144032×45=1440. The decimal point moves 2 places to the left, resulting in 14.40.
What is percent? Provide a definition.
A percent expresses a number as a part of a whole, comparing it to 100.
What is the absolute value of -5? Write your answer using absolute value notation.
The absolute value of -5 is |-5| = 5.
Order the following rational numbers from least to greatest: 2/3, 1/2, 3/4.
1/2, 6/12, 2/3, 8/12, 3/4, 9/12
Explain how to divide the fractions 2/5 by 1/3.
11/5 = 2 1/5
What is the result of dividing 7.5 by 1.5? Show your work.
75 ÷ 15 = 5.0
Find 20% of 50. Show your calculation.
20% of 50 = 10 (0.20 x 50 = 10).
If you compare -4 and -2, which is greater? Explain why.
-2 is greater than -4 (since -2 is to the right of -4 on the number line).
What is the least common multiple (LCM) of 4 and 6? Show your work.
The LCM of 4 and 6 is 12.
Solve the problem 2/3 divided by 4/5 and provide the answer in simplified form.
5/6
Divide 225 by 15 and provide the answer.
225 ÷ 15 = 15.
A store sells 80 out of 200 shirts. What percent of the shirts were sold?
40%