Number Families
Any number that can be written as a fraction of two integers.
A rational number
What is the opposite of −3.5 on a number line?
+3.5 — the same distance from zero, on the other side
On a horizontal number line, numbers to the right of zero are ______ and numbers to the left are ______.
Positive and negative
Which rational number is greater: −3.5 or −1.2? How do you know?
−1.2 — it sits farther to the right on the number line
Write 40% as a decimal, and explain the move.
0.4 — divide the percent by 100
Name the three number families in order from the smallest set to the largest set.
Whole numbers → integers → rational numbers
What do you always get when you add a number and its opposite?
Zero
Between which two integers does −1.5 sit, and where exactly?
Between −2 and −1, exactly halfway
Fill in the symbol: 1/2 ____ 0.75
1/2 < 0.75, because 1/2 = 0.5
Write 3/4 and 9/8 as decimals.
3/4 = 0.75 and 9/8 = 1.125
Sort each number into the smallest family it belongs to: 15, −8, −2.5
15 is a whole number, −8 is an integer, −2.5 is rational only
A $30 deposit is written +30. Write the number for spending $15, and explain the sign.
−15 — spending moves value in the opposite direction
To plot 3/4, how many equal parts do you split the unit into, and how many jumps do you take from zero?
4 equal parts (the denominator), 3 jumps to the right (the numerator)
Which is greater: −1/3 or −2/3?
−1/3 — for negatives, the value closer to zero is greater
Order from least to greatest: 120%, 0.5, −1/4, −1.5
−1.5, −1/4, 0.5, 120%
True or false: every integer is also a rational number. Explain how you know.
True — any integer can be written over 1, like −8 = −8/1
A reservoir rises 15 feet in a storm, then drops 15 feet in a drought. What does 0 represent in this story?
The starting water level, before the storm and the drought
Which point is farther from zero: −2 1/4 or 1 1/4? How far is each?
−2 1/4 — it is 2.25 units from zero, while 1 1/4 is only 1.25 units
Compare 1.3 and 8/5 using <, >, or =. Show the conversion.
8/5 = 1.6, so 1.3 < 8/5
Order from least to greatest: −2.5, 1/4, −0.5, 1.75
−2.5, −0.5, 1/4, 1.75
Which of these is NOT an integer, and why? −10, 0, 3/4, 7
3/4 — it is rational, but integers cannot be fractions
Zero is neither positive nor negative. Give two real-world situations where 0 is the neutral starting point.
Sea level, a $0 bank balance, or 0 degrees — any two
Plot these on one line and read them left to right: −0.6, 0.2, −2.4, 1.4
−2.4, −0.6, 0.2, 1.4
It is −2.5°F today and it was −1.5°F yesterday. Which day was warmer? Write it as an inequality.
Yesterday — −1.5 > −2.5
Order from GREATEST to least: 160%, 1.25, 9/8, 0.6, 3/4, 32%
160%, 1.25, 9/8, 3/4, 0.6, 32% (1.6, 1.25, 1.125, 0.75, 0.6, 0.32)