Operations with
Rational Numbers
Rational Numbers
What is the sum of −3 1/2 and 2 2/5?
-11/10 or -1.1
Compute (−4)×6
-24
Write 3/4 as a decimal.
0.75
A skateboarder owes $12.50 and pays $5.75. How much remains owed?
$6.75
Evaluate the expression when x = 2
3x + 1/2
6 1/2 or 6.5
Compute (−5/6)−(2/3) and give the answer in simplest form.
-3/2
Explain why (−3)×(−5)=15 uses the distributive property (give a short sentence).
Using distributive property,
(−3+3)×(−5)= 0
(−3)(−5)+3(−5)= 0
3(-5) = -15 so (−3)(−5) = 15
7/20
Terminating
0.35
A worker makes $14 per hour and receives a 15% raise. How much is the new hourly rate? Show work.
15% of $14 is 0.15 times 14 = $2.10, so the new rate is $16.10
Solve for x
1/3x = 9
x = 27
Put these numbers in increasing order: 0.25, −1/3, 0.2, −0.05
-1/3, -0.05, 0.2, 0.25
Calculate (-2/3) ⋅ (9/4) and simplify.
-3/2
Convert 5/6 to a decimal.
0.833333...
Mix 2/3 cup of syrup with 1 1/2 cups of water. What fraction of the total mixture is syrup?
Total = 2/3 + 1 1/2 = 2/3 + 3/2 = 4/6 + 9/6 = 13/6.
Fraction that is syrup = 2/3 divided by 13/6 = 2/3 times 6/13 = 12/39 or 4/13
-2x +7 - 7 = 15 - 7
-2x = 8
Divide by 2 on both sides
x = -4
A point is at −2.75. Move right 1 1/2. What is the new location?
-1.25 or -1 1/4
Compute (-15)/(-3) and explain why the sign is positive.
5 because negative divided by negative is positive
Give the decimal form of 11/12 and underline the repeating block.
0.9166666...
Repeating block is 6
The bank account balance is -$28.40. A deposit of $45.60 is made and a fee of $3.50 is charged. What is the final balance?
-$28.40 + $45.60 = $17.20; then 17.20 -3.50 = $13.70
Simplify then evaluate for x = -3/2.
2(x-1/4) + 3
2x - 1/2 + 3 = 2x + 5/2
2(-3/2) + 5/2 = -3 + 5/2 = -6/2 + 5/2 = -1/2
-3/4 + 7/8 - (-1/2)
5/8
Use the distributive property to simplify and compute.
-2(3 1/2 - 1 1/4)
-9/2 or -4 1/2
Without doing full long division, explain whether 13/40 will terminate or repeat; then give the decimal.
Denominator is 40 which is divisible by 2 and 5, so the decimal terminates
0.325
You buy 3 notebooks for $2.45 each and 2 packs of pencils at $1.30 each. Sales tax is 7% on the total purchase. What is the final amount paid?
(Show steps and round to the nearest cent)
Notebooks: 3 * 2.45 = $7.35. Pencils: 2 *1.30 = $2.60. Subtotal = $9.95
Tax: 0.07 * 9.95 = 0.6965 about $0.70
Subtotal + Tax = $9.95 + $0.70 = $10.65
A rectangle's length is 2.5 times its width. The perimeter is 56 units. Let w be the width. Write an equation and solve for w.
L = 2.5w
Perimeter = 2L +2w = 2(2.5w) + 2w = 5w + 2w = 7w
7w = 56
w = 8