Piece of Cake
What number is 1/5 of 2/3?
"Of" indicates multiplication. So 1/5 of 2/3 means 1/5 times 2/3, which is 2/15.
Fill the missing exponent in the following expression:
115 × 11 = 11?
We begin by writing out the powers as multiplication:
(11 × 11 × 11 × 11 × 11) × 11 = 116
So ? = 6.
Place parentheses in the equation below to make it a true statement:
5 × 2 + 3 = 25
5 × (2 + 3) = 25
Evaluate the following expression when n = 6
33 - n
33 - n = 33 - 6 = 27
Compute the following sum:
-4 + 9 + (-5)
When adding integers, the first number tells us where to start on a number line.
The second number tells us which direction to go and how far.
We move right when adding a positive and left when adding a negative.
For the expression -4 + 9 + (-5), we start at -4, move 9 units to the right, then 5 units to the left. This brings us to 0:
-4 + 9 + (-5) = 0.
What number is 2/9 of 36?
Of means multiplication, so 2/9 of 36 means 2/9 times 36.
Answer: 8
Fill in the missing exponent in the following equation:
33 × 32 × 3? = 39
We begin by writing out the exponents on the left-hand side as a multiplication:
(3 × 3 × 3) x (3 × 3) × 3? = 39
We can consolidate (3 × 3 × 3) x (3 × 3) as 35.
35 × 3? = 39.
Divide both sides by 35 (or multiply both sides by 3-5):
3-5 × 35 × 3? = 3-5 × 39
3? = 34
So ? = 4.
Evaluate the following expression:
8 × 23 - 8 × 3
8 × 23 - 8 × 3 = 8 × (23 - 3) = 8 × 20 = 160
Provide an expression that describes the following sequence:
3, 6, 9, 12, 15, ...
(Check your work! Evaluate the the expression you chose for some values of n.)
3 × n
Order the following decimals from greatest to least:
1.70; .017; 7.10; 1.07
Answer: 7.10; 1.70; 1.07; .017.
Amira bought 15 books. 8 of the books were fiction and the rest were nonfiction. What is the ratio of nonfiction to fiction books?
There are 15 - 8 = 7 nonfiction books. The ratio of nonfiction to fiction books is 7:8.
Fill in the missing exponent in the following equation:
(52)3 = 5?
We begin by writing out the exponents on the left-hand side as a multiplication:
(5 × 5)3 = (5 × 5) × (5 × 5) × (5 × 5) = 56.
So ? = 6.
Use the distributive property to evaluate the expression below:
79 × 6 - 6 × 19
79 × 6 - 6 × 19
= 6 × 79 - 6 × 19
= 6 × (79 - 19)
= 6 x 60
= 360
Fifteen years ago, Devin was thirty-three years old. How many years old is Devin today? Use d to represent Devin's current age in years.
Let d represent Devin's current age in years. If Devin was 33 years old 15 years ago, then
d - 15 = 33.
Adding 15 to both sides,
d = 33 + 15 = 48
Compute the following sum:
0.3 + 0.55 + 0.777
Answer: 1.627
Three identical bags of ice weigh a total of 8 pounds. How many pounds do ten identical bags of ice weigh?
If three identical bags of ice weigh a total of 8 pounds, then each bag of ice weighs 8/3 pounds.
Ten identical bags of ice would weigh 10 × 8/3 pounds = 80/3 pounds. As a mixed number, this is 26⅔ pounds.
What is the greatest common factor of x = 22 · 32 · 7 · 11 and y = 23 · 3 · 52 · 7?
All factors of x = 22 · 32 · 7 · 11 must have the following form:
2a · 3b · 5c · 7d · 11f,
where a is 0, 1, or 2; b is 0, 1, or 2; c is 0; d is 0 or 1; and f is 0 or 1.
All factors of y = 23 · 3 · 52 · 7 must have the following form:
2p · 3q · 5r · 7s · 11t,
where p is 0, 1, 2 or 3; q is 0 or 1; r is 0, 1, or 2; s is 0 or 1; and t is 0.
So the greatest common factor of x and y is 22 · 3 · 7 = 84.
Grogg completed 7 math problems. Lennin completed 19 times as many math problems as Grogg. How many problems did Grogg and Lennin complete all together?
They completed
7 + 19 × 7
= 1 × 7 + 19 × 7
= (1 + 19) × 7
= 20 × 7
= 140
problems
Evaluate the expression below for x = 8 and y =6.
5xy + 4x + 3y + 2
Substituting x = 8 and y = 6:
5xy + 4x + 3y + 2
= 5 · 8 · 6 + 4 · 8 + 3 · 6 + 2
= 240 + 32 + 18 + 2
= 292
The 18 students with sparkly glitter swim caps make up 30% of the swimmers on the swim team. How many students are on the swim team?
Let x be the number of students on the swim team. Then 0.3x = 18. So x = 18/.3 = 180/3 = 60.
If a ÷ (1/16) = 20, what is the value of a?
Remember that dividing by a number is the same as multiplying by its reciprocal. So we can rewrite the equation
a ÷ (1/16) = 20
as
a × 16 = 20.
Dividing both sides by 16, we get:
a = 20/16 = 5/4.
What is the smallest integer that is a factor of x = 22 · 32 · 7 · 11 but is not a factor of y = 23 · 3 · 52 · 7?
All factors of x = 22 · 32 · 7 · 11 must have the following form:
2a · 3b · 5c · 7d · 11f,
where a is 0, 1, or 2; b is 0, 1, or 2; c is 0; d is 0 or 1; and f is 0 or 1.
All factors of y = 23 · 3 · 52 · 7 must have the following form:
2p · 3q · 5r · 7s · 11t,
where p is 0, 1, 2 or 3; q is 0 or 1; r is 0, 1, or 2; s is 0 or 1; and t is 0.
So, the smallest integer that is a factor of x but not a factor of y is 32 = 9.
Use the distributive property to evaluate the following expression:
14 × 97 + 2 × 14
14 × 97 + 2 × 14
= 14 × 97 + 14 × 2
= 14 × (97 + 2)
= 14 × 99
= 14 × (100 - 1)
= 14 × 100 - 14 × 1
= 1400 - 14
= 1386
Solve the following equation by isolating the variable.
(b - 11) · 3 = 57
We start by dividing both sides of the equation by 3:
(b - 11) · 3 ÷ 3 = 57 ÷ 3
b - 11 = 19
Add 11 to both sides:
b = 30.
Ileana grew 80% as many rutabagas as Stephanie. Ileana grew 30 fewer rutabagas than Stephanie. How many rutabagas did Stephanie grow?
Let y be the number of rutabagas that Stephanie grew. So we can represent the problem using the following equation:
0.8y = y - 30
Subtract 0.8y from both sides:
0 = .2y - 30
Add 30 to both sides:
.2y = 30
Divide both sides by .2:
y = 30/.2 = 300/2 = 150
So Stephanie grew 150 rutabagas.