Square Roots/Exponents
Write the following product using exponential notation:
4 × 4 × 4 = ?
43
Is 387 divisible by 3? Explain using the divisibility rule.
Yes. 3 + 8 + 7 = 18, which is divisible by 3.
Determine the least common multiple (LCM) of 15 and 40.
120
Calculate:
10 + 4 × 11
54
Ana is preparing three piñatas for a birthday party.
She purchases:
4 bags of 72 chocolate bars
3 bags of 50 candies
95 gummy candies
4 bags of 10 toys
If she divides everything equally among the three piñatas, how many items will be in each?
(4 × 72 + 3 × 50 + 95 + 4 × 10) ÷ 3 = 191 items
Write the following power in expanded notation:
6⁵ = ?
6 × 6 × 6 × 6 × 6
Which of the following numbers divide evenly into 387?
2, 3, 4, 5, 6, 8, 9, or 10.
3 and 9
Vincent goes to the grocery store every 8 days, and Juan goes every 6 days.
If they both went today, in how many days will they both be there again?
24 days (LCM of 8 and 6)
Calculate:
(1 + 5) × 3 ÷ (4 + 2)
3
Julie has a budget of $650 for a party.
She purchases:
80 invitations at $1 each
$120 in decorations
5 dozen cupcakes at $2 each
A room rental for $250
How much money will Julie have left?
650 − 80 − 120 − (5 × 12 × 2) − 250 = $80
Antoine wants to change the allowance he receives from his parents. He asks for 1 cent in January, 2 cents in February, 4 cents in March, 8 cents in April, and 16 cents in May.
If the pattern continues, how much will he receive in June? Write your answer in exponential and standard notation.
25 = 32 cents
Which of the following numbers divide evenly into 28,974?
2, 3, 4, 5, 6, 8, 9, or 10.
2, 3, and 6
Rachelle is making identical fruit baskets for the Salvation Army.
She has 250 pears, 375 oranges, and 625 apples.
What is the maximum number of identical baskets she can make using all the fruit?
125 baskets (GCF of 250, 375, and 625)
Calculate:
(50 + 2) × 4 ÷ (5 − 1)
52
A computer repair shop starts the day with $1,800.
During the day:
A customer purchases a computer for $675.
The shop purchases 3 boxes of hard drives at $800 each.
Two customers pay $315 each for repairs.
What is the shop's final balance?
1,800 + 675 − (3 × 800) + (2 × 315) = $705
Robert and John collect golf balls every morning for five days.
Robert collects 2⁰, 2¹, 2², 2³, and 2⁴ golf balls from Monday to Friday.
John collects 5 golf balls every day.
Who collected the most golf balls over the five days, and by how many?
Robert collected 31 golf balls, and John collected 25. Robert collected 6 more golf balls.
Which of the following numbers is divisible by 2, 3, and 4, but NOT by 5 or 8?
375, 672, 492, 602, 861, 126
492
A sporting goods store receives a shipment containing:
240 footballs
320 Frisbees
640 hockey sticks
What is the maximum number of identical boxes that can be prepared using all the items and what will each box contain?
80 boxes (GCF of 240, 320, and 640)
Each box contains 3 footballs, 4 Frisbees, and 8 hockey sticks.
Calculate:
(2⁰ + 2² ÷ 4) × [10 ÷ (4 − 4⁰ × 3)]
20
Carlos starts the month with $540 in his bank account. The month has exactly four weeks.
Each week:
He earns $95 walking dogs.
He earns $30 twice from babysitting.
He tutors for 3 hours at $15 per hour.
He also spends $80 on a monthly bus pass.
How much money will Carlos have at the end of the month?
540 + (4 × 95) + (4 × 2 × 30) + (4 × 15 × 3) − 80 = $1,260