Factors & Multiples
Write the prime factorization of 36.
2 × 2 × 3 × 3, or 2² × 3²
In 156 ÷ 12 = 13, identify the dividend, divisor, and quotient.
Dividend: 156; divisor: 12; quotient: 13.
Calculate: 18.6 ÷ 3.
6.2
What is the reciprocal of 3/5?
5/3
Maya walks 1.25 miles in the morning and 0.8 mile in the afternoon. How far does she walk altogether?
Addition: 1.25 + 0.8 = 2.05 miles.
Without calculating, is 5 ÷ 8 greater than or less than 1? Explain.
Less than 1 because the dividend is smaller than the divisor.
Evaluate: 3² + 12 ÷ 4.
12
What is the greatest common factor of 24 and 40?
8
Calculate: 1,248 ÷ 6.
208
Calculate: 14 ÷ 0.4.
35
How many 1/4-size pieces are in 3/4? Write and solve a division equation.
3/4 ÷ 1/4 = 3 pieces.
A container holds 7/8 liter of juice. Jordan pours out 1/4 liter. How much juice remains?
Subtraction: 7/8 − 1/4 = 5/8 liter.
Estimate 2,394 ÷ 31 using friendly numbers.
About 80, using 2,400 ÷ 30.
A club charges a $5 registration fee plus $3 per meeting. Write an expression for the total cost of attending m meetings. Then find the cost for 4 meetings.
3m + 5; $17 for 4 meetings.
What is the least common multiple of 6 and 8?
24
Calculate: 3,744 ÷ 24.
156
Calculate: 8.64 ÷ 0.24.
36
Calculate: 2/3 ÷ 5/6. Simplify your answer.
4/5
A container holds 7/8 liter of juice. Jordan pours out 1/4 of the juice. How much juice does he pour out?
Multiplication: 1/4 × 7/8 = 7/32 liter.
Three friends share 2 pizzas equally. Write a division equation and state how much pizza each friend receives.
2 ÷ 3 = 2/3 pizza per friend.
Simplify: 4(x + 3) + 2x.
6x + 12.
A teacher has 48 pencils and 60 erasers. She makes the greatest possible number of identical supply bags, using all the supplies. How many bags can she make, and what goes in each bag?
12 bags, each containing 4 pencils and 5 erasers. Use the GCF.
Calculate 125 ÷ 6. Write your answer as both a mixed number and a repeating decimal.
20 5/6 and 20.8333… with only the 3 repeating.
A student rewrites 6.3 ÷ 0.09 as 6.3 ÷ 9. What is the mistake? Write a correct equivalent division expression and solve.
Both numbers must be multiplied by 100 to keep the quotient the same. 630 ÷ 9 = 70.
Calculate: 2 1/4 ÷ 3/5.
3 3/4
A ribbon is 3/4 yard long. Each bow requires 1/8 yard of ribbon. How many bows can be made?
Division: 3/4 ÷ 1/8 = 6 bows.
You have 5 1/2 cups of flour. Each batch of muffins requires 3/4 cup. How many complete batches can you make? Explain how you interpret the quotient.
7 complete batches. 5 1/2 ÷ 3/4 = 7 1/3, but there is not enough flour for an eighth complete batch.
Solve: 3x + 4 = 25. Check your solution using substitution.
x = 7
Two lights flash together. One flashes every 8 seconds and the other every 12 seconds. How many seconds until they next flash together? Explain whether you used GCF or LCM.
24 seconds. Use LCM because we need the first time both flashing schedules match again.
There are 157 students going on a trip. Each van holds 12 students. What is the fewest number of vans needed? Explain what happens to the remainder.
14 vans. 157 ÷ 12 = 13 R1, so one additional van is needed for the remaining student.
A club has $50. It buys 3 packs of markers for $6.75 each and 4 poster boards for $2.40 each. How much money remains?
$20.15. Markers cost $20.25 and poster boards cost $9.60. Total spent: $29.85.
A pitcher holds 2 1/2 liters of juice. Each glass holds 3/8 liter. How many full glasses can be filled?
6 full glasses.
2 1/2 ÷ 3/8 = 6 2/3. Round down because there isn’t enough juice to fill a seventh glass.
A class has 28 students. Three-fourths of the students participate in a club. Two-thirds of those club participants play a sport. How many students participate in both a club and a sport?
Multiplication: 28 × 3/4 × 2/3 = 14 students.
A team has 6 1/2 gallons of water. Each cooler holds 1 1/4 gallons. What is the fewest number of coolers needed to hold all the water? Explain.
6 coolers. 6 1/2 ÷ 1 1/4 = 5 1/5, so a sixth cooler is needed to hold the remaining water.
Solve: 3c + 8 ≥ 20. Describe how to graph the solution.
c ≥ 4