Place Value & Powers of 10
In the number 64,382, what is the value of the digit 6?
Answer: 60,000
Calculate 3.45 + 2.30.
Answer: 5.75
Calculate 24 x 6.
Answer: 144
Calculate 936 divide 3.
Answer: 312
Round 48,672 to the nearest thousand.
Answer: 49,000
How many times greater is the value of the 8 in 8,426 than the value of the 8 in 3,185?
Answer: 100 times greater (8,000 ÷ 80 = 100)
Calculate 8.6 - 3.78.
Answer: 4.82
Calculate 326 x 14.
Answer: 4,564
Calculate 1,728 divide 12.
Answer: 144
Round 6.847 to the nearest hundredth.
Answer: 6.85
What is 4.728 x 10? Explain how the digits change place value.
Answer: 47.28. Each digit shifts one place to the left.
Calculate 4.26 x 3.
Answer: 12.78
A school orders 28 boxes of pencils. Each box contains 144 pencils. How many pencils does the school order?
Answer: 4,032 pencils.
A school has 2,856 stickers to divide equally among 24 classrooms. How many stickers does each classroom receive?
Answer: 119 stickers.
A school buys 18 calculators for $12.75 each. Estimate the total cost by rounding the price to the nearest dollar. Then calculate the exact cost.
Answer:
Estimate: 18 x $13 = $234.
Exact cost: 18 x $12.75 = $229.50.
A student says 36.5 divide 100 = 3.65. Explain the mistake and give the correct answer.
Answer: The decimal moves two places left when dividing by 100. The correct answer is 0.365.
Calculate 6.24 x 2.5. Show how you can use a whole-number multiplication fact to help.
Answer: 15.6.
Since 2.5 = 25 divide 10, calculate 6.24 x 25 = 156, then divide by 10.
Calculate 4,306 x 27. Show how you break apart the factors to solve.
Answer: 116,262.
For example, 4,306 x (20 + 7) = 86,120 + 30,142.
Calculate 5,376 divide 32. Prove your answer by multiplying the quotient by the divisor.
Answer: 168.
Check: 168 x 32 = 5,376.
A school has a budget of $500. It buys 24 books for $8.75 each and 16 games for $12.50 each. How much money remains? Show the two costs and the subtraction.
Answer: Books: $210. Games: $200. Total: $410. Money remaining: $90.
A number has a 7 in the hundreds place, a 7 in the tenths place, and a 7 in the thousandths place. How many times greater is the value of the first 7 than the value of the last 7?
Answer: 100,000 times greater (700 ÷ 0.007 = 100,000).
A ribbon is 12.6 meters long. A teacher cuts it into 4 equal pieces. Each piece is then cut into 3 equal smaller pieces. How long is each smaller piece?
Answer: 1.05 meters.
12.6 divide 4 = 3.15, then 3.15 divide 3 = 1.05.
A theater has 36 rows with 48 seats in each row. Every seat is filled for 25 performances. How many tickets are sold in total?
Answer: 43,200 tickets.
36 x 48 = 1,728 seats per performance;
1,728 x 25 = 43,200.
A factory produces 7,425 notebooks. They pack 36 notebooks into each full box. How many full boxes can they pack, and how many notebooks will be left over? Explain what the remainder means.
Answer: 206 full boxes with 9 notebooks left over.
36 x 206 = 7,416, and 7,425 - 7,416 = 9.
A field trip has 8 buses with 48 seats per bus. There are 347 students and 21 adults attending. Each person needs one seat. Are there enough seats? How many seats will be empty, or how many more seats are needed? Justify your answer.
Answer: There are 8 x 48 = 384 seats.
There are 347 + 21 = 368 people.
Yes, there are enough seats, with 384 - 368 = 16 seats empty.