Powers of 10
What is 6.42 ÷ 10?
0.642
What is 7.2 ÷ 3?
2.4
What is 0.35 ÷ 5?
0.07
What is 0.32 ÷ 0.08?
4
True or false: Dividing always makes a number smaller.
False.
What is 48.3 ÷ 100?
0.483
What is 4.68 ÷ 6?
0.78
What is 3.24 ÷ 4?
0.81
What is 3.6 ÷ 0.6?
6
Give an example where dividing makes the quotient greater than the dividend.
Example: 0.80 ÷ 0.05 = 16
The answer is greater because we are counting how many small groups fit inside 0.80.
Explain why 35 ÷ 100 = 0.35, not 3.5.
Because dividing by 100 makes the number 100 times smaller. Each digit’s place value becomes two places smaller.
Solve: 6.15 ÷ 3
2.05
Solve: $10.00 ÷ 4
$2.50
Rewrite 1.42 ÷ 1.4 as an equivalent problem with a whole-number divisor.
14.2 ÷ 14
A student solves 4.55 ÷ 3.5 by changing it to 4.55 ÷ 35. What mistake did they make?
They moved the decimal only in the divisor. They must move the decimal the same number of places in both numbers. It should become 45.5 ÷ 35
What is 0.704 ÷ 1000?
0.000704
A student solves 8.55 ÷ 5 and gets 17.1. How do you know that cannot be right?
Because 8.55 ÷ 5 should be close to 9÷5, which is about 1.8, not 17.1.
Solve 0.912 ÷ 8
0.114
Solve 0.96 ÷ 0.08
12
Why is “just move the decimal” a weak explanation?
Because it hides the place-value meaning. The digits are not magically moving; their place value changes depending on the operation.
A student says 18.5 ÷ 100 = 1.85. What is wrong, and what is the correct answer?
They only divided by 10, not by 100. The correct answer is 0.185
Solve and explain the place value:
2.48 ÷ 4
0.62.
2 ones, 4 tenths, and 8 hundredths are split into 4 equal groups. Each group gets 6 tenths and 2 hundredths.
Solve $5.25 ÷ 4 to the nearest cent.
$1.31, because 5.25 ÷ 4 = 1.3125, which rounds to $1.31.
Solve 3.24 ÷ 0.4 and explain why the quotient is greater than 3.
3.24 ÷ 0.4 = 8.1.
The quotient is greater than 3 because we are asking how many groups of 0.4 fit inside 3.24. Since 0.4 is less than 1, many groups can fit inside 3.24.
A student gets 0.384 ÷ 4 = 0.96. Use estimation to prove this is wrong.
0.384 is less than 0.4, and 0.4 ÷ 4 = 0.1
So the answer must be less than 0.1.
0.96 is much too large. The correct answer is 0.096.