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MATH 15
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DECIMAL OPERATIONS EXPLORATION
1. Use base ten blocks to explore the idea of equivalence involving decimals.
a. Show that 2/5 and 0.4 represent the same number.
b. Show that 3/4 and 0.75 are equal.
c. Show that these three decimals are all equal:
0.1
0.10
d. Show that these two decimals represent the same number:
0.100
0.3
0.30
e. Explain how the first number in each case above can be changed into the second
number by multiplying by an appropriate form of 1 (i.e., a well-chosen fraction).
2. Use base ten blocks to explore addition and subtraction of decimals.
a. 2.78 + 1.34 =
b. 5.4 + 6.17 =
c. 0.92 – 0.35 =
d. 2 – 1.56 =
e. Why does “lining up the decimal places” work in the standard algorithm for adding or
subtracting decimals?
3. Use base ten blocks to explore multiplication and division of decimals by whole numbers.
a. 5 x 1.3 =
b. 2.67 x 3 =
c. 13.6 ÷ 4 =
d. 2.57 ÷ 2 =
MATH 15
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e. How does multiplying and dividing decimals by whole numbers compare to ordinary
whole-number multiplication and division?
4. Use fractional equivalents to explore multiplication involving two decimals. Specifically,
perform each of the following calculations in two ways: first by changing the decimals to
fractional form and then multiplying, and second by using the standard multiplication
algorithm for decimals.
a. 0.1 x 0.3 =
b. 1.2 x 2.6 =
c. 0.8 x 1.45 =
d. 0.63 x 0.17 =
e. Why does “counting the number of decimal places” work in the standard algorithm for
multiplying decimals?
5. Use fractional equivalents to explore division involving two decimals. Specifically,
perform each of the following calculations in three ways: first, by changing the decimals to
fractional form and then dividing (notice what’s happening!); second, by writing the
division as a fraction and then multiplying by an appropriate fractional form of 1 to
eliminate all the decimal places; and third, by using the standard long division algorithm
for decimals.
a. 2.1 ÷ 0.7 =
b. 0.48 ÷ 1.2 =
c. 18.2 ÷ 0.35 =
d. 0.1734 ÷ 0.03 =
e. Why does “move the decimal points the same number of places in the divisor and the
dividend, and place the decimal point in the quotient above the moved point in the
dividend” work in the standard algorithm for dividing decimals?