We can use the standard algorithm to divide decimals by whole numbers.

To illustrate, let's compute 7.2 \div 3.

First, we write down the problem using long division notation, keeping the decimal point in the dividend:

3 \!\require{enclose}\enclose{longdiv}{7 {\,\bbox[2px, lightgray]{\color{blue}.}\,} 2}{\:\phantom{|}}

We also bring the decimal point up into the quotient, placing it directly above the decimal point in the dividend:


\,\phantom{0} \bbox[2px, lightgray]{\color{blue}.}
3 \!\require{enclose}\enclose{longdiv}{7 {\bbox[2px, lightgray]{\color{blue}.} 2{\:\phantom{|}}}}

Now, we carry out the long division process as usual:

\,2 {\,\, . \,} 4
3 \!\require{enclose}\enclose{longdiv}{7 {\,\, . \,} 2}
-\!\!\!\!\! 6
1 2
-\!\!\!\!\! 1 2
0

Therefore, 7.2 \div 3 = 2.4 \, .

Note: The "standard algorithm" is the same as "long division." The two phrases can be used interchangeably.

FLAG

What is 54.8 \div 4?

EXPLANATION

We will use the standard algorithm.

First, we write down the problem using long division notation, keeping the decimal point in the dividend:

4 \!\require{enclose}\enclose{longdiv}{5 {\:\phantom{|}} 4 {\,\bbox[2px, lightgray]{\color{blue}.}\,} 8}

We also bring the decimal point up into the quotient, placing it directly above the decimal point in the dividend:

\,\, \,\phantom{0} \bbox[2px, lightgray]{\color{blue}.}
4 \!\require{enclose}\enclose{longdiv}{5 {\:\phantom{|}} 4 {\,\bbox[2px, lightgray]{\color{blue}.}\,} 8}

Now, we carry out the long division process as usual:

\,\, 1 {\:\phantom{|}} 3 {\,\, . \,} 7
4 \!\require{enclose}\enclose{longdiv}{5 {\:\phantom{|}} 4 {\,\, . \,} 8}
-\!\!\!\!\! 4
1 4
-\!\!\!\!\! 1 2
2 8
-\!\!\!\!\! 2 8
0

Therefore, 54.8 \div 4 = 13.7 \, .

FLAG

What is $76.5 \div 5?$

a
$15.3$
b
$15.1$
c
$15.5$
d
$15.7$
e
$15.8$

What is $9.6 \div 8?$

a
$1.4$
b
$1.1$
c
$1.7$
d
$1.2$
e
$1.3$

To make 4 servings of ice cream, Rita used 3.4 ounces of cocoa powder. How much cocoa powder did she use for each serving?

EXPLANATION

To determine the amount of cocoa powder Rita used to make each serving, we need to divide 3.4 by 4. To do this, we can use the standard algorithm.

First, we write down the problem using long division notation, keeping the decimal point in the dividend:

4 \!\require{enclose}\enclose{longdiv}{3 {\,\bbox[2px, lightgray]{\color{blue}.}\,} 4}{\:\phantom{|}}

We also bring the decimal point up into the quotient, placing it directly above the decimal point in the dividend:

\:\; \phantom{0} \bbox[2px, lightgray]{\color{blue}.}
4 \!\require{enclose}\enclose{longdiv}{3 {\,\bbox[2px, lightgray]{\color{blue}.}\,} 4}{\:\phantom{|}}

Now, we carry out the long division process as usual:

\, 0 {\,\, . \,} 8 {\:\phantom{|}}5
4 \!\!\require{enclose}\enclose{longdiv}{\, 3 {\,\, . \,} 4 {\:\phantom{|}}0}
\,-\!\!\!\!\! 3 2
2 0
-\!\!\!\!\! 2 0
0

Therefore, 3.4 \div 4 = 0.85 \, .

We conclude that Rita used 0.85 ounces of cocoa powder to make each serving of ice cream.

FLAG

A store owner evenly distributed $71.5$ pounds of salmon into $5$ refrigerators. How much salmon did he put into each refrigerator?

a
$14.5$ pounds
b
$14.7$ pounds
c
$11.9$ pounds
d
$14.3$ pounds
e
$13.9$ pounds

Albert cut a $5.6$-foot piece of wire into $4$ pieces of equal length. How long is each piece?

a
$0.9$ feet
b
$1.9$ feet
c
$1.4$ feet
d
$1.6$ feet
e
$1.8$ feet

We can also use the standard algorithm to divide decimals by other decimals. The only difference is that we first need to find an equivalent division problem where the divisor is a whole number.

To illustrate, let's compute 1.11\div 0.3 \, . First, we write this division problem as a fraction: \dfrac{1.11}{0.3}

Then, we multiply the numerator and denominator by 10 so that we get a whole number in the denominator: \dfrac{1.11 \times 10}{0.3\times 10} = \dfrac{11.1}{3}

Now we see that the division problem is equivalent to 11.1 \div 3. We can compute this using long division as usual:

\,\, 0 {\:\phantom{|}} 3 {\,\, . \,} 7
3 \!\require{enclose}\enclose{longdiv}{1 {\:\phantom{|}} 1 {\,\, . \,} 1}
-\!\!\!\!\! 9
2 1
-\!\!\!\!\! 2 1
0

From the long division, we find that 11.1 \div 3 = 3.7, so we conclude that 1.11 \div 0.3 = 3.7 \, .

FLAG

0.0694 \div 0.2=

EXPLANATION

We can write this division problem as a fraction, as follows:

\dfrac{0.0694}{0.2}

Multiplying the numerator and denominator by 10, we get a whole number in the denominator:

\dfrac{0.0694 \times 10}{0.2\times 10} = \dfrac{0.694}{2}

Now we see that the division problem is equivalent to 0.694 \div 2. We can compute this using long division as usual:



0 {\, . \,} 3 {\:\phantom{|}} 4 {\:\phantom{|}} 7
2 \!\!\require{enclose}\enclose{longdiv}{0 {\, . \,} 6 {\:\phantom{|}} 9 {\:\phantom{|}} 4 }
-\!\!\! 6
0 9
-\!\!\! 8
1 4
-\!\!\! 1 4
0

From the long division, we find that 0.694 \div 2 = 0.347, so we conclude that 0.0694 \div 0.2 = 0.347 \, .

FLAG

$8.19 \div 0.7=$

a
$11.5$
b
$11.6$
c
$11.9$
d
$11.7$
e
$11.3$

$0.92 \div 0.4=$

a
$2.2$
b
$2.3$
c
$2.5$
d
$2.4$
e
$2.1$

What is 0.471 \div 0.02?

EXPLANATION

We can write this division problem as a fraction, as follows: \dfrac{0.471}{0.02}

Multiplying the numerator and denominator by 100, we get a whole number in the denominator:

\dfrac{0.471 \times 100}{0.02\times 100} = \dfrac{47.1}{2}

Now we see that the division problem is equivalent to 47.1 \div 2. We can compute this using the standard algorithm:

\,2\,\, \,3\,. \,5\,\, \,5\,\,
2 \!\!\require{enclose}\enclose{longdiv}{4 {\:\phantom{|}} 7 {\:\phantom{|}\,} \!\!\!.\, \!1 {\:\phantom{|}} 0}
-\!\!\! 4
0 7
-\!\!\! 6
1 1
-\!\!\! 1 0
1 0
-\!\!\! 1 0
0

From the long division, we find that 47.1 \div 2 = 23.55, so we conclude that 0.471 \div 0.02 = 23.55 \, .

FLAG

What is $7.563 \div 0.03?$

a
$252.3$
b
$252.5$
c
$252.2$
d
$252.4$
e
$252.1$

What is $2.823 \div 0.04?$

a
$70.575$
b
$707.05$
c
$705.75$
d
$70.705$
e
$70.75$
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