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Common Core: 6th Grade Math : The Number System

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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Example Questions

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Example Question #1 : How To Multiply And Divide Decimals

Menu 1

Above is the menu at the concession stand at a school carnival.

David wants to buy some chicken strips for himself and his companions. He wants six strips, his brother Mickey wants five strips, his girlfriend Vickie wants three, and Mickey's girlfriend Jenny wants five. Since the concession stand only sells the strips in orders of four, he has decided to just purchase as many orders as it takes to feed the entire group. How much will he spend on enough orders of strips to satisfy the group?

(No tax is charged, since this is a school event)

Possible Answers:

$\$11.97$

$\$18.95$

$\$15.96$

$\$19.95$

Correct answer:

$\$19.95$

Explanation:

The group wants a total of 6+5+ 3 + 5 = 19 strips; since

$19 \div 4 = 4 \textup{ R }3$ ,

Dave will need to purchase five orders of strips (he cannot purchase a partial order). This will cost him

$\$3.99 \times 5 = \$19.95$ .

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Example Question #1 : How To Solve Arithmetic Word Problems

The menu of a local coffeehouse reads as follows:

$\begin{matrix} \textrm{Espresso}\; \; \; & \$1.79 \\ \textrm{Cafe Latte} & \$2.19 \\ \textrm{Cappucino} & \$2.29 \\ \textrm{Americano} & \$2.39 \\ \textrm{Turkish\; \; } & \$2.09 \\ \textrm{Iced Tea}\; \; \; & \$1.59 \end{matrix}$

Sandy orders some drinks for herself and some friends. She orders three cappuccinos, two iced teas, two cafe lattes, and an espresso. The sales tax is five percent. How much change does she receive back for a twenty-dollar bill?

Possible Answers:

$\$4.59$

$\$ 2.97$

$\$3.78$

A twenty-dollar bill isn't enough to buy the drinks.

$\$4.85$

Correct answer:

$\$ 2.97$

Explanation:

The three cappuccinos cost: $\$2.29 \times 3 = \$6.87$

The two iced teas cost $\$1.59 \times 2 = \$3.18$

The two cafe lattes cost $\$2.19 \times 2 = \$4.38$

The espresso costs $\$1.79$ .

Add these amounts to get the cost before tax:

$\$ 6.87 + 3.18 + 4.38 + 1.79 = \$ 16.22$

The tax is five percent of $\$16.22$ or:

$\$16.22 \times 0.05 \approx \$ 0.81$

Add both values in order to obtain the total cost after tax.

$\$16.22 + 0.81 = \$ 17.03$

As a result, the change from a twenty-dollar bill is as follows:

$\$20.00- 17.03= \$ 2.97$

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Example Question #61 : The Number System

Solve:

${0.42{\overline{\smash{)}4.19348}}}$

Possible Answers:

{9.984R20}

{9R20}

{9R984}

{20R9.984}

Correct answer:

{9.984R20}

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. We do this by moving the decimal place to the right:

${0.42\rightarrow 42}$

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend:

${4.19348\rightarrow 419.348}$

The new division problem should look as follows:

$\ \ \ \ .\\42{\overline{\smash{)}419.348}}$

*Notice how we've already placed the decimal in our answer. When we divide decimals, we place the decimal directly above the decimal in the dividend, but only after we've completed the first two steps of moving the decimal point in the divisor and dividend.

Now we can divide like normal:

$\ \ \ \ .\\42{\overline{\smash{)}419.348}}$

Think: how many times can 42 go into 419

42 can go into 419 nine times times so we write a 9 over the 9 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000} 9.~\phantom{~~0} } \\[-3pt]42\ )419.348\ \end{array}$

Next, we multiply 9 and 42 and write that product underneath the 419 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}9.~\phantom{~~0} } \\[-3pt] 42) \ 419.348\\ \underline{-378\phantom{~000}} \\41\phantom{~000} \end{array}$

Now we bring down the 3 from the dividend to make the 41 into a 413.

Think: how many times can 42 go into 413?

42 can go into 413 nine times so we write a 9 above the 3 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}9.9\phantom{00} } \\[-3pt]42) \ 419.348\\ \underline{-378\phantom{~000}} \\ 413\phantom{~00} \end{array}$

Next, we multiply 9 and 42 and write that product underneath the 413 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}9.9 \phantom{00} } \\[-3pt]42) \ 419.348 \\ \underline{-378\phantom{~000}} \\ 413 \phantom{~00} \\ \underline{-378\phantom{~00}} \\35\phantom{~00} \end{array}$

Now we bring down the 4 from the dividend to make the 35 into a 354.

Think: how many times can 42 go into 354?

42 can go into 354 eight times so we write a 8 above the 4 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}9.98 \phantom{0} } \\[-3pt]42) \ 419.348 \\ \underline{-378\phantom{~000}} \\ 413\phantom{~00} \\ \underline{-378\phantom{~00}} \\ 354 \phantom{~0} \end{array}$

Next, we multiply 8 and 42 and write that product underneath the 354 and subtract:

Now we bring down the 8 from the dividend to make the 18 into a 188.

Think: how many times can 42 go into 188?

42 can go into 188 four times so we write a 4 above the 8 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}9.984 } \\[-3pt]42) \ 419.348 \\ \underline{-378\phantom{~000}} \\ 413\phantom{~00} \\ \underline{-378\phantom{~00}} \\ 354 \phantom{~0} \\ \underline{-336\phantom{~0}} \\188 \phantom{~} \end{array}$

Next, we multiply 4 and 42 and write that product underneath the 188 and subtract:

Notice our remainder is 20 so our answer is 9.984R20.

Report an Error

Example Question #62 : The Number System

Solve:

${0.88{\overline{\smash{)}3.19851}}}$

Possible Answers:

{3R59}

{3.634R59}

{3R634}

{59R3.634}

Correct answer:

{3.634R59}

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. We do this by moving the decimal place to the right:

${0.88\rightarrow 88}$

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend:

${3.19851\rightarrow 319.851}$

The new division problem should look as follows:

$\ \ \ \ .\\88{\overline{\smash{)}319.851}}$

Now we can divide like normal:

$\ \ \ \ .\\88{\overline{\smash{)}319.851}}$

Think: how many times can 88 go into 319

88 can go into 319 three times times so we write a 3 over the 9 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000} 3.~\phantom{~~0} } \\[-3pt]88\ )319.851\ \end{array}$

Next, we multiply 3 and 88 and write that product underneath the 319 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}3.~\phantom{~~0} } \\[-3pt] 88) \ 319.851\\ \underline{-264\phantom{~000}} \\55\phantom{~000} \end{array}$

Now we bring down the 8 from the dividend to make the 55 into a 558.

Think: how many times can 88 go into 558?

88 can go into 558 six times so we write a 6 above the 8 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}3.6\phantom{00} } \\[-3pt]88) \ 319.851\\ \underline{-264\phantom{~000}} \\ 558\phantom{~00} \end{array}$

Next, we multiply 6 and 88 and write that product underneath the 558 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}3.6 \phantom{00} } \\[-3pt]88) \ 319.851 \\ \underline{-264\phantom{~000}} \\ 558 \phantom{~00} \\ \underline{-528\phantom{~00}} \\30\phantom{~00} \end{array}$

Now we bring down the 5 from the dividend to make the 30 into a 305.

Think: how many times can 88 go into 305?

88 can go into 305 three times so we write a 3 above the 5 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}3.63 \phantom{0} } \\[-3pt]88) \ 319.851 \\ \underline{-264\phantom{~000}} \\ 558\phantom{~00} \\ \underline{-528\phantom{~00}} \\ 305 \phantom{~0} \end{array}$

Next, we multiply 3 and 88 and write that product underneath the 305 and subtract:

Now we bring down the 1 from the dividend to make the 41 into a 411.

Think: how many times can 88 go into 411?

88 can go into 411 four times so we write a 4 above the 1 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}3.634 } \\[-3pt]88) \ 319.851 \\ \underline{-264\phantom{~000}} \\ 558\phantom{~00} \\ \underline{-528\phantom{~00}} \\ 305 \phantom{~0} \\ \underline{-264\phantom{~0}} \\411 \phantom{~} \end{array}$

Next, we multiply 4 and 88 and write that product underneath the 411 and subtract:

Notice our remainder is 59 so our answer is 3.634R59.

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Example Question #63 : The Number System

Solve:

${0.64{\overline{\smash{)}3.00216}}}$

Possible Answers:

{4.690R56}

{4R56}

{4R690}

{56R4.690}

Correct answer:

{4.690R56}

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. We do this by moving the decimal place to the right:

${0.64\rightarrow 64}$

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend:

${3.00216\rightarrow 300.216}$

The new division problem should look as follows:

$\ \ \ \ .\\64{\overline{\smash{)}300.216}}$

Now we can divide like normal:

$\ \ \ \ .\\64{\overline{\smash{)}300.216}}$

Think: how many times can 64 go into 300

64 can go into 300 four times times so we write a 4 over the 0 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000} 4.~\phantom{~~0} } \\[-3pt]64\ )300.216\ \end{array}$

Next, we multiply 4 and 64 and write that product underneath the 300 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}4.~\phantom{~~0} } \\[-3pt] 64) \ 300.216\\ \underline{-256\phantom{~000}} \\44\phantom{~000} \end{array}$

Now we bring down the 2 from the dividend to make the 44 into a 442.

Think: how many times can 64 go into 442?

64 can go into 442 six times so we write a 6 above the 2 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}4.6\phantom{00} } \\[-3pt]64) \ 300.216\\ \underline{-256\phantom{~000}} \\ 442\phantom{~00} \end{array}$

Next, we multiply 6 and 64 and write that product underneath the 442 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}4.6 \phantom{00} } \\[-3pt]64) \ 300.216 \\ \underline{-256\phantom{~000}} \\ 442 \phantom{~00} \\ \underline{-384\phantom{~00}} \\58\phantom{~00} \end{array}$

Now we bring down the 1 from the dividend to make the 58 into a 581.

Think: how many times can 64 go into 581?

64 can go into 581 nine times so we write a 9 above the 1 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}4.69 \phantom{0} } \\[-3pt]64) \ 300.216 \\ \underline{-256\phantom{~000}} \\ 442\phantom{~00} \\ \underline{-384\phantom{~00}} \\ 581 \phantom{~0} \end{array}$

Next, we multiply 9 and 64 and write that product underneath the 581 and subtract:

Now we bring down the 6 from the dividend to make the 5 into a 56.

Think: how many times can 64 go into 56?

64 can go into 56 zero so we write a 0 above the 6 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}4.690 } \\[-3pt]64) \ 300.216 \\ \underline{-256\phantom{~000}} \\ 442\phantom{~00} \\ \underline{-384\phantom{~00}} \\ 581 \phantom{~0} \\ \underline{-576\phantom{~0}} \\56 \phantom{~} \end{array}$

Next, we multiply 0 and 64 and write that product underneath the 56 and subtract:

Notice our remainder is 56 so our answer is 4.690R56.

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Example Question #64 : The Number System

Solve:

${0.82{\overline{\smash{)}1.99402}}}$

Possible Answers:

{2.431R60}

{2R60}

{60R2.431}

{2R431}

Correct answer:

{2.431R60}

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. We do this by moving the decimal place to the right:

${0.82\rightarrow 82}$

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend:

${1.99402\rightarrow 199.402}$

The new division problem should look as follows:

$\ \ \ \ .\\82{\overline{\smash{)}199.402}}$

Now we can divide like normal:

$\ \ \ \ .\\82{\overline{\smash{)}199.402}}$

Think: how many times can 82 go into 199

82 can go into 199 two times times so we write a 2 over the 9 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000} 2.~\phantom{~~0} } \\[-3pt]82\ )199.402\ \end{array}$

Next, we multiply 2 and 82 and write that product underneath the 199 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}2.~\phantom{~~0} } \\[-3pt] 82) \ 199.402\\ \underline{-164\phantom{~000}} \\35\phantom{~000} \end{array}$

Now we bring down the 4 from the dividend to make the 35 into a 354.

Think: how many times can 82 go into 354?

82 can go into 354 four times so we write a 4 above the 4 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}2.4\phantom{00} } \\[-3pt]82) \ 199.402\\ \underline{-164\phantom{~000}} \\ 354\phantom{~00} \end{array}$

Next, we multiply 4 and 82 and write that product underneath the 354 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}2.4 \phantom{00} } \\[-3pt]82) \ 199.402 \\ \underline{-164\phantom{~000}} \\ 354 \phantom{~00} \\ \underline{-328\phantom{~00}} \\26\phantom{~00} \end{array}$

Now we bring down the 0 from the dividend to make the 26 into a 260.

Think: how many times can 82 go into 260?

82 can go into 260 three times so we write a 3 above the 0 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}2.43 \phantom{0} } \\[-3pt]82) \ 199.402 \\ \underline{-164\phantom{~000}} \\ 354\phantom{~00} \\ \underline{-328\phantom{~00}} \\ 260 \phantom{~0} \end{array}$

Next, we multiply 3 and 82 and write that product underneath the 260 and subtract:

Now we bring down the 2 from the dividend to make the 14 into a 142.

Think: how many times can 82 go into 142?

82 can go into 142 one time so we write a 1 above the 2 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}2.431 } \\[-3pt]82) \ 199.402 \\ \underline{-164\phantom{~000}} \\ 354\phantom{~00} \\ \underline{-328\phantom{~00}} \\ 260 \phantom{~0} \\ \underline{-246\phantom{~0}} \\142 \phantom{~} \end{array}$

Next, we multiply 1 and 82 and write that product underneath the 142 and subtract:

Notice our remainder is 60 so our answer is 2.431R60.

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Example Question #65 : The Number System

Solve:

${0.44{\overline{\smash{)}3.44256}}}$

Possible Answers:

{44R7.823}

{7.823R44}

{7R823}

{7R44}

Correct answer:

{7.823R44}

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. We do this by moving the decimal place to the right:

${0.44\rightarrow 44}$

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend:

${3.44256\rightarrow 344.256}$

The new division problem should look as follows:

$\ \ \ \ .\\44{\overline{\smash{)}344.256}}$

Now we can divide like normal:

$\ \ \ \ .\\44{\overline{\smash{)}344.256}}$

Think: how many times can 44 go into 344

44 can go into 344 seven times times so we write a 7 over the 4 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000} 7.~\phantom{~~0} } \\[-3pt]44\ )344.256\ \end{array}$

Next, we multiply 7 and 44 and write that product underneath the 344 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}7.~\phantom{~~0} } \\[-3pt] 44) \ 344.256\\ \underline{-308\phantom{~000}} \\36\phantom{~000} \end{array}$

Now we bring down the 2 from the dividend to make the 36 into a 362.

Think: how many times can 44 go into 362?

44 can go into 362 eight times so we write a 8 above the 2 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}7.8\phantom{00} } \\[-3pt]44) \ 344.256\\ \underline{-308\phantom{~000}} \\ 362\phantom{~00} \end{array}$

Next, we multiply 8 and 44 and write that product underneath the 362 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}7.8 \phantom{00} } \\[-3pt]44) \ 344.256 \\ \underline{-308\phantom{~000}} \\ 362 \phantom{~00} \\ \underline{-352\phantom{~00}} \\10\phantom{~00} \end{array}$

Now we bring down the 5 from the dividend to make the 10 into a 105.

Think: how many times can 44 go into 105?

44 can go into 105 two times so we write a 2 above the 5 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}7.82 \phantom{0} } \\[-3pt]44) \ 344.256 \\ \underline{-308\phantom{~000}} \\ 362\phantom{~00} \\ \underline{-352\phantom{~00}} \\ 105 \phantom{~0} \end{array}$

Next, we multiply 2 and 44 and write that product underneath the 105 and subtract:

Now we bring down the 6 from the dividend to make the 17 into a 176.

Think: how many times can 44 go into 176?

44 can go into 176 three times so we write a 3 above the 6 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}7.823 } \\[-3pt]44) \ 344.256 \\ \underline{-308\phantom{~000}} \\ 362\phantom{~00} \\ \underline{-352\phantom{~00}} \\ 105 \phantom{~0} \\ \underline{-88\phantom{~0}} \\176 \phantom{~} \end{array}$

Next, we multiply 3 and 44 and write that product underneath the 176 and subtract:

Notice our remainder is 44 so our answer is 7.823R44.

Report an Error

Example Question #66 : The Number System

Solve:

${0.84{\overline{\smash{)}1.59708}}}$

Possible Answers:

{1R24}

{1R901}

{24R1.901}

{1.901R24}

Correct answer:

{1.901R24}

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. We do this by moving the decimal place to the right:

${0.84\rightarrow 84}$

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend:

${1.59708\rightarrow 159.708}$

The new division problem should look as follows:

$\ \ \ \ .\\84{\overline{\smash{)}159.708}}$

Now we can divide like normal:

$\ \ \ \ .\\84{\overline{\smash{)}159.708}}$

Think: how many times can 84 go into 159

84 can go into 159 one time times so we write a 1 over the 9 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000} 1.~\phantom{~~0} } \\[-3pt]84\ )159.708\ \end{array}$

Next, we multiply 1 and 84 and write that product underneath the 159 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}1.~\phantom{~~0} } \\[-3pt] 84) \ 159.708\\ \underline{-84\phantom{~000}} \\75\phantom{~000} \end{array}$

Now we bring down the 7 from the dividend to make the 75 into a 757.

Think: how many times can 84 go into 757?

84 can go into 757 nine times so we write a 9 above the 7 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}1.9\phantom{00} } \\[-3pt]84) \ 159.708\\ \underline{-84\phantom{~000}} \\ 757\phantom{~00} \end{array}$

Next, we multiply 9 and 84 and write that product underneath the 757 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}1.9 \phantom{00} } \\[-3pt]84) \ 159.708 \\ \underline{-84\phantom{~000}} \\ 757 \phantom{~00} \\ \underline{-756\phantom{~00}} \\1\phantom{~00} \end{array}$

Now we bring down the 0 from the dividend to make the 1 into a 10.

Think: how many times can 84 go into 10?

84 can go into 10 zero so we write a 0 above the 0 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}1.90 \phantom{0} } \\[-3pt]84) \ 159.708 \\ \underline{-84\phantom{~000}} \\ 757\phantom{~00} \\ \underline{-756\phantom{~00}} \\ 10 \phantom{~0} \end{array}$

Next, we multiply 0 and 84 and write that product underneath the 10 and subtract:

Now we bring down the 8 from the dividend to make the 10 into a 108.

Think: how many times can 84 go into 108?

84 can go into 108 one time so we write a 1 above the 8 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}1.901 } \\[-3pt]84) \ 159.708 \\ \underline{-84\phantom{~000}} \\ 757\phantom{~00} \\ \underline{-756\phantom{~00}} \\ 10 \phantom{~0} \\ \underline{-0\phantom{~0}} \\108 \phantom{~} \end{array}$

Next, we multiply 1 and 84 and write that product underneath the 108 and subtract:

Notice our remainder is 24 so our answer is 1.901R24.

Report an Error

Example Question #67 : The Number System

Solve:

${0.81{\overline{\smash{)}1.90494}}}$

Possible Answers:

{2.351R63}

{2R351}

{2R63}

{63R2.351}

Correct answer:

{2.351R63}

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. We do this by moving the decimal place to the right:

${0.81\rightarrow 81}$

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend:

${1.90494\rightarrow 190.494}$

The new division problem should look as follows:

$\ \ \ \ .\\81{\overline{\smash{)}190.494}}$

Now we can divide like normal:

$\ \ \ \ .\\81{\overline{\smash{)}190.494}}$

Think: how many times can 81 go into 190

81 can go into 190 two times times so we write a 2 over the 0 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000} 2.~\phantom{~~0} } \\[-3pt]81\ )190.494\ \end{array}$

Next, we multiply 2 and 81 and write that product underneath the 190 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}2.~\phantom{~~0} } \\[-3pt] 81) \ 190.494\\ \underline{-162\phantom{~000}} \\28\phantom{~000} \end{array}$

Now we bring down the 4 from the dividend to make the 28 into a 284.

Think: how many times can 81 go into 284?

81 can go into 284 three times so we write a 3 above the 4 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}2.3\phantom{00} } \\[-3pt]81) \ 190.494\\ \underline{-162\phantom{~000}} \\ 284\phantom{~00} \end{array}$

Next, we multiply 3 and 81 and write that product underneath the 284 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}2.3 \phantom{00} } \\[-3pt]81) \ 190.494 \\ \underline{-162\phantom{~000}} \\ 284 \phantom{~00} \\ \underline{-243\phantom{~00}} \\41\phantom{~00} \end{array}$

Now we bring down the 9 from the dividend to make the 41 into a 419.

Think: how many times can 81 go into 419?

81 can go into 419 five times so we write a 5 above the 9 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}2.35 \phantom{0} } \\[-3pt]81) \ 190.494 \\ \underline{-162\phantom{~000}} \\ 284\phantom{~00} \\ \underline{-243\phantom{~00}} \\ 419 \phantom{~0} \end{array}$

Next, we multiply 5 and 81 and write that product underneath the 419 and subtract:

Now we bring down the 4 from the dividend to make the 14 into a 144.

Think: how many times can 81 go into 144?

81 can go into 144 one time so we write a 1 above the 4 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}2.351 } \\[-3pt]81) \ 190.494 \\ \underline{-162\phantom{~000}} \\ 284\phantom{~00} \\ \underline{-243\phantom{~00}} \\ 419 \phantom{~0} \\ \underline{-405\phantom{~0}} \\144 \phantom{~} \end{array}$

Next, we multiply 1 and 81 and write that product underneath the 144 and subtract:

Notice our remainder is 63 so our answer is 2.351R63.

Report an Error

Example Question #68 : The Number System

Solve:

${0.78{\overline{\smash{)}4.26323}}}$

Possible Answers:

{5.465R53}

{5R465}

{53R5.465}

{5R53}

Correct answer:

{5.465R53}

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. We do this by moving the decimal place to the right:

${0.78\rightarrow 78}$

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend:

${4.26323\rightarrow 426.323}$

The new division problem should look as follows:

$\ \ \ \ .\\78{\overline{\smash{)}426.323}}$

Now we can divide like normal:

$\ \ \ \ .\\78{\overline{\smash{)}426.323}}$

Think: how many times can 78 go into 426

78 can go into 426 five times times so we write a 5 over the 6 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000} 5.~\phantom{~~0} } \\[-3pt]78\ )426.323\ \end{array}$

Next, we multiply 5 and 78 and write that product underneath the 426 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}5.~\phantom{~~0} } \\[-3pt] 78) \ 426.323\\ \underline{-390\phantom{~000}} \\36\phantom{~000} \end{array}$

Now we bring down the 3 from the dividend to make the 36 into a 363.

Think: how many times can 78 go into 363?

78 can go into 363 four times so we write a 4 above the 3 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}5.4\phantom{00} } \\[-3pt]78) \ 426.323\\ \underline{-390\phantom{~000}} \\ 363\phantom{~00} \end{array}$

Next, we multiply 4 and 78 and write that product underneath the 363 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}5.4 \phantom{00} } \\[-3pt]78) \ 426.323 \\ \underline{-390\phantom{~000}} \\ 363 \phantom{~00} \\ \underline{-312\phantom{~00}} \\51\phantom{~00} \end{array}$

Now we bring down the 2 from the dividend to make the 51 into a 512.

Think: how many times can 78 go into 512?

78 can go into 512 six times so we write a 6 above the 2 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}5.46 \phantom{0} } \\[-3pt]78) \ 426.323 \\ \underline{-390\phantom{~000}} \\ 363\phantom{~00} \\ \underline{-312\phantom{~00}} \\ 512 \phantom{~0} \end{array}$

Next, we multiply 6 and 78 and write that product underneath the 512 and subtract:

Now we bring down the 3 from the dividend to make the 44 into a 443.

Think: how many times can 78 go into 443?

78 can go into 443 five times so we write a 5 above the 3 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}5.465 } \\[-3pt]78) \ 426.323 \\ \underline{-390\phantom{~000}} \\ 363\phantom{~00} \\ \underline{-312\phantom{~00}} \\ 512 \phantom{~0} \\ \underline{-468\phantom{~0}} \\443 \phantom{~} \end{array}$

Next, we multiply 5 and 78 and write that product underneath the 443 and subtract:

Notice our remainder is 53 so our answer is 5.465R53.

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