- Interpret the final partial dividend as tenths. - Use the divisor to find how many equal groups fit into those tenths.

1. The displayed problem is \(4.2\div2\). 2. The final partial dividend is \(2\) tenths. 3. \(2\) tenths divided by \(2\) is \(1\) tenth, so the missing quotient digit is \(1\), and the subtraction row is \(2\).

Missing quotient digit: \(1\); subtraction row: \(2\).

- Count the equal segments from \(0\) to \(1.2\). - Division can represent splitting a total into equal parts. - Check by multiplying one segment length by the number of segments.

1. The distance from \(0\) to \(1.2\) is split into \(3\) equal segments. 2. \(1.2\div3=0.4\), so each segment has length \(0.4\).

\(0.4\); \(1.2\div3=0.4\)

- Find the weight of one bag before finding the weight of \(100\) bags. - Use decimal division for part a). - Think about how multiplying by \(100\) changes place value.

1. \(12.6\div12=1.05\), so one bag weighs \(1.05\,\text{lb}\). 2. \(1.05\times100=105\), so \(100\) bags weigh \(105\,\text{lb}\).

a) \(1.05\,\text{lb}\) b) \(105\,\text{lb}\)

- Divide the total cost by the number of identical sets. - Keep the decimal point aligned as you divide. - Multiply your quotient by \(8\) to check it.

1. Divide the total cost by the number of sets: \(\$62.00 \div 8 = \$7.75\). 2. Check: \(8 \times \$7.75 = \$62.00\).

One paintbrush set costs \(\$7.75\).

- Divide the total bill by the number of friends. - Keep the decimal point aligned during the division. - Multiply the amount per person by \(9\) to check your answer.

1. Divide the total bill equally among the nine friends: \(\$110.70 \div 9 = \$12.30\). 2. Check: \(9 \times \$12.30 = \$110.70\).

Each friend should pay \(\$12.30\).

- The answer should be a little more than \(2\,\text{m}\). - Use place value to keep the quotient aligned with the dividend. - Check by multiplying your quotient by \(6\).

1. Divide the total length by the number of equal pieces: \(13.5 \div 6\). 2. Using decimal division, \(13.5 \div 6 = 2.25\). 3. Each piece is \(2.25\,\text{m}\) long.

Each piece is \(2.25\,\text{m}\) long.

- Interpret the second displayed partial dividend by place value, not just as the whole number \(15\). - Decide how many groups of \(3\) fit into those tenths. - Match that step to the corresponding place in the quotient.

1. Three goes into \(7\) two times, leaving \(1\) one. 2. Regroup the remaining \(1\) one as \(10\) tenths and combine it with the \(5\) tenths to make the displayed partial dividend \(15\) tenths. 3. Since \(15\div3=5\), the missing quotient digit is \(5\). 4. That digit counts tenths, so it is written in the tenths place. The quotient is \(2.5\).

The missing quotient digit is \(5\). The displayed \(15\) represents \(15\) tenths, and \(15\) tenths divided by \(3\) is \(5\) tenths, so the digit belongs to the right of the decimal point. The quotient is \(2.5\).

- Express \(4.7\,\text{L}\) as tenths of a liter. - Share the available \(0.1\)-liter portions equally among the three bottles. - Interpret both the quotient and the remainder in liters.

1. \(4.7\,\text{L}\) is \(47\) tenths of a liter, so the dispenser can make \(47\) presses. 2. \(47\div3=15\) remainder \(2\). 3. Each bottle gets \(15\) presses, or \(1.5\,\text{L}\). Two presses' worth, or \(0.2\,\text{L}\), remains.

\(1.5\,\text{L}\) in each bottle, with \(0.2\,\text{L}\) left.

- Compare the dividend with the divisor before calculating. - Can you rewrite the dividend using one place-value unit that makes the division easier? - Multiply your quotient by \(8\) to check.

1. Since \(7.2<8\), splitting \(7.2\) into \(8\) equal groups gives a quotient less than \(1\). 2. \(7.2\div8=0.9\). 3. Check: \(0.9\times8=7.2\).

\(0.9\); it is less than \(1\) because \(7.2<8\). Check: \(0.9\times8=7.2\).

- Read the amount using the ones and tenths columns. - One whole can be traded for \(10\) tenths. - Share the resulting tenths equally among \(3\) groups.

1. Trading \(1\) one for \(10\) tenths turns \(1.8\) into \(18\) tenths. 2. \(18\) tenths shared among \(3\) groups gives \(6\) tenths per group. 3. \(6\) tenths is \(0.6\), so \(1.8\div3=0.6\).

a) \(18\) tenths b) \(6\) tenths in each group; \(1.8\div3=0.6\)

- Divide each shipment's total weight by its number of bags. - Compare the two unit weights. - Use the stated conversion for the final difference.

1. First shipment: \(312.5\div25=12.5\,\text{lb}\) per bag. 2. Second shipment: \(480\div40=12\,\text{lb}\) per bag. 3. The first bag is heavier by \(0.5\,\text{lb}\). 4. \(0.5\times16=8\,\text{oz}\).

a) First shipment: \(12.5\,\text{lb}\); second shipment: \(12\,\text{lb}\) b) The first bag is heavier by \(8\,\text{oz}\).

- Divide the total amount equally among the bottles. - For part b), find the total amount needed if every bottle gets the proposed amount.

1. For a), divide the concentrate equally: \(12.5\div50=0.25\) cup per bottle. 2. For b), \(0.3\times50=15\) cups would be needed. 3. Since \(15>12.5\), the club does not have enough concentrate.

a) \(0.25\) cup per bottle b) The plan would require \(15\) cups, but only \(12.5\) cups are available.

- You may divide first and convert afterward, or convert first if that is easier. - Use the stated unit relationships for the conversion step. - Check by multiplying each quotient by the divisor.

1. a) \(4.5\div6=0.75\,\text{m}\), and \(0.75\,\text{m}=75\,\text{cm}\). 2. b) \(0.12\div8=0.015\,\text{km}\), and \(0.015\,\text{km}=15\,\text{m}\).

a) \(75\,\text{cm}\) b) \(15\,\text{m}\)

- Choose a nearby dollar amount that is easy to divide by \(6\). - Divide the exact total by \(6\). - Subtract the exact amount from the estimate to compare them.

1. Estimate with \(\$120\div6=\$20\). 2. Exactly, \(\$112.50\div6=\$18.75\). 3. The exact amount is \(\$20.00-\$18.75=\$1.25\) less than the estimate.

Estimate: \(\$20\) per student Exact: \(\$18.75\) per student The exact amount is \(\$1.25\) less than the estimate.

- Find the total cost of the notebooks first. - Subtract that amount from the full bill. - Divide the remaining amount equally among the four pens.

1. The notebooks cost \(5 \times \$2.40 = \$12.00\). 2. The four pens cost \(\$22.00 - \$12.00 = \$10.00\). 3. One pen costs \(\$10.00 \div 4 = \$2.50\).

One pen costs \(\$2.50\).

- First find the total amount Lucas spends. - How much do the three highlighters cost altogether? - Subtract the highlighter cost to find the cost of all five notebooks. - Then divide to find the cost of one notebook.

1. Find the total amount spent: \(\$10.00 - \$2.50 = \$7.50\). 2. Find the cost of the three highlighters: \(3 \times \$1.50 = \$4.50\). 3. Find the cost of all five notebooks: \(\$7.50 - \$4.50 = \$3.00\). 4. Divide by the number of notebooks: \(\$3.00 \div 5 = \$0.60\).

One notebook costs \(\$0.60\).

- Find the price of one pencil. - Multiply the unit price by \(15\). - Check that six times the unit price equals \(\$4.20\).

1. One pencil costs \(\$4.20 \div 6 = \$0.70\). 2. Fifteen pencils cost \(15 \times \$0.70 = \$10.50\).

The \(15\) pencils cost \(\$10.50\).

- Divide Offer A’s total price by the number of bottles. - Compare the two unit prices. - Subtract the smaller unit price from the larger one.

1. Offer A costs \(\$3.90 \div 3 = \$1.30\) per bottle. 2. Since \(\$1.30 < \$1.45\), Offer A costs less per bottle. 3. The difference is \(\$1.45 - \$1.30 = \$0.15\).

a) Offer A costs \(\$1.30\) per bottle. b) Offer A costs less by \(\$0.15\) per bottle.

- How much does the entire purchase cost after accounting for the change? - How much do the two loaves cost? - What is the total cost of the rolls? - Divide that amount by ten to find the price of one roll.

1. Find the total cost of the purchase: \(\$20 - \$7 = \$13\). 2. Find the cost of the two loaves: \(2 \times \$4 = \$8\). 3. Find the cost of all ten rolls: \(\$13 - \$8 = \$5.00\). 4. Divide by the number of rolls: \(\$5.00 \div 10 = \$0.50\).

One roll costs \(\$0.50\).

- Find the price of one binder at each store. - You can change each dollar amount to cents before dividing. - Compare the two unit prices.

1. Find the unit price at the first store: \(840\text{ cents} \div 4 = 210\text{ cents}\), or \(\$2.10\). 2. Find the unit price at the second store: \(660\text{ cents} \div 3 = 220\text{ cents}\), or \(\$2.20\). 3. Compare the unit prices: \(\$2.10 < \$2.20\).

One binder is less expensive at the first store because it costs \(\$2.10\), compared with \(\$2.20\) at the second store.

- Interpret the remainder after the tenths step in terms of tenths. - A trailing zero can be added to a decimal without changing its value. - Use the displayed final partial dividend to determine the last quotient digit.

1. After the tenths step, \(2\) tenths remain. 2. Writing \(12.6\) as \(12.60\) does not change its value. The remaining \(2\) tenths become \(20\) hundredths. 3. Since \(20\div4=5\), the missing hundredths digit is \(5\), and the missing subtraction row is \(20\). 4. The quotient is \(3.15\).

The missing quotient digit is \(5\), the subtraction row is \(20\), and the quotient is \(3.15\). Writing \(12.6\) as \(12.60\) does not change its value, so the remaining \(2\) tenths can be written as \(20\) hundredths.

- First compare the ones in the dividend with the divisor. - Use the displayed partial dividend \(33\) to determine the tenths quotient digit. - The same multiplier determines the missing subtraction row.

1. Since \(3<8\), the quotient has \(0\) ones. 2. Regroup to \(33\) tenths. The greatest multiple of \(8\) not exceeding \(33\) is \(32=8\times4\). The missing tenths digit is \(4\), and the subtraction row is \(32\). 3. The remainder is \(1\) tenth; bringing down \(6\) gives \(16\) hundredths, and \(16\div8=2\). 4. The quotient is \(0.42\).

The missing tenths digit is \(4\), the subtraction row is \(32\), and the quotient is \(0.42\). It begins with \(0\) ones because \(3<8\).