Question

divide by using an area model. then check your work.

1. 234 ÷ 18

check:
234 = ____ × 18

estimate the partial quotients as you divide. then check your work.

1. 436 ÷ 17

check:
436 = __ × 17 + __

grid with 17)436

quotient: ____
remainder: ____

Explanation:

Problem 2: \(234\div18\)

Area Model Division:

1. Break down the dividend and divisor:

• We know that the area of a rectangle is \( \text{length} \times \text{width} \). Here, the total area (dividend) is \(234\) and the width (divisor) is \(18\). We want to find the length (quotient).
• We can break \(234\) into parts that are multiples of \(18\). Let's start with a larger multiple. \(18\times10 = 180\). Then, \(234 - 180=54\).
• Now, \(18\times3 = 54\).
• So, the total number of times \(18\) fits into \(234\) is \(10 + 3=13\).

Check:

We know that in division, \( \text{dividend}=\text{quotient}\times\text{divisor} \). So, \(234 = 13\times18\) (since \(13\times18=(10\times18)+(3\times18)=180 + 54 = 234\)).

Problem 3: \(436\div17\)

Partial Quotients Method:

1. Estimate the first partial quotient:

• We see how many times \(17\) can go into \(436\). Let's start with a multiple of \(17\). \(17\times20 = 340\) (since \(17\times20\) is a relatively easy multiple to calculate).
• Subtract \(340\) from \(436\): \(436-340 = 96\).

1. Estimate the second partial quotient:

• Now, we look at how many times \(17\) can go into \(96\). \(17\times5=85\) (a multiple of \(17\) less than \(96\)).
• Subtract \(85\) from \(96\): \(96 - 85=11\).

1. Find the quotient and remainder:

• The quotient is the sum of the partial quotients: \(20 + 5=25\).
• The remainder is \(11\) (since we can't divide \(11\) by \(17\) anymore).

Check:

In division with remainder, \( \text{dividend}=\text{quotient}\times\text{divisor}+\text{remainder} \). So, \(436=25\times17 + 11\) (since \(25\times17 = 425\) and \(425+11 = 436\)).

Final Answers:

Problem 2:

• Quotient (from division): \(13\)
• Check: \(234=\boldsymbol{13}\times18\)

Problem 3:

• Quotient: \(\boldsymbol{25}\)
• Remainder: \(\boldsymbol{11}\)
• Check: \(436=\boldsymbol{25}\times17+\boldsymbol{11}\)

Answer:

Problem 2: \(234\div18\)

Area Model Division:

1. Break down the dividend and divisor:

• We know that the area of a rectangle is \( \text{length} \times \text{width} \). Here, the total area (dividend) is \(234\) and the width (divisor) is \(18\). We want to find the length (quotient).
• We can break \(234\) into parts that are multiples of \(18\). Let's start with a larger multiple. \(18\times10 = 180\). Then, \(234 - 180=54\).
• Now, \(18\times3 = 54\).
• So, the total number of times \(18\) fits into \(234\) is \(10 + 3=13\).

Check:

We know that in division, \( \text{dividend}=\text{quotient}\times\text{divisor} \). So, \(234 = 13\times18\) (since \(13\times18=(10\times18)+(3\times18)=180 + 54 = 234\)).

Problem 3: \(436\div17\)

Partial Quotients Method:

1. Estimate the first partial quotient:

• We see how many times \(17\) can go into \(436\). Let's start with a multiple of \(17\). \(17\times20 = 340\) (since \(17\times20\) is a relatively easy multiple to calculate).
• Subtract \(340\) from \(436\): \(436-340 = 96\).

1. Estimate the second partial quotient:

• Now, we look at how many times \(17\) can go into \(96\). \(17\times5=85\) (a multiple of \(17\) less than \(96\)).
• Subtract \(85\) from \(96\): \(96 - 85=11\).

1. Find the quotient and remainder:

• The quotient is the sum of the partial quotients: \(20 + 5=25\).
• The remainder is \(11\) (since we can't divide \(11\) by \(17\) anymore).

Check:

In division with remainder, \( \text{dividend}=\text{quotient}\times\text{divisor}+\text{remainder} \). So, \(436=25\times17 + 11\) (since \(25\times17 = 425\) and \(425+11 = 436\)).

Final Answers:

Problem 2:

• Quotient (from division): \(13\)
• Check: \(234=\boldsymbol{13}\times18\)

Problem 3:

• Quotient: \(\boldsymbol{25}\)
• Remainder: \(\boldsymbol{11}\)
• Check: \(436=\boldsymbol{25}\times17+\boldsymbol{11}\)