Question

divide. use base - ten blocks.

1. $4.9\div7 = \underline{\quad\quad}$
2. $3.6\div9 = \underline{\quad\quad}$
3. $2.4\div8 = \underline{\quad\quad}$
4. $6.48\div4 = \underline{\quad\quad}$
5. $3.01\div7 = \underline{\quad\quad}$
6. $4.26\div3 = \underline{\quad\quad}$

Explanation:

Problem 3: \(4.9\div7\)

Step1: Recall division of decimals

We can think of \(4.9\) as \(49\) tenths. So, \(49\) tenths divided by \(7\) is \(7\) tenths, because \(49\div7 = 7\). Since we are dealing with tenths, \(7\) tenths is \(0.7\).

Step2: Verify with base - ten blocks (conceptually)

If we have \(4\) ones and \(9\) tenths. We can't divide \(4\) ones evenly by \(7\), so we convert the \(4\) ones into \(40\) tenths. Then we have \(40 + 9=49\) tenths. Dividing \(49\) tenths into \(7\) equal groups, each group gets \(7\) tenths, which is \(0.7\).

Problem 4: \(3.6\div9\)

Step1: Rewrite the decimal as tenths

\(3.6\) is equal to \(36\) tenths. Now, we divide \(36\) tenths by \(9\).

Step2: Perform the division

Since \(36\div9 = 4\), \(36\) tenths divided by \(9\) is \(4\) tenths. \(4\) tenths is \(0.4\).

Problem 5: \(2.4\div8\)

Step1: Express as tenths

\(2.4\) can be written as \(24\) tenths.

Step2: Divide the tenths

We divide \(24\) tenths by \(8\). Since \(24\div8=3\), \(24\) tenths divided by \(8\) is \(3\) tenths, which is \(0.3\).

Problem 6: \(6.48\div4\)

Step1: Divide the whole number part

First, divide the whole number part \(6\) by \(4\). \(6\div4 = 1\) with a remainder of \(2\).

Step2: Combine with the decimal part

The remainder \(2\) (which is \(2\) ones) is converted to \(20\) tenths. Add the \(4\) tenths from \(6.48\), so we have \(20 + 4=24\) tenths. \(24\) tenths divided by \(4\) is \(6\) tenths (\(0.6\)).

Step3: Divide the hundredths part

Now, we have \(8\) hundredths. \(8\) hundredths divided by \(4\) is \(2\) hundredths (\(0.02\)).

Step4: Combine the results

Adding the results together: \(1+0.6 + 0.02=1.62\).

Problem 7: \(3.01\div7\)

Step1: Rewrite the decimal

\(3.01\) can be thought of as \(301\) hundredths (since \(3.01=3+\ 0.01\times1=300\) hundredths \(+ 1\) hundredth \( = 301\) hundredths).

Step2: Perform the division

Divide \(301\) hundredths by \(7\). Since \(301\div7 = 43\), \(301\) hundredths divided by \(7\) is \(43\) hundredths. \(43\) hundredths is \(0.43\).

Problem 8: \(4.26\div3\)

Step1: Divide the whole number part

Divide \(4\) by \(3\). \(4\div3 = 1\) with a remainder of \(1\).

Step2: Convert the remainder and add the tenths

The remainder \(1\) (one) is converted to \(10\) tenths. Add the \(2\) tenths from \(4.26\), so we have \(10 + 2 = 12\) tenths. \(12\) tenths divided by \(3\) is \(4\) tenths (\(0.4\)).

Step3: Divide the hundredths part

We have \(6\) hundredths. \(6\) hundredths divided by \(3\) is \(2\) hundredths (\(0.02\)).

Step4: Combine the results

Adding the results: \(1+0.4 + 0.02=1.42\).

Answer:

1. \(0.7\)
2. \(0.4\)
3. \(0.3\)
4. \(1.62\)
5. \(0.43\)
6. \(1.42\)