\(7.2\) is \(72\) tenths. Dividing \(72\) by \(3\) gives \(24\) tenths.

Twenty-four tenths is \(2.4\). Check: \(2.4\times3=7.2\).

Answer

\(2.4\)

Divide the total by the multiplier: \(7.5\div5\).

\(75\) tenths divided by \(5\) gives \(15\) tenths, or \(1.5\).

Answer

\(\square=1.5\); \(7.5\div5=1.5\).

\(12\div6=2\), and the remaining \(0.6\div6=0.1\). Thus the quotient is \(2.1\).

The multiplication check is \(2.1\times6=12.6\).

Answer

Option B: \(2.1\).

Correct option: B

Each length is \(9.24\div7\). In hundredths of a metre, \(924\div7=132\).

This gives \(132\) hundredths of a metre, or \(1.32\,\mathrm{m}\). Check: \(7\times1.32=9.24\).

Answer

\(1.32\,\mathrm{m}\)

\(4.8\div6=0.8\), and \(7.35\div3=2.45\).

For C, \(12.600\div8=1.575\). Appending zeros allows the division to continue exactly.

Comparing the three amounts gives \(0.8\lt 1.575\lt 2.45\), so B is largest.

Answer

A: \(0.8\,\mathrm{L}\); B: \(2.45\,\mathrm{L}\); C: \(1.575\,\mathrm{L}\). Batch B gives the largest amount.

\(8\div4=2\). There is only \(1\) tenth left, so four groups cannot each receive a whole tenth: write a zero in the tenths position.

The \(16\) hundredths divide into \(4\) hundredths per group, giving \(2.04\). Check: \(2.04\times4=8.16\).

The incorrect value \(2.4\) would give \(2.4\times4=9.6\), not the original total.

Answer

\(8.16\div4=2.04\). The zero in the tenths position is necessary.

Dividing by \(3\) and then \(5\) divides the original amount into \(3\times5=15\) equal shares.

Calculate in two steps: \(18.9\div3=6.3\), then \(6.3\div5=1.26\). Check: \(1.26\times15=18.9\).

Answer

Yes. Both methods give \(1.26\).

The exact quotient is \(29.95\div7=4.278571\ldots\), which rounds to \(4.28\) pounds.

If all seven pay \(4.28\), they pay \(29.96\), one penny too much.

Reducing one payment by one penny gives \(6\times4.28+4.27=29.95\). The payments differ by only one penny.

Answer

Rounded share: \(4.28\) pounds. Six friends pay \(4.28\) pounds and one pays \(4.27\) pounds.

Divisors \(3,4,5,6\) give quotients at least \(18.72\div6=3.12\), so they fail the size condition. Only \(7,8,9\) remain.

The amount \(18.72\) contains \(1872\) hundredths. For the quotient to have at most two decimal places, this hundredths count must divide exactly.

\(1872=7\times267+3\), so \(7\) does not divide \(1872\) exactly, but \(1872\div8=234\) and \(1872\div9=208\). Therefore the two stated quotients are the only possibilities.

Answer

\(d=8\), quotient \(2.34\); or \(d=9\), quotient \(2.08\).

A quotient strictly between \(0.5\) and \(1\) requires the original number to be strictly between \(2\) and \(4\). Hence its whole-number digit must be \(2\).

The possible originals are \(2.048,2.084,2.408,2.480,2.804,2.840\). Their quotients are \(0.512,0.521,0.602,0.620,0.701,0.710\), respectively.

Only \(0.620=0.62\) and \(0.710=0.71\) can be written with at most two decimal places. All arrangements with the required whole-number digit have been checked.

Answer

\(2.480\div4=0.62\) and \(2.840\div4=0.71\).