7th Grade Multiplying and Dividing Rational Numbers Test Solutions and Scoring (PDF)

1. \(-63\)
2. \(9\)
3. \(-30\) (three negative factors)
4. \(0\)

-63, 9, -30, 0

Scoring: Half a point for each correct value; round the total up.

Multiplying by a negative number reverses direction, so doing it twice returns to the original direction.

Example: \(-3\times(-4)=12\), and the pattern \(-3\times 2=-6,\; -3\times 1=-3,\; -3\times 0=0,\; -3\times(-1)=3\) continues upward by 3 each time.

The product is positive

Scoring: 1 point for a correct reason; 1 point for a correct example.

1. \(-0.6\)
2. \(30\)

-0.6; 30

Scoring: 1 point for each.

1. \(-\frac{30}{45}=-\frac{2}{3}\)
2. \(\frac{7}{8}\times 4=\frac{28}{8}=\frac{7}{2}=3\frac{1}{2}\)

\(-\frac{2}{3}\); \(3\frac{1}{2}\)

Scoring: 1 point for each.

1. \(3\div 16=0.1875\), terminating.
2. \(7\div 12=0.58333\)= \(0.58\overline{3}\), repeating.

0.1875 terminating; \(0.58\overline{3}\) repeating

Scoring: 1 point for each decimal with the correct type.

Three jumps of 2.5 to the left: \(0\to -2.5\to -5\to -7.5\).

\(3\times(-2.5)=-7.5\)

-7.5

Scoring: 1 point for the repeated addition or jumps; 1 point for -7.5.

Three negative factors give a negative product.

\(\frac{3}{2}\times\frac{5}{3}\times\frac{2}{5}=\frac{30}{30}=1\)

-1

Scoring: 1 point for the sign; 1 point for the value.

1. \(-4.25\times 6=-25.5\), so $25.50 less.
2. \(-25.5\div 3=-8.5\), so $8.50 less in each.
3. \(-51\div(-4.25)=12\) weeks.

Scoring: 1 point for each part.

1. \(-3+5-2.5-4.5=-5\) degrees.
2. \(-5\div 4=-1.25\) degrees per day.
3. \(-1.25\times 10=-12.5\) degrees.

Scoring: 1 point for each part.