Rational Numbers: Decimals, Fractions and Word Problems: Grade 7 Math Test Answer Key – PDF Download

Question 1: Convert to decimals (2 points)

1. \(70: 16=4\) r 6, \(60: 16=3\) r 12, \(120: 16=7\) r 8, \(80: 16=5\) r 0: 0.4375.
2. \(50: 12=4\) r 2, \(20: 12=1\) r 8, \(80: 12=6\) r 8, and the remainder 8 repeats: \(0.41\overline{6}\).

Scoring: 1 point for each part: correct digits from the division; in (b) the bar over only the 6 is required.

Question 2: Is it exact? (2 points)

\(10: 6=1\) r 4, \(40: 6=6\) r 4, and the remainder 4 repeats forever. The decimal does not stop, so Ethan is not correct: \(\frac{1}{6}=0.1\overline{6}\).

Scoring: 1 point for carrying out the division and seeing the repeated remainder (or noting that it never reaches 0); 1 point for the correct decimal \(0.1\overline{6}\) with the bar.

Question 3: Order temperatures (2 points)

As decimals: \(-2.25,\ -2.6,\ -2.2,\ -2.75\). The more negative a number is, the lesser it is: \(-2.75<-2.6<-2.25<-2.2\).

\(-2\frac{3}{4},\ -2.6,\ -2.25,\ -2.2\)

Scoring: 1 point for converting all values to one form; 1 point for the correct order.

Question 4: Add and subtract (3 points)

1. \(7.35-4.8=2.55\), positive. 2.55
2. \(-\frac{10}{12}-\frac{3}{12}=-\frac{13}{12}\). \(-\frac{13}{12}\) (or \(-1\frac{1}{12}\))
3. \(\frac{3\times 4}{8\times 9}=\frac{12}{72}=\frac{1}{6}\), positive because both factors are negative. \(\frac{1}{6}\)

Scoring: 1 point for each part. In (b) accept the mixed number; deduct nothing for an unsimplified fraction that is equal.

Question 5: Multiply and divide (3 points)

1. \(2.4: 0.8=3\), different signs. \(-3\)
2. \(-\frac{3}{4}\times \frac{10}{9}=-\frac{30}{36}=-\frac{5}{6}\). \(-\frac{5}{6}\)
3. \(-\frac{3}{2}\times \frac{8}{3}=-\frac{24}{6}=-4\). \(-4\)

Scoring: 1 point for each part: correct value and sign.

Question 6: Overnight cold (3 points)

1. \(5\times (-2.75)=-13.75\).
2. \(9.5-13.75=-4.25\).
3. \(-4.25+6.5=2.25\).

(a) \(-13.75^{\circ}\text{F}\) (b) \(-4.25^{\circ}\text{F}\) (c) \(2.25^{\circ}\text{F}\)

Scoring: 1 point for each part. Allow follow-through: a correct method on an earlier wrong value earns the point.

Question 7: Bank account (3 points)

1. \(-12.40+50.00=37.60\). $37.60
2. \(3\times 8.25=24.75\). $24.75
3. \(37.60-24.75=12.85\). $12.85

Scoring: 1 point for each part.

Question 8: Mean change (2 points)

Sum: \(-1.50+0.75=-0.75\); \(-0.75-2.25=-3.00\); \(-3.00+1.00=-2.00\). Mean: \(-2.00: 4=-0.50\).

The mean daily change is \(-\$0.50\).

Scoring: 1 point for the sum of the four changes (-2.00); 1 point for dividing by 4 to get -0.50.

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