Solving Real-World Problems: Mastering the Four Operations with Rational Numbers

Basic Multiple Choice Questions

1. What is the result of adding $-\frac{3}{4}$ and $\frac{5}{8}$?
   a) $-\frac{1}{8}$
   b) $\frac{1}{8}$
   c) $-\frac{7}{8}$
   d) $\frac{7}{8}$
2. Simplify: $2.5 \times (-4)$.
   a) $10$
   b) $-10$
   c) $-6.5$
   d) $6.5$
3. What is the result of subtracting $2.3$ from $-1.7$?
   a) $4.0$
   b) $0.6$
   c) $-0.6$
   d) $-4.0$
4. If you divide $-\frac{7}{3}$ by $-\frac{2}{3}$, what is the result?
   a) $-\frac{7}{2}$
   b) $\frac{7}{2}$
   c) $\frac{6}{7}$
   d) $-\frac{6}{7}$
5. Calculate: $4 - \left(-2.5\right)$.
   a) $1.5$
   b) $6.5$
   c) $7.5$
   d) $-6.5$

Challenging Multiple Choice Questions

6. Jane is cooking and she needs $\frac{3}{4}$ cup of sugar for each batch of cookies. If she wants to make $2.5$ batches, how much sugar does she need in total?
   a) $1.875$ cups
   b) $2.25$ cups
   c) $1.50$ cups
   d) $3.00$ cups
7. A tank holds $15.6$ gallons of water. If $4.2$ gallons are drained, how much water is left?
   a) $11.8$ gallons
   b) $11.4$ gallons
   c) $9.2$ gallons
   d) $12.4$ gallons
8. Mike practices shooting free throws and scores on $\frac{5}{8}$ of his attempts. If he takes $32$ shots, how many did he make?
   a) $16$
   b) $20$
   c) $24$
   d) $26$
9. A recipe requires $-\frac{2}{3}$ cup of lemon juice. If you add $\frac{1}{2}$ cup more than required, how much lemon juice do you use?
   a) $-\frac{5}{6}$
   b) $-\frac{1}{6}$
   c) $\frac{1}{6}$
   d) $\frac{5}{6}$
10. Sarah spent $-9.5$ dollars buying lunch and $12.75$ dollars on tickets. How much did she spend in total?
    a) $3.25$
    b) $22.25$
    c) $5.25$
    d) $-22.25$
11. A car travels $45.6$ miles using $12$ gallons of gas. What is the car's fuel efficiency in miles per gallon?
    a) $3.8$
    b) $3.2$
    c) $4.0$
    d) $4.5$
12. You have a debt of $-\frac{7}{2}$ dollars and you repay $\frac{3}{2}$ dollars. What is your remaining debt?
    a) $-2$
    b) $-1$
    c) $1$
    d) $2$
13. A hiker descends $-120$ feet in $15$ minutes. What is his rate of descent in feet per minute?
    a) $-8$
    b) $8$
    c) $12$
    d) $-12$
14. If the temperature drops from $6.5^\circ C$ to $-3.2^\circ C$, what is the change in temperature?
    a) $3.3^\circ C$
    b) $-9.7^\circ C$
    c) $9.0^\circ C$
    d) $-8.7^\circ C$
15. A piece of ribbon is $\frac{4}{9}$ meter long. If you cut it into $6$ equal pieces, how long is each piece?
    a) $\frac{2}{27}$ meter
    b) $\frac{4}{54}$ meter
    c) $\frac{2}{9}$ meter
    d) $\frac{1}{27}$ meter

Helpful Hints

1. Consider finding a common denominator to add the fractions.
2. Remember that multiplying by a negative number reverses the sign.
3. Subtracting a number is equivalent to adding its negative.
4. Division by a fraction involves multiplying by its reciprocal.
5. Subtracting a negative value is equivalent to adding its positive counterpart.
6. Multiplying a fraction by a whole number converts the whole number into a fraction first.
7. Subtract the drained gallons from the total to find what's left.
8. Multiply the number of shots by the probability of scoring.
9. Simply add the given extra cup to the required amount.
10. Combine the negative and positive values to get the net amount.
11. Divide miles traveled by the gallons used to find the miles per gallon.
12. Subtract the amount repaid from the total debt.
13. Divide the total feet descended by the total minutes.
14. Find the difference in final and initial temperatures.
15. Divide the total length of the ribbon by the number of pieces.

Correct Answers

1. b) $$\frac{1}{8}$$
2. b) $-10$
3. d) $-4.0$
4. b) $\frac{7}{2}$
5. c) $7.5$
6. a) $1.875$ cups
7. b) $11.4$ gallons
8. b) $20$
9. d) $\frac{5}{6}$
10. a) $3.25$
11. a) $3.8$
12. a) $-2$
13. a) $-8$
14. b) $-9.7^\circ C$
15. a) $\frac{2}{27}$ meter