Testinar Grade 6 math

Solving Rate and Ratio Word Problems

Students will build Grade 6 mastery of solving rate and ratio word problems using models, equations, and test-style reasoning.

CH01-09 Ratios, Rates, and Percents
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. A printer prints \(30\) pages in \(5\) minutes. At this rate, how many pages will it print in \(12\) minutes?

    1. \(36\)
    2. \(60\)
    3. \(90\)
    4. \(72\)

  2. A recipe uses \(2\) cups of flour for every \(3\) eggs. How many cups of flour are needed for \(12\) eggs?

    Solving Rate and Ratio Word Problems visual for G6-C01-T09-Q002
    1. \(4\)
    2. \(6\)
    3. \(8\)
    4. \(10\)

  3. A sports team won \(15\) games and lost \(5\) games. What is the ratio of wins to total games played?

    1. \(3:1\)
    2. \(3:4\)
    3. \(15:20\)
    4. \(20:15\)

  4. Store A sells \(8\) oranges for $2. Store B sells \(12\) oranges for $3. Which store offers the better price per orange?

    1. Store A
    2. Store B
    3. Both are the same
    4. Cannot be determined

  5. If \(\frac{4}{6} = \frac{x}{15}\), what is the value of \(x\)?

    1. \(8\)
    2. \(18\)
    3. \(12\)
    4. \(10\)

  6. A model train is built at a scale of \(1:50\). If the model is \(8\) inches long, how many inches long is the real train?

    1. \(200\)
    2. \(300\)
    3. \(400\)
    4. \(500\)

  7. The table below shows a proportional relationship between distance and time. What is the missing value?

    Solving Rate and Ratio Word Problems visual for G6-C01-T09-Q007
    1. \(240\)
    2. \(260\)
    3. \(270\)
    4. \(300\)

  8. A car travels \(120\) miles in \(2\) hours. At the same rate, how far will it travel in \(5\) hours?

    1. \(240\) miles
    2. \(300\) miles
    3. \(360\) miles
    4. \(420\) miles
Teacher and parent reference

Answer key and explanations

  1. D. \(72\)

    The unit rate is \(30\div5=6\) pages per minute. In \(12\) minutes the printer prints \(6\times12=72\) pages.

  2. C. \(8\)

    The ratio is \(2:3\) (flour to eggs). For \(12\) eggs, multiply both parts by \(4\): \(2 \times 4 = 8\) cups of flour.

  3. B. \(3:4\)

    Total games: \(15 + 5 = 20\). Ratio of wins to total is \(15:20\), which simplifies to \(3:4\) by dividing both by \(5\).

  4. C. Both are the same

    Store A: \(2 \div 8 = 0.25\) per orange. Store B: \(3 \div 12 = 0.25\) per orange. Same unit rate.

  5. D. \(10\)

    Cross-multiply: \(4 \times 15 = 6 \times x\), so \(60 = 6x\), thus \(x = 10\).

  6. C. \(400\)

    At a scale of \(1:50\), the real object is \(50\) times larger. \(8 \times 50 = 400\) inches.

  7. C. \(270\)

    Rate is \(90 \div 2 = 45\) miles per hour. For \(6\) hours: \(45 \times 6 = 270\) miles.

  8. B. \(300\) miles

    Step 1: Rate is \(120 \div 2 = 60\) mph. Step 2: Distance in \(5\) hours is \(60 \times 5 = 300\) miles.

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