zMath 160  - Unit 13: Ratios & Proportions; Estimate Reasons Solutions with Fractions and Decimals

Ratios

Use the ribbons to write ratios for problems #1 through #4. Write the ratios three ways. (Sample Answer: 4:5, 4/5, 4 to 5)0


1)

Yellow ribbon to red ribbons


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2)

Red ribbons to blue ribbons


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3)

White ribbons to all ribbons


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4)

All ribbons to yellow ribbon


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Unit Rate


5)

If Mark works 105 hours every 3 weeks, how many hours does he work in 1 week? Show your work and be sure to label your answer.


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6)

Using the unit rate you found in the previous problem, how many hours does Mark work if he works for 12 weeks? Show your work and be sure to label your answer.


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7)

Mikayla can make 15 ice cream cones in 1 hour.  Fill in the table below to find out how many ice cream cones she can make in 6 hours. (Write you answers as so, 1:15, 2:_,…


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8)

You can buy a 3 pack of t-shirts for $12.50 or 1 t-shirt for $4.25.  Which is the better deal, buying the 3 pack or buying 3 individual t-shirts? Explain why.


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9)

Which is not a way a unit rate should be written?


10)

Create and solve your own unit rate word problem.   Remember what a unit rate includes. Show your work and be sure to label your answer.


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Ratios & Proportions


11)

On a map, two inches represents 5 actual miles. What would be the actual miles represented by 14 inches? Write a proportion, write an equation, and then solve. (Sample answer: 3/8 = n/32, 8n = 96, n = 12)


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12)

Which equation is correct for this proportion?


13)

Study the map closely. Write a proportion to find the distance from St. Clairsville to Cambridge. You will need to use a ruler to measure the distance in inches on the map. The scale is 1 inch = 10 mi. State the proportion, the equation, and the answer. You will need to print out the map for accuracy.


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14)

If Betsy’s boat travels one mile in 7.5 minutes, how many miles will her boat travel in 1 hour? Write a proportion. Express the proportion as an equation. Solve.


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15)

In a recent survey, 2 out of 5 persons selected reality TV shows as their favorite type of shows. If 300 persons selected reality shows, how many person were surveyed? Write a proportion. Express the proportion as an equation. Solve.


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Use this scenario to solve problems #16 and #17. The school principal made 7 baskets out of 50 free throw shots attempted with a basketball. Ms. Jones, the sixth grade teacher, made 6 baskets out of 40 free throw shots attempted.


16)

Write a ratio for both the principal and Ms. Jones, comparing the number of baskets made to their total number of free throw shots attempted.


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17)

Who had the higher ratio of baskets made, the principal or Ms. Jones? Explain how you decided on your answer.


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Estimate a Reasonable Solution with Fractions and Decimals

Estimate to select the answer that is a reasonable solution for problems #18 through #21.


18)

Solve.


19)

Solve.


20)

Solve.


21)

Solve.


Review


22)

Find the quotient.


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23)

Find the missing numbers in the sequence. {11, 7, 10, ____, 9, 5, ____, 4, 7, 3}


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24)

Find the sum. Express the answer as a decimal and also as a decimal fraction. (Sample answer: 14.27, 14 27/100)

9.342 + 5.8 + 2


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25)

Use the problem in #24. Estimate a reasonable answer and then check to see if the answer that you entered for #24 is reasonable. State the rounded number you used for each addend (numbers that are added) and state the estimated sum.


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26)

Select the symbol that completes the statement correctly, = or ≠.


27)

Estimate the product, then find the actual product. State the estimated and actual answers.

7.09 × 4.8


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28)

Find the quotient. Round the answer to the nearest tenth.

53 ÷ 2.8


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29)

Solve.


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30)

State the measurement of the green arrow to the nearest eighth.


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31)

Find the cross products for the following equivalent fractions.


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