Ratio and Rates – Assignment 1
Name: Due: Monday, April 16th, 2007
1. A Ratio is a .
There are 3 ways that you can write a ratio.
E.g. In a bowel of fruit there are 3 oranges, 4 apples. Write the ratio for oranges to apples in 3 different ways.
Way 1 – with words.3 to 4
Way 2 – with a “ : “3 : 4
Way 3 – as a fraction3
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2. Write each ratio in 3 different ways
a) /squares to total
/ b) /
circles to triangles
c) /
square to triangles
/ d) /
squares to triangles
e) /
all figures to square
/ f. /
circle to triangles
Word problems are part of stage 3 questioning which you will have to do in grade 9. Here are some simplified stage 3 word problems.
3. A pod of 20 whales includes 3 newborns. Write the ratio comparingthe number of newborns with the total pod in three different ways.
4. 8 of 15 caterpillars have begun to build cocoons.Write the ratio comparing the number of cocoons with the total in three different ways.
Groups of ratios can be equivalent which means that the terms are related by a multiplication factor, ie what you need to multiply one ratio to get the other.
5. Find the missing value, x or y, so that the ratios are equivalent. What is the multiplication factor.
a) 1:2: 3 = x:6:9x = multiplication factor =
b) 6: x : 12 = y : 1 : 6x = y = ___multiplication factor =
c)7 : 5 : x = 21: y : 3x = y = ___multiplication factor =
d)x : 16 : 36 = 3 : 4 : yx = y = ___multiplication factor =
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When working with ratios that have been converted to fractions you can use the method of cross-multiplying.
X / = / 816 / 9
E.g. Multiply along the diagonal and then divide by the remaining number.
X = (8 x 16) ÷ 9 = 14.2
6. Use the method of cross multiplying to solve the equivalent fractions, show your work in the box below.
a) / X / = / 4 / b) / 9 / = / 3 / c) / 12 / = / 11 / d) / 2 / = / X12 / 16 / X / 27 / 144 / X / 9 / 13
Stage 3 problems again. Here we are going to make proportions from the information given in the question and use that proportion to solve the question.
7. Timothy has just started his collection of plastic cars and obtained twenty-three new plastic cars. Isaac has fifty-six old plastic cars. Aaron has one hundred one old plastic cars. If all their collections were combined answer the following questions.
a) How many new plastic cars are there?
b) How many old plastic cars are there?
c) Ratios for:New to old
(3 ways)New to total
Old to total
8. Mr. Quirk had approximately 58% of the mid-term tests graded. There are 26 tests in total
a)Written as a proportion with twenty-six as a denominator, approximately how many of the tests did he have graded?
58 / = / X100 / 26
X =
b) How many tests have been graded? ***Round your answer in (a) to the nearest whole number *** Write your answer in a sentence.
c) How many tests have not been graded? Write your answer in a sentence.
d) What is the approximate graded test to upgraded test ratio? Write your answer in a sentence.
9. It was recently estimated by the Extraterrestrial Alien Monitoring Agency, that unregistered extraterrestrials outnumber registered ones by about seven-to-five. If there are a total of 2,280 extraterrestrials, about how many of them are registered?
Step 1: If the ratio of unregistered to registered is 7:5 what would be the total altogether
Step 2: Make a ratio, registered to total
Step 3: Take step 2’s answer and turn it into a fraction
Step 4: Make a proportion using step 3’s answer and the fact that there is 2,280 aliens in total.
Unregistered / = / X / =Total / 2280
Step 5: Find X and answer in a complete sentence.
10. Smallville had a great football team last year. They outperformed their opponents in almost every category of play. One of their more impressive statistics was that, on average, they outscored their opponents by 3:1 in every game they played. If they scored an average of 18 points per game, what was the average number of points scored by their opponents per game? ***try this one on your own***
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