Grade 7 Math
Ch. 2 Ratio, Rate and Percent Study Notes
Ratio of days of sunshine to days of rain is 5 : 3 (part to part ratio)
Question: In 8 weeks (or 56 days) how many days of sunshine should there be?
First add the two terms in the ratio to find the total number of days included: 5 + 3 = 8
Since 56 ÷ 8 = 7 you now know the scale factor to multiply each term in the ratio.
5 : 3
x7
x7
35 : 21 Therefore there will be 35 days of sunshine in 8 weeks.
Ratio of vans to sedans at the Honda plant is 7 : 15. (part to part ratio)
Question: If in one week 63 vans were assembled, how many sedans would be produced?
Set up equivalent ratios. 7 = 63
63 ÷ 7 = 9 ,
9 is the scale factor to multiply
15
?
each term in the ratio.
7 x 9 = 63
15 x 9 135
So, 135 sedans will be produced that same week.
Ratio of cats to dogs in a neighbourhood is 3 : 2.
Question: What percent of the neighbourhood pets are dogs?
First add the two terms to determine the total number of pets. 3 + 2 = 5
Then set up a fraction of the number of dogs as a percent of the total number of pets.
2 = 4 = 40
5
10 100
40% of the neighbourhood pets are dogs.
Rate of typing speed for a person named Melody is 950 words / 25 minutes.
Question: How many words can she type in 12 minutes?
First calculate the number of words typed in 1 minute then multiply each term by 25.
950 ÷ 25 = 38 x 12 = 456 words
25
1
12 min
Melody can type 456 words/12 min.
Scale drawings rely on a scale which is a ratio of the Drawing Size to Actual Size of the object.
Eg. If a 1: 1000 scale is used to draw a picture of the 200 m tall cell phone tower, how tall will the tower
be in the drawing?
Remember the units in the scale are the same, and drawings almost always are in cm.
So, d = 1 cm = __?__
1 cm = __?__
1 cm x 20 = __20 cm__
a 1000 cm 200 m
1000 cm 20 000 cm 1000 cm x 20 20 000 cm
The cell phone tower will be 20 cm in the drawing.
Eg. A tiny 2 mm bug is magnified in a drawing so that it is 15 cm in length. What scale was used to
enlarge the bug?
d = 15 cm x 10 = 150 mm = 75
The scale used was 75 : 1.
a
2 mm
2 mm
1
Need same units!
Grade 7 Math
CASE I To find a percent of a number you must multiply the decimal equivalent (or fraction equivalent)
of the percent number with the given amount.
Think about this: you are being asked to calculate a fraction of the total amount. In most percent
problems with percent values less than 100% the answer to this calculation will be smaller than the total
amount. So percentage problems involving finding the percent of a number, discounts, calculation of tax,
… will give a smaller value than the original total amount.
Eg. The top speed of a car is 260 km per hour. Steve drove his car at 30% of that maximum speed.
How fast was he travelling? In other words, what is 30% of 260?
260
x 0.3
Steve was driving 78 km/h.
78.0
Menta Math: 100% of the speed is 260 km/h
÷ 10
10% “
÷ 10
“
“
x3
30% “
26 km/h
x3
“
“
78 km/h
Eg. a) A watch normally priced $95 is discounted 20%. What is the sale price of the watch?
Here 20% of $95 will give you the discount amount, not the sale price. You can calculate the discount
amount first, then subtract it from the regular price to find the sale price.
95 x 0.2 = 19.0 So the watch was discounted $19. The sale price is: 95 – 19 = $76
If you want to find the sale price in one step you can subtract the discount from 100% to find out what
percent of the regular price you are actually paying:
100% - 20% = 80% So now find 80% of $95: 95 x 0.8 = 76
The sale price is $76.
Remember for any question asking you to calculate the total with tax included:
Either multiply the amount by 0.13 (13% HST) and then add the tax amount to the ticket price;
or multiply the amount by 1.13 (113%) to arrive at the total with the tax already added on.
b) What would the total cost including tax be, for the sale priced watch? Tax is always calculated on the
price you pay; so if the watch is on sale you only pay tax on the sale price of $76.
$76
x 0.13
228
760
9.88
76.00
+ 9.88
$85.88
OR
76
x 1.13
228
760
7600
$85.88
The total cost of the watch with tax included is $85.88
Grade 7 Math
Case II To calculate what percent a given amount is of the total amount you must set up a fraction &
then multiply by 100%.
Given Amount x 100% (Whatever value comes after the word “of” is the total amount
Total Amount
which is the denominator.)
Eg. During Leonard’s 8 hour work day he spends 3 hours in his office. What percent of his work day is
spent in the office?
Here you are being asked what percent 3 is of 8, 3 x 100%
calculation:
0. 3 7 5
8
8)3.000
= 0.375 x 100% = 37.5%
-2 4
Leonard spends 37.5 % of his work day in his office.
60
- 56
- In certain types of word problems you must be careful to identify what is
40
being asked – especially in percent increase or decrease problems.
-40
0
Eg. A small cup holds 150 mL of pop and a large cup contains 250 mL. What percent increase in the
amount of pop do you get when you buy the large cup?
First subtract the two quantities. 250 – 150 = 100, this tells us that the large cup contains 100 mL
more pop than the small cup.
Then set up a fraction of the increased volume
over the small cup’s volume:
100 = 10 = 2
0. 6 6 6 x 100% = 66.7%
150
15
3
3) 2.000
-1 8
You get 66.7% more pop when you buy
2 0
the large cup of pop.
-1 8
2
Case III: Here you are trying to determine what the whole is from a given number which
represents a percentage of the whole.
Eg. Suki buys a dress on sale for 20% off the original price. She saves $40. What was the original
price of the dress?
Mental Math strategy
20% of the original price is $40.
÷2
÷2
10% of the original price is $20
x 10
x 10
100% of the original price is $200
The original price of the dress was $200.
OR
20 = $40
100
?
20 x 2 = $40
100 x 2 $200
Eg. A factory has increased production by 12% which means it produces 30 more units per day.
How many units did the factory produce before this increase?
12% of the original production is 30
OR
12 =
30
30 ÷ 12 = 2.5
Grade 7 Math
÷3
÷3
100
?
4% of the original production is 10
x 25
x 25
100% of the original production is 250.
x 2.5
12
100 x 2.5
The factory produced 250 units
= 30
before this increase.
250