Mathematics Magazine for Grades 1-12  

Grade 7

Theory

Temperature Conversion from Fahrenheit to Celsius

The metric system uses the Celsius scale to measure temperature. However, temperatures are still measured on the Fahrenheit scale in the U.S.

Water freezes at 0^o Celsius and boils at 100^o Celsius which is a difference of 100^o.

Water freezes at 32^o Fahrenheit and boils at 212^o Fahrenheit which is a difference of 180^o. Therefore each degree on the Fahrenheit scale is equal to 100/180 or 5/9 degrees on the Celsius scale.

How to convert Fahrenheit temperatures to Celsius

Subtract 32^o to adjust for the offset in the Fahrenheit scale.

Multiply the result by 5/9.

Example: convert 98.6^o Fahrenheit to Celsius.
98.6 - 32 = 66.6
66.6  5 9 = 333 9 = 37^o C.

There is a mental math method to approximate the Fahrenheit to Celsius conversion. The ratio of 5/9 is approximately equal to 0.55555....

How to approximate the conversion of Fahrenheit temperatures to Celsius with mental math.

Subtract 32^o to adjust for the offset in the Fahrenheit scale.

Divide the Celsius temperature by 2 (multiply by 0.5).

Take 1/10 of this number (0.5  1/10 = 0.05) and add it from the number above.

Example: convert 98.6^o F to Celsius.
98.6 - 32 = 66.6
66.6  1/2 = 33.3
33.3  1/10 = 3.3
33.3 + 3.3 = 36.6 which is an approximation of the Celsius temperature

Example of converting negative Fahrenheit temperatures to Celsius

Convert -4^o F to Celsius.

-4 - 32 = -36

-36  5/9 = -180/9 = -20^o C

Solutions from the Previous Issue:

1.        Find the dimensions of all rectangles such that their perimeter and area are numerically equal. (Consider only integral answers.)

Solution:

3 x 6 = 3 + 3 + 6 + 6;

4 x 4 = 4 + 4 + 4 + 4

2.        Jesse has a season's subscription to the local drama theater. His seat is in the 5th row from the front and the 12th row from the back of the theater. His seat is 8 seats from the right aisle and 12 seats from the left aisle. If each row has the same number of seats, how many seats are in the entire theater?

Solution:

There are: 12 + 5 -1= 16 rows

There are: 8 + 12 –1 = 19 seats per row

There are: 19 x 16 = 304 seats in the entire theatre

3.        Darlene bought some 30 cent and some 60 cent candy bars. Altogether she bought 10 candy bars and paid a total of $4.20. How many candy bars at each price did she buy?

Solution:   Let x the number of 30 cents candy bar and y = the number of 60 cents candy bar x + y = 10

30x + 60y = 420

30(10 - y) + 60y = 420

300 – 30y + 60y = 420

30y = 120

y = 4 x = 6

Darlene bought six candy bars at 30 cents; four candy bars at 60 cents.

Proposed Exercises:

Compare. Write <, >, or =.

1. 6¹¹    ________7¹¹
2. 10^{10 _________} 14¹⁰
3. 1,736^{1 _________}12³

Read more on the written version of the publication.