Bell WorkKara is planning to drive from New York to San Francisco in her car. Kara started to fill out

the table below showing how far in miles she can travel for each gallon of gas she uses.

a. Complete the table for Kara. Assume the relationship in the table is proportional.

 

b. Based on the table, how many miles per gallon did Kara’s car get?

 

 

c. Write an equation that Kara can use to find the distance (d) he can drive on any number of gallons of gas (g).

 

 

 

d. When Kara’s tank is full, it holds 17 gallons. How far can Kara’s drive on a full tank of

gas?

Gallons 2 4 6 8 10 12

Miles 62 124 186 248 310 372

31 mpg

D = 31g

D = 31(17) = 527

Decimals, Fractions, and

Percents

Converting Fractions to Decimals

• To convert a fraction to a decimal, divide the numerator by the denominator. You will get a decimal that terminates or repeats. If it repeats,

place a bar (--- ) over the first number that repeats. Example 1: Convert 3/4 to a decimal

3/4 = 3÷4= 0.75

( terminating decimal) Example 2: Convert 2/3 to a decimal

2/3= 2÷3= 0.66 ( repeating decimal )

Converting Decimals to Percents

• In order to convert a decimal to a percent, either multiply the decimal by 100 and write the percent sign (%), or move the decimal point two places to the right and write the percent sign (%).

Example 1: Convert 0.20 to a percent

0.20x 100= 20% or 0.20= 0. 2 0= 20%

Example 2: Convert 4.00 to a percent

4x 100=400% or 4.00= 4. 0 0=400%

Converting Percents to Decimals

• When converting a percent to a decimal, either divide the percent by 100 and put the decimal point, or move the decimal point two places to the left and put the decimal point.

Example 1: Convert 72% to a decimal

72%= 72÷ 100= 0.72 or 7 2 . 0= 0.72

Example 2: Convert 62.5% to a decimal

62.5%= 62.5÷ 100= 0.625 or 6 2 . 5= 0.625

Copy and complete this chart

Percentage Decimal Decimal Percentage

1. 27% .27 7. 0.87 87%

2. 2% .02 8. 0.08 8%

3. 55% .55 9. 0.42 42%

4. 5% .05 10. 0.04 4%

5. 17% .17 11. 0.71 71%

6. 98% .98 12. 0.07 7%

Converting Fractions to Percents

• To convert a fraction to a percent, change the fraction to a decimal ( by dividing the numerator by the denominator ). Then multiply the decimal by 100 and put a percent sign (%). Another way is to move the decimal point two places to the right and put a percent sign (%).

Example 1: Convert 1/2 to a percent

1/2= 1÷ 2 = 0.50

0.50x 100= 50.00=50% or 0.50= 0. 5 0= 50%

Example 2: Convert 1/3 to a percent

1/3= 1÷3= 0.333

0.333x 100= 33.300=33.3% or 0.333=0. 3 3 3=33.3%

Another way to Convert Fractions to Percents

• Make a proportion by putting a 100 under the percent. Then use cross products or mental math. Then add a percent sign.

Example 1: Convert 1/5 to a percent

Multiply the top and the bottom by 20 so x = 20%

Example 2: Convert 3/25 to a percent

Multiply the top and the bottom by 4 so x = 12%

1005

1 x

10025

3 x

Try these:

1.Work out your percentage if you got 12 out of 25

2.  Work out your percentage if you got 15 out of 25

3.Work out your percentage if you got 17 out of 20

4.A player scores 4 times out of 10 shots. What percentage did they make?

5. Calculate the score percentage if out of 15 shots 12 are successful

48%

60%

85%

40%

80%

Converting Decimals to Fractions

• In order to convert a decimal to a fraction, say it, write it, then simplify as necessary.

Example 1: Convert 0.7 to a fraction0.7= 7/10Example 2: Convert 0.25 to a fraction0.25= 25/100= 1/4Example 3: Convert 1.625 to a fraction

8

51

1000

6251

Converting Percents to Fractions

• When converting percents to fractions, put the percent over 100 then simplify as necessary.

Example 1: Convert 85% to a fraction85% = 85/100= 17/20

Example 2: Convert 12.5% to a fraction12.5%= 12.5/100= 125/1000 = 1/8

Copy and complete this chart

Percentage Fraction

1. 23% 23/100

2. 24% 6/25

3. 55% 11/20

4. 20% 1/5

5. 17% 17/100

“Mathematics is the door

and key to the sciences.”

Roger Bacon