Question

gateway to tech iii math (act prep)
unit #1 basic mathematics (2017)
example 12. sue and joan are driving from new york to san diego, a total distance of 3000 miles. they traveled 1/10 of the distance on the first day and 2/10 of the distance on the second day. how many miles are yet to be driven?
solution. distance travelled: 1/10 + 2/10 = 3/10 → find 3/10 of 3,000 (fraction of the whole)
3/10(3,000)=900 miles (fraction × whole)
distance remaining: 3,000 - 900 = 2,100 miles
answer. 2,100 miles are yet to be driven.
example 13. a recipe for crunch - top potatoes calls for 3 large potatoes, 2 tablespoons butter, and 3/4 cup crushed cornflakes. if the recipe is cut in half, what amount of cornflakes will be needed? (hint. some information given is irrelevant.)
solution. dividing by 2 is the same as ... 3/4÷2 = 3/4÷2/1
multiplying by 1/2 (half). = 3/4·1/2 = 3/8 invert and multiply.
answer. 3/8 cup of cornflakes
exercise 8. fractional part of a whole
answer as a proper fraction or mixed number in simplest form.

1. there are 18 boys and 12 girls in a class. what fractional part of the class are girls?

hint. reduce fraction to lowest terms.

1. a team played a total of 40 games and lost 6 of those games. what fraction of the games played did the team win? hint. total = wins + losses
2. what fractional part of an hour elapses between 3:45 p.m. and 4:09 p.m.?

hint. simplify the fraction. number of minutes between 3:45 and 4:09 / number of minutes in one hour

1. a camp employs 4 men, 6 women, 12 girls, and 8 boys. if 3 girls are fired and replaced by 3 women, then what fractional part of the staff are women?
2. a family budgets their monthly income as follows: 1/3 food, 1/4 rent, 1/10 clothing, 1/5 savings, and the remainder for miscellaneous expenses. what fractional part is left for miscellaneous expenses? hint. fractional whole = 1
3. your physical science class performs an experiment to determine the calories in one ounce of peanuts. upon completion, 3 1/2 ounces of peanuts are left. if the remaining peanuts are divided equally among you and your two lab partners, then about how many ounces will each person receive? hint. don’t forget to include yourself.

Explanation:

1.

Step1: Find total number of students

Total number of students = 18 (boys) + 12 (girls)=30

Step2: Calculate fraction of girls

Fraction of girls = $\frac{12}{30}$

Step3: Simplify the fraction

$\frac{12\div6}{30\div6}=\frac{2}{5}$

Step1: Find number of wins

Number of wins = 40 (total games) - 6 (losses)=34

Step2: Calculate fraction of wins

Fraction of wins = $\frac{34}{40}$

Step3: Simplify the fraction

$\frac{34\div2}{40\div2}=\frac{17}{20}$

Step1: Find number of minutes elapsed

From 3:45 p.m. to 4:00 p.m. is 15 minutes, and from 4:00 p.m. to 4:09 p.m. is 9 minutes. So total minutes elapsed = 15 + 9=24

Step2: Calculate fraction of an hour

There are 60 minutes in an hour. Fraction = $\frac{24}{60}$

Step3: Simplify the fraction

$\frac{24\div12}{60\div12}=\frac{2}{5}$

Answer:

$\frac{2}{5}$

2.