This handy Math in Focus Grade 7 Workbook Answer Key Chapter 10 Probability detailed solutions for the textbook questions.
Math in Focus Grade 7 Course 2 B Chapter 10 Answer Key Probability
Math in Focus Grade 7 Chapter 10 Quick Check Answer Key
Solve.
Question 1.
Express 10 ounces out of 25 ounces of baking flour as a fraction in the simplest form.
Answer:
Explanation:
In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole.
This can be written as 10/25
– In the fraction 10/25, the numerator is 10 and the denominator is 25.
– A more illustrative example could involve a box with 25 ounces of baking flour. 1 of those 10 ounces would constitute the numerator of a fraction, while the total of 25 ounces that comprises the whole box would be the denominator.
– Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined.
Question 2.
12 out of 40 pieces of fruit in a basket are lemons. What fraction of the pieces of fruit are lemons? Write your answer in the simplest form.
Answer: 12/40
Explanation:
The total number of fruits in a basket=40
The number of lemons is there=12
We need to write the fraction of the pieces of fruit are lemons=X
– In the fraction 12/40, the numerator is 12 and the denominator is 40.
– A more illustrative example could involve a box with 40 pieces of fruits. 12 of those are lemons would constitute the numerator of a fraction, while the total of 40 pieces of fruits that comprises the whole box would be the denominator.
– Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined.
X=12/40
Question 3.
If there are 36 boys in a group of 50 students, what percent of the students are girls?
Answer:28% are girls.
Explanation:
The total number of students=50
Number of boys Number of girls
Write each fraction as a percent. Round your answer to 2 decimal places when you can.
Question 4.
\(\frac{5}{8}\)
Answer: 62.5%
This can be written in a fraction like 5/8.
When it converted into percentage then it becomes 62.5%.
Calculation:
= (5/8) × 100%
= 62.5%
Therefore, 62.5 rounded to 2 decimal places is 62.50.
Question 5.
\(\frac{2}{5}\)
Answer: 40%
This can be written in a fraction like 2/5.
When it is converted into percentage then it becomes 40%.
Calculation:
= (2/5) × 100%
= 40%
Therefore, 40 rounded to 2 decimal places is 40.00.
Question 6.
\(\frac{24}{9}\)
Answer: 266.66666667%
Explanation:
This can be written in a fraction like 24/9.
When it is converted into a percentage then it becomes 266.66666667%
Calculation:
= (24/9) × 100%
= 266.66666667%
Therefore, 266.6666 rounded to 2 decimal places is 266.67
Write each percent as a fraction or a mixed number in simplest form.
Question 7.
54%
Answer: 27/50
Explanation:
To convert percentages to fractions:
Step 1: Write down the percent divided by 100 like this: percent/100.
Step 2: If the percent is not a whole number, then multiply both top and bottom by 10 for every number after the decimal point. (For example, if there is one number after the decimal, then use 10, if there are two then use 100, etc.)
Therefore, 54/100=0.54
This can be simplified as:
The mixed number can be written as:
since 27/50 is a proper fraction, it cannot be written as a mixed number.
If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction. In that case, you could convert it into a whole number or mixed number fraction.
Therefore, 27/50 = Proper Fraction.
Question 8.
19.5%
Answer:39/200
To convert percentages to fractions:
Step 1: Write down the percent divided by 100 like this: percent/100.
Step 2: If the percent is not a whole number, then multiply both top and bottom by 10 for every number after the decimal point. (For example, if there is one number after the decimal, then use 10, if there are two then use 100, etc.)
Therefore, 19.5/100=0.195
This can be simplified as:
The mixed number can be written as:
since 39/200 is a proper fraction, it cannot be written as a mixed number.
If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction. In that case, you could convert it into a whole number or mixed number fraction.
Therefore, 39/200 = Proper Fraction.
The fraction is already in mixed form.
Question 9.
1.4%
Answer: 7/500
To convert percentages to fractions:
Step 1: Write down the percent divided by 100 like this: percent/100.
Step 2: If the percent is not a whole number, then multiply both top and bottom by 10 for every number after the decimal point. (For example, if there is one number after the decimal, then use 10, if there are two then use 100, etc.)
Therefore, 1.4/100=0.014
This can be simplified as:
The mixed number can be written as:
since 7/500 is a proper fraction, it cannot be written as a mixed number.
If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction. In that case, you could convert it into a whole number or mixed number fraction.
Therefore, 7/500 = Proper Fraction.
The fraction is already in mixed form.
Question 10.
115%
Answer: 23/20
Explanation:
To convert percentages to fractions:
Step 1: Write down the percent divided by 100 like this: percent/100.
Step 2: If the percent is not a whole number, then multiply both top and bottom by 10 for every number after the decimal point. (For example, if there is one number after the decimal, then use 10, if there are two then use 100, etc.)
Therefore, 115/100=1.15
This can be simplified as:
The mixed number can be written as:
– Convert the fraction to a mixed number by using long division to find the quotient and remainder.
23÷20=1R3
– The quotient will be the whole number in the fraction, and the remainder will be the numerator in the mixed fraction.
23/20=1 3/20
Write each percent as a decimal.
Question 11.
28%
Answer: 0.28
Explanation:
Percent” means “per 100” or “over 100”. To convert 28% to a decimal rewrite 28 percent in terms of per 100 or over 100.
28% = 28 over 100 or,
28%= 28/100
28 over 100 is the same as 28 divided by 100. Completing the division we get:
28 ÷ 100 = 0.28
Therefore, we have shown that:
28% = 0.28
Simplified conversion:
Remove the percent sign % and divide by 100.
28 ÷ 100 = 0.28
Shortcut conversion:
Move the decimal point 2 places to the left and remove the percent sign %
28% becomes 0.28.
Question 12.
9%
Answer: 0.09
Explanation:
“Percent” means “per 100” or “over 100”. To convert 9% to a decimal rewrite 9 percent in terms of per 100 or over 100.
9% = 9 over 100 or,
9%=9/100.
9 over 100 is the same as 9 divided by 100. Completing the division we get:
9 ÷ 100 = 0.09
Therefore, we have shown that
9% = 0.09
Simplified conversion:
Remove the percent sign % and divide by 100.
9 ÷ 100 = 0.09
Shortcut conversion:
Move the decimal point 2 places to the left and remove the percent sign %
9% becomes 0.09
Question 13.
34.5%
Answer: 0.345
Explanation:
“Percent” means “per 100” or “over 100”. To convert 34.5% to a decimal rewrite 34.5 percent in terms of per 100 or over 100.
34.5% = 34.5 over 100 or,
34.5%=34.5/100
34.5 over 100 is the same as 34.5 divided by 100. Completing the division we get:
34.5 ÷ 100 = 0.345
Therefore, we have shown that
34.5% = 0.345
Simplified conversion:
Remove the percent sign % and divide by 100.
34.5 ÷ 100 = 0.345
Shortcut conversion:
Move the decimal point 2 places to the left and remove the percent sign %
34.5% becomes 0.345
Question 14.
256%
Answer: 2.56
Explanation:
“Percent” means “per 100” or “over 100”. To convert 256% to a decimal rewrite 256 percent in terms of per 100 or over 100.
256% = 256 over 100 or,
256%=256/100
256 over 100 is the same as 256 divided by 100. Completing the division we get:
256 ÷ 100 = 2.56
Therefore, we have shown that
256% = 2.56
Simplified conversion:
Remove the percent sign % and divide by 100.
256 ÷ 100 = 2.56
Shortcut conversion:
Move the decimal point 2 places to the left and remove the percent sign %
256% becomes 2.56
Solve.
Question 15.
A flower bed contains marigolds and zinnias. The ratio of marigolds to zinnias is 7 to 11.
a) What fraction of the flowers in the garden are marigolds? Write your answer a? a fraction in simplest form.
Answer:
Explanation:
The total number of flower beds= 7+11=18
The number of marigolds=7
The number of zinnias=11
The ratio of marigolds to zinnias=7:11
In the above-given question, we need to write the fraction of the flowers in the garden are marigolds.
Already we know that the marigolds are 7.
– In fraction 7/18, the numerator is 7 and the denominator is 18.
– A more illustrative example could involve a box with 18. 7 of those are marigolds would constitute the numerator of a fraction, while the total of 18 flower beds that comprises the whole box would be the denominator.
– Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined.
b) What percent of the flowers in the garden are marigolds? Round your answer to the nearest whole number percent.
Answer: 39%
The fraction of flowers in the garden are marigods=7/18 (check in the above question (a))
When it is converted into percentages then it becomes 38.888888889%
Calculation:
(7/18) × 100%
= 38.888888889%
= 0.38888888889
The nearest whole number percentage of 38.888888889% is 39%.
Note:
– When rounding percentages, we rounded up or down to the nearest number of decimals you wanted.
– We rounded up if the next decimal was five or above, and down if it was four or less.
Question 16.
A bookcase holds 20 history books, 23 science fiction books, and 49 mystery books.
a) What fraction of the books are science fiction books?
Answer:
Explanation:
The total number of books a bookcase holds=20+23+49=92
The number of history books=20
The number of science fiction books=23
The number of mystery books=49
In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole.
This can be written as 23/92
– In the fraction 23/92, the numerator is 23 and the denominator is 92.
.
– A more illustrative example could involve a box with 92 books. 23 of those are science fiction books would constitute the numerator of a fraction, while the total of 92 books that comprises the whole box would be the denominator.
– Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined.
b) What percent of the books are science fiction books?
Answer: 25%
Explanation:
The fraction of science fiction books=23/92 (check in the above question (a))
When it is converted into percentages then it becomes 25%
Calculation:
(23/92) × 100%
= 25%
Solve.
Question 17.
The table shows the mass of 100 steel bars rounded to the nearest kilogram.
a) Draw a histogram to display this information.
Answer:
A histogram is the graphical representation of data where data is grouped into continuous number ranges and each range corresponds to a vertical bar.
– The horizontal axis displays the number range.
– The vertical axis (frequency) represents the amount of data that is present in each range.
– The number ranges depend upon the data that is being used.
Histogram graph:
A histogram graph is a bar graph representation of data. It is a representation of a range of outcomes into columns formation along the x-axis. in the same histogram, the number count or multiple occurrences in the data for each column is represented by the y-axis. It is the easiest manner that can be used to visualize data distributions. Let us understand the histogram graphby plotting one for the given below example.
b) How many steel bars have a mass from 10 to 39 kilograms?
Answer: 66 steel bars.
Explanation:
The number of steel bars of mass from 10-19=15
The number of steel bars of mass from 20-29=33
The number of steel bars of mass from 30-39=18
Add all the number of steel bars=15+33+18
therefore, the number of steel bars of the mass 10-39 kgs=66
c) What percent of the steel bars have a mass of at least 20 kilograms, but less than 50 kilograms?
Answer: 75%
Explanation:
The number of steel bars of the mass 20-29 kgs=33
The number of steel bars of the mass 30-39 kgs=18
The number of steel bars of the mass 40-49 kgs=24
The total number of steel bars have a mass of at least 20 kgs, but less than 50 kgs=75
The total number of steel bars=15+33+18+24+10=100
Now first write the fraction.
Fraction=75/100
When it is converted into percentages then it becomes 75%
Calculation:
(75/100) × 100%
= 75%
= 0.75