The ratio of the number of boys to the number of girls at your school is 5 to 8. Which statements are accurate according to this ratio?
The ratio of number of boys to girls is [tex]\frac{5}{8}[/tex]. That means:
[tex]\frac{boys}{girls} =\frac{5}{8}[/tex]
Let's look at the first choice.
a. If a class has 16 girls, it is reasonable to expect there are approximately 10 boys in the same class.
Make the amount as a fraction with boys over girls.
[tex]\frac{boys}{girls} =\frac{10}{16}[/tex]
10 and 16 can be simplified. The greatest common factor of 10 and 16 is 2, so divide by 2.
[tex]\frac{boys}{girls} =\frac{10 \div 2}{16 \div 2} =\frac{5}{8}[/tex]
Since the ratio is the same, choice a is correct.
Let's move onto the second choice.
b. In a group of 52 students, about 20 are boys.
If 20 students are boys, then the amount of girls is equal to 52 - 20, which is 32. Make the amount as a fraction with boys over girls.
[tex]\frac{boys}{girls} =\frac{20}{32}[/tex]
20 and 32 can be simplified. The greatest common factor of 10 and 16 is 4, so divide by 4.
[tex]\frac{boys}{girls} =\frac{20 \div 4}{32 \div 4}=\frac{5}{8}[/tex]
Since the ratio is the same, choice b is correct.
Let's go to the third choice.
c. The ratio of girls to total students is 8 to 13.
If the ratio of girls to total students is 13, that means there are 8 girls. The number of boys can be found by subtracting 8 from 13, which is 5. Make the amount as a fraction with boys over girls.
[tex]\frac{boys}{girls} =\frac{5}{8}[/tex]
Since the ratio is the same, choice c is correct.
Let's go to the fourth choice.
d. The Algebra class has 24 girls and 16 boys. This is the same ratio as girls to boys in the school.
Make the amount as a fraction with boys over girls.
[tex]\frac{boys}{girls} =\frac{16}{24}[/tex]
16 and 24 can be simplified. The greatest common factor of 16 and 24 is 8, so divide by 8.
[tex]\frac{boys}{girls} =\frac{16 \div 8}{24 \div 8} =\frac{2}{3}[/tex]
Since the ratio is not the same, choice d is not correct.
Lastly, the fifth choice.
e. If there are 208 students in the school, it is reasonable to expect there are 128 girls.
If there are 128 girls out of 208 students, the number of boys can be found by subtracting the number of girls from the amount of total students. 208 - 128 is 80, so there are 80 boys. Make the amount as a fraction with boys over girls.
[tex]\frac{boys}{girls} =\frac{80}{128}[/tex]
80 and 128 can be simplified. The greatest common factor of 80 and 128 is 16, so divide by 16.
[tex]\frac{boys}{girls} =\frac{80 \div 16}{128 \div 16}=\frac{5}{8}[/tex]
Since the ratio is the same, choice e is correct.
choice a ✔
choice b ✔
choice c ✔
choice d x
choice e ✔
Your answer is choice a, b, c, and e.
