High School

A group of preschoolers has 20 boys and 30 girls. What is the ratio of boys to all children? Select all that apply.

A. [tex]\frac{10}{19}[/tex]
B. [tex]\frac{20}{50}[/tex]
C. [tex]20:30[/tex]
D. [tex]2:5[/tex]
E. [tex]20:50[/tex]
F. [tex]10:19[/tex]
G. [tex]200:500[/tex]

Answer :

To find the ratio of boys to all children in the group, follow these steps:

1. Determine the total number of children:
- There are 20 boys and 30 girls.
- Total children = Number of boys + Number of girls = 20 + 30 = 50.

2. Set up the ratio of boys to all children:
- The ratio is the number of boys to the total number of children.
- Ratio of boys to children = 20 (boys) : 50 (total children).

3. Simplify the ratio:
- Both 20 and 50 can be divided by their greatest common divisor, which is 10.
- Simplifying 20 : 50 by dividing each part by 10 gives us 2 : 5.

Now, let's match the simplified ratio with the options provided:

- 10: 19 - This does not match because the simplified ratio is 2:5.
- 20: 50 - This matches the original calculation before simplification.
- 2 to 5 - This is the simplified form of the ratio we calculated.
- 20 ⋅ 30 - This is not a ratio; it's a product of numbers.
- 10 to 19 - Again, this does not match the simplified ratio.
- 200: 500 - This simplifies to 2:5 and therefore matches.

The correct options for the ratio of boys to all children are:
- 20: 50
- 2 to 5
- 200: 500

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