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Answer :
Sure! Let's go through each question step by step:
1. What is the sum of a fraction and a whole number called?
When you add a fraction to a whole number, the result is called a "mixed number." A mixed number is made up of a whole number and a fraction combined. An example of a mixed number might look like 3[tex]\( \frac{1}{2} \)[/tex], which means 3 plus one-half.
Correct Answer: B. mixed number
2. Which kind of fraction describes the sum of [tex]\( \frac{1}{4} \)[/tex] and [tex]\( \frac{3}{5} \)[/tex]?
First, we need to find the sum of these two fractions:
[tex]\[
\frac{1}{4} + \frac{3}{5}
\][/tex]
To add these, we first find a common denominator, which is 20 in this case. We'll convert each fraction:
[tex]\[
\frac{1}{4} = \frac{5}{20} \quad \text{and} \quad \frac{3}{5} = \frac{12}{20}
\][/tex]
Now, add them together:
[tex]\[
\frac{5}{20} + \frac{12}{20} = \frac{17}{20}
\][/tex]
A fraction like [tex]\( \frac{17}{20} \)[/tex] is a "proper fraction" because the numerator (17) is smaller than the denominator (20).
Correct Answer: C. proper fraction
3. What is the LCD of [tex]\( \frac{3}{4} \)[/tex] and [tex]\( \frac{5}{6} \)[/tex]?
The Least Common Denominator (LCD) is the smallest multiple that the denominators (4 and 6) can both divide into evenly.
To find the LCD, factor the denominators:
- 4 = 2 x 2
- 6 = 2 x 3
Take the highest power of each prime factor:
- For 2, the highest power is [tex]\( 2^2 \)[/tex] from 4.
- For 3, the highest power is [tex]\( 3^1 \)[/tex] from 6.
Multiply these together to get the LCD:
[tex]\[
LCD = 2^2 \times 3 = 4 \times 3 = 12
\][/tex]
Correct Answer: A. 12
I hope this explanation helps clarify the solutions! If you have any more questions, feel free to ask!
1. What is the sum of a fraction and a whole number called?
When you add a fraction to a whole number, the result is called a "mixed number." A mixed number is made up of a whole number and a fraction combined. An example of a mixed number might look like 3[tex]\( \frac{1}{2} \)[/tex], which means 3 plus one-half.
Correct Answer: B. mixed number
2. Which kind of fraction describes the sum of [tex]\( \frac{1}{4} \)[/tex] and [tex]\( \frac{3}{5} \)[/tex]?
First, we need to find the sum of these two fractions:
[tex]\[
\frac{1}{4} + \frac{3}{5}
\][/tex]
To add these, we first find a common denominator, which is 20 in this case. We'll convert each fraction:
[tex]\[
\frac{1}{4} = \frac{5}{20} \quad \text{and} \quad \frac{3}{5} = \frac{12}{20}
\][/tex]
Now, add them together:
[tex]\[
\frac{5}{20} + \frac{12}{20} = \frac{17}{20}
\][/tex]
A fraction like [tex]\( \frac{17}{20} \)[/tex] is a "proper fraction" because the numerator (17) is smaller than the denominator (20).
Correct Answer: C. proper fraction
3. What is the LCD of [tex]\( \frac{3}{4} \)[/tex] and [tex]\( \frac{5}{6} \)[/tex]?
The Least Common Denominator (LCD) is the smallest multiple that the denominators (4 and 6) can both divide into evenly.
To find the LCD, factor the denominators:
- 4 = 2 x 2
- 6 = 2 x 3
Take the highest power of each prime factor:
- For 2, the highest power is [tex]\( 2^2 \)[/tex] from 4.
- For 3, the highest power is [tex]\( 3^1 \)[/tex] from 6.
Multiply these together to get the LCD:
[tex]\[
LCD = 2^2 \times 3 = 4 \times 3 = 12
\][/tex]
Correct Answer: A. 12
I hope this explanation helps clarify the solutions! If you have any more questions, feel free to ask!
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