Math / Numbers & Operations

Question5 Which statement about the fractions $\frac{3}{6}$ and $\frac{5}{10}$ is true?
A These fractions are not equivalent, because they are less than $\frac{1}{2}$ .
B These fractions are equivalent, because their numerators are half their denominators. C These fractions are equivalent, because their numerators are twice their denominators. D These fractions are not equivalent, because they are greater than one.

Studdy Solution

STEP 1

1. We are given two fractions: $\frac{3}{6}$ and $\frac{5}{10}$ .
2. We need to determine if these fractions are equivalent.
3. We will compare the fractions by simplifying them and analyzing their properties.

STEP 2

1. Simplify each fraction.
2. Compare the simplified fractions.
3. Evaluate each statement to determine which is true.

STEP 3

Simplify the fraction $\frac{3}{6}$ .
$\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}$

STEP 4

Simplify the fraction $\frac{5}{10}$ .
$\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}$

STEP 5

Compare the simplified fractions $\frac{1}{2}$ and $\frac{1}{2}$ .
Since both fractions simplify to $\frac{1}{2}$ , they are equivalent.

STEP 6

Evaluate each statement:
- Statement A: These fractions are not equivalent, because they are less than $\frac{1}{2}$ . - This is false because both fractions are equal to $\frac{1}{2}$ .
- Statement B: These fractions are equivalent, because their numerators are half their denominators. - This is true because both $\frac{3}{6}$ and $\frac{5}{10}$ simplify to $\frac{1}{2}$ .
- Statement C: These fractions are equivalent, because their numerators are twice their denominators. - This is false because the numerators are not twice the denominators.
- Statement D: These fractions are not equivalent, because they are greater than one. - This is false because both fractions are equal to $\frac{1}{2}$ , which is less than one.
The correct statement is:
$\boxed{\text{B These fractions are equivalent, because their numerators are half their denominators.}}$

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Studdy Solution

STEP 1

1. We are given two fractions: $\frac{3}{6}$ and $\frac{5}{10}$ .
2. We need to determine if these fractions are equivalent.
3. We will compare the fractions by simplifying them and analyzing their properties.

STEP 2

1. Simplify each fraction.
2. Compare the simplified fractions.
3. Evaluate each statement to determine which is true.

STEP 3

Simplify the fraction $\frac{3}{6}$ .
$\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}$

STEP 4

Simplify the fraction $\frac{5}{10}$ .
$\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}$

STEP 5

Compare the simplified fractions $\frac{1}{2}$ and $\frac{1}{2}$ .
Since both fractions simplify to $\frac{1}{2}$ , they are equivalent.

STEP 6

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Studdy Solution

STEP 1

1. We are given two fractions: 36\frac{3}{6}63​ and 510\frac{5}{10}105​.2. We need to determine if these fractions are equivalent.3. We will compare the fractions by simplifying them and analyzing their properties.

STEP 2

1. Simplify each fraction.2. Compare the simplified fractions.3. Evaluate each statement to determine which is true.

STEP 3

Simplify the fraction 36\frac{3}{6}63​.36=3÷36÷3=12\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}63​=6÷33÷3​=21​

STEP 4

Simplify the fraction 510\frac{5}{10}105​.510=5÷510÷5=12\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}105​=10÷55÷5​=21​

STEP 5

Compare the simplified fractions 12\frac{1}{2}21​ and 12\frac{1}{2}21​.Since both fractions simplify to 12\frac{1}{2}21​, they are equivalent.

STEP 6

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1. We are given two fractions: $\frac{3}{6}$ and $\frac{5}{10}$ .
2. We need to determine if these fractions are equivalent.
3. We will compare the fractions by simplifying them and analyzing their properties.

1. Simplify each fraction.
2. Compare the simplified fractions.
3. Evaluate each statement to determine which is true.

Simplify the fraction $\frac{3}{6}$ .
$\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}$

Simplify the fraction $\frac{5}{10}$ .
$\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}$

Compare the simplified fractions $\frac{1}{2}$ and $\frac{1}{2}$ .
Since both fractions simplify to $\frac{1}{2}$ , they are equivalent.