Finding the Number of Groups

Oct 13, 2025 by thesweetdesigns.com 108 views

Understanding the Problem

In this article, we will explore two problems that involve converting fractions and mixed numbers to decimals. The first problem asks us to find the number of groups of $\frac{1}{3}$ inch in $\frac{3}{4}$ inch. The second problem involves finding the volume of a box that contains a salt lick, given its dimensions in feet.

Problem a: Converting Fractions to Decimals

To solve the first problem, we need to convert the fractions $\frac{1}{3}$ and $\frac{3}{4}$ to decimals.

Converting $\frac{1}{3}$ to a Decimal

To convert $\frac{1}{3}$ to a decimal, we can divide the numerator (1) by the denominator (3).

$\frac{1}{3} = 1 ÷ 3 = 0.33\overline{3}$

Converting $\frac{3}{4}$ to a Decimal

To convert $\frac{3}{4}$ to a decimal, we can divide the numerator (3) by the denominator (4).

$\frac{3}{4} = 3 ÷ 4 = 0.75$

Finding the Number of Groups

Now that we have converted both fractions to decimals, we can find the number of groups of $\frac{1}{3}$ inch in $\frac{3}{4}$ inch.

$\frac{3}{4} ÷ \frac{1}{3} = 0.75 ÷ 0.33\overline{3} = 2.25$

Therefore, there are 2.25 groups of $\frac{1}{3}$ inch in $\frac{3}{4}$ inch.

Problem b: Finding the Volume of a Box

The second problem involves finding the volume of a box that contains a salt lick, given its dimensions in feet.

Converting Mixed Numbers to Decimals

To solve this problem, we need to convert the mixed numbers $1 \frac{1}{4}$ , $1 \frac{2}{3}$ , and $\frac{5}{6}$ to decimals.

Converting $1 \frac{1}{4}$ to a Decimal

To convert $1 \frac{1}{4}$ to a decimal, we can add the whole number part (1) to the decimal part ( $\frac{1}{4}$ ).

$1 \frac{1}{4} = 1 + \frac{1}{4} = 1 + 0.25 = 1.25$

Converting $1 \frac{2}{3}$ to a Decimal

To convert $1 \frac{2}{3}$ to a decimal, we can add the whole number part (1) to the decimal part ( $\frac{2}{3}$ ).

$1 \frac{2}{3} = 1 + \frac{2}{3} = 1 + 0.67 = 1.67$

Converting $\frac{5}{6}$ to a Decimal

To convert $\frac{5}{6}$ to a decimal, we can divide the numerator (5) by the denominator (6).

$\frac{5}{6} = 5 ÷ 6 = 0.83\overline{3}$

Finding the Volume of the Box

Now that we have converted all the mixed numbers to decimals, we can find the volume of the box.

Volume = length × width × height = $1.25 \times 1.67 \times 0.83\overline{3}$ = 1.875

Therefore, the volume of the box is approximately 1.875 cubic feet.

Conclusion

$In this article, we have explored two problems that involve converting fractions and mixed numbers to decimals. The first problem asked us to find the number of groups of $\frac{1}{3}$ inch in $\frac{3}{4}$ inch, while the second problem involved finding the volume of a box that contains a salt lick, given its dimensions in feet. We have used various techniques, including division and addition, to convert the fractions and mixed numbers to decimals. By following these techniques, we have been able to solve both problems and find the desired answers.<br/> **Frequently Asked Questions (FAQs)**$

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a decimal is a way of expressing a number as a sum of powers of 10.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you can divide the numerator (the top number) by the denominator (the bottom number). For example, to convert $\frac{1}{2}$ to a decimal, you can divide 1 by 2, which equals 0.5.

Q: How do I convert a mixed number to a decimal?

A: To convert a mixed number to a decimal, you can add the whole number part to the decimal part. For example, to convert $2 \frac{1}{4}$ to a decimal, you can add 2 to $\frac{1}{4}$ , which equals 2.25.

Q: What is the difference between a terminating decimal and a non-terminating decimal?

A: A terminating decimal is a decimal that has a finite number of digits after the decimal point, while a non-terminating decimal is a decimal that has an infinite number of digits after the decimal point.

Q: How do I convert a fraction to a percentage?

A: To convert a fraction to a percentage, you can divide the numerator by the denominator and multiply by 100. For example, to convert $\frac{1}{2}$ to a percentage, you can divide 1 by 2 and multiply by 100, which equals 50%.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, you can express the decimal as a sum of powers of 10 and then simplify the fraction. For example, to convert 0.5 to a fraction, you can express it as $\frac{5}{10}$ and then simplify it to $\frac{1}{2}$ .

Q: What is the difference between a rational number and an irrational number?

A: A rational number is a number that can be expressed as a ratio of two integers, while an irrational number is a number that cannot be expressed as a ratio of two integers.

Q: How do I add and subtract fractions with different denominators?

A: To add and subtract fractions with different denominators, you need to find the least common multiple (LCM) of the denominators and then convert both fractions to have the LCM as the denominator.

Q: How do I multiply and divide fractions?

A: To multiply fractions, you can multiply the numerators and denominators separately. To divide fractions, you can invert the second fraction and then multiply.

Q: What is the order of operations for fractions?

A: The order of operations for fractions is:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

By following these steps, you can simplify complex fraction expressions and solve problems involving fractions.