What is 1 3/4 Divided by 1/2?

Dividing fractions may seem complex at first, but it’s a fundamental mathematical operation that can be easily understood and mastered. In this blog post, we’ll break down the process of dividing the mixed number 1 3/4 by the fraction 1/2 into simple steps, provide explanations, and offer examples to illustrate the concept.

What is 1 3/4 Divided by 1/2?

1 3/4 divided by 1/2 equals 3 1/2. To solve this, convert the mixed number 1 3/4 to an improper fraction (7/4), then multiply by the reciprocal of 1/2, which is 2/1. The result is 7/4 multiplied by 2/1, which simplifies to 7/2 or 3 1/2 when expressed as a mixed number.

Step 1: Convert the Mixed Number to an Improper Fraction

Before we can proceed with the division, we need to convert the mixed number 1 3/4 into an improper fraction. An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number).

To convert 1 3/4 into an improper fraction, follow these steps:

• Multiply the whole number (1) by the denominator of the fraction (4): 1 × 4 = 4.
• Add the result (4) to the numerator of the fraction (3): 4 + 3 = 7.
• Keep the denominator (4) the same.

So, 1 3/4 can be expressed as the improper fraction 7/4.

Step 2: Divide the Improper Fraction by the Fraction

Now that we have the improper fraction 7/4, we can proceed with the division. To divide one fraction by another, we use the following rule:

Dividing Fraction A (7/4) by Fraction B (1/2) is equivalent to multiplying Fraction A by the reciprocal of Fraction B.

Reciprocal means “flipping” the fraction upside down, swapping the numerator and denominator. For 1/2, the reciprocal is 2/1.

So, we’ll multiply 7/4 by 2/1:

(7/4) ÷ (1/2) = (7/4) × (2/1)

Step 3: Multiply the Fractions

To multiply fractions, multiply the numerators together to get the new numerator and multiply the denominators together to get the new denominator. So, let’s calculate it:

Numerator: 7 × 2 = 14 Denominator: 4 × 1 = 4

Now we have the fraction:

(7/4) × (2/1) = 14/4

Step 4: Simplify the Fraction (if needed)

In this case, we can simplify the fraction 14/4. To simplify a fraction, we find the greatest common factor (GCF) of the numerator and denominator and divide both by it.

The GCF of 14 and 4 is 2.

Dividing both the numerator and denominator by 2:

Numerator: 14 ÷ 2 = 7 Denominator: 4 ÷ 2 = 2

So, the simplified fraction is:

14/4 = 7/2

Step 5: Express the Result as a Mixed Number (if desired)

Now that we have the fraction 7/2, we can express it as a mixed number if needed. To do this, we divide the numerator (7) by the denominator (2) and express the remainder as a fraction.

7 ÷ 2 = 3 with a remainder of 1.

So, the mixed number equivalent of 7/2 is 3 1/2.

FAQs

How do you divide 1 3/4 in Half? To divide 1 3/4 in half, you can first convert the mixed number to an improper fraction. 1 3/4 is equivalent to 7/4 as an improper fraction. Then, divide 7/4 by 2, which yields 7/8. So, half of 1 3/4 is 7/8.

What is Half of 3/4 as a fraction? Half of 3/4 is 3/8. To find half of a fraction, simply divide the numerator (top number) by 2 while keeping the denominator (bottom number) the same.

What is a 1 3/4 fraction divided by 2? 1 3/4 divided by 2 is 7/8. To solve this, convert 1 3/4 to an improper fraction (7/4) and then divide the numerator (7) by the denominator (4) to get 7/8.

How to divide 3/4 in Half? To divide 3/4 in half, simply multiply it by 1/2. This results in (3/4) × (1/2) = 3/8, which is half of 3/4.

What’s half of 1 3/4 cup of water? Half of 1 3/4 cups of water is 7/8 cups. You can find this by converting the mixed number to an improper fraction (7/4) and then dividing it by 2.

What is 3/4 cups divided by half? When you divide 3/4 cups by half (1/2), you are essentially multiplying 3/4 by 2. This equals 3/2 or 1 1/2 cups.

How to divide fractions? To divide fractions, you can use the rule: Divide the first fraction by the second fraction by multiplying it by the reciprocal (flipped version) of the second fraction. For example, to divide A/B by C/D, you would multiply A/B by D/C.

How do you half a fraction? To find half of a fraction, simply divide the numerator (top number) by 2 while keeping the denominator (bottom number) the same. For example, half of 3/4 is 3/8.

What is 1 3/4 fraction to decimal? To convert the mixed number 1 3/4 to a decimal, first convert it to an improper fraction, which is 7/4. Then, divide the numerator (7) by the denominator (4). This results in a decimal of 1.75. So, 1 3/4 as a decimal is 1.75.

Step 6: Conclusion

In conclusion, when you divide the mixed number 1 3/4 by the fraction 1/2, the result is 3 1/2. This process involves converting the mixed number to an improper fraction, multiplying by the reciprocal of the divisor, simplifying the result if necessary, and expressing it as a mixed number. Dividing fractions becomes straightforward with practice, and it’s a valuable skill in various mathematical and real-life situations.