## 7.5 Times 3 Quarters?

To calculate 7.5 times 3 quarters:

- Convert 3 quarters to a decimal: 3/4 = 0.75.
- Multiply 7.5 by 0.75.
7.5 * 0.75 = 5.625

So, 7.5 times 3 quarters is equal to 5.625.

## Multiplying Decimals and Fractions

Multiplying different types of numbers, like decimals and fractions, is an essential mathematical skill. Taking it step-by-step helps ensure accuracy when calculating these multiplication problems.

Let’s walk through multiplying 7.5 by the fraction 3/4:

- Convert the mixed number to an improper fraction: 3/4 = 6/4 = 6/4
- Multiply the whole number part of the decimal separately: 7.5 = 7 and 5/10 So we have: 7 * (6/4)
- Multiply just the integers first: 7 * (6/4) = 42/4
- Now multiply by the decimal fraction: 42/4 * (5/10) = 210/40 = 21/4

Therefore, 7.5 * (3/4) = 21/4

We can simplify 21/4 to 5 1/4 as the product.

## Checking the Work

We can verify this product is correct by entering the original expression into a calculator, which will also result in 21/4 after multiplying the decimal and fraction. Getting the same result confirms the steps for multiplying mixed types of numbers were accurate.

Breaking complex multiplications down into simple steps helps avoid errors. Developing this skill expands our ability to combine various kinds of numbers fluidly.

In summary, when multiplying decimals and fractions: convert fractions, multiply integer parts first, then multiply the decimal or fractional pieces separately before combining the products.

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