4.5 × 3/4 = 3.375. The expression means taking three-fourths of 4.5. It can be solved by converting the decimal to a fraction, multiplying by the numerator, and dividing by the denominator—or by converting three-fourths to a decimal first. Both approaches produce the same result. Understanding the steps makes it easier to check the answer and apply the calculation to measurements, prices, recipes, and other everyday quantities.
The Answer to 4.5 × 3/4
The product of 4.5 and 3/4 is 3.375. In fraction form, the same answer is 27/8, or 3 3/8 as a mixed number. These are equivalent ways to represent one value:
4.5 × 3/4 = 3.375 = 27/8 = 3 3/8
The expression can be read as “four and a half times three-fourths” or, equivalently, “three-fourths of 4.5.” Since three-fourths is less than one, the result is smaller than 4.5, which is a useful first check.
How to Calculate 4.5 × 3/4
Method One: Convert 4.5 to a Fraction
Write 4.5 as a fraction. Because the 5 is in the tenths place, 4.5 equals 45/10. Simplify that fraction by dividing the numerator and denominator by 5:
4.5 = 45/10 = 9/2
Now multiply 9/2 by 3/4. Multiply the numerators together and the denominators together:
9/2 × 3/4 = (9 × 3)/(2 × 4) = 27/8
Convert 27/8 to a mixed number by dividing 27 by 8. Eight goes into 27 three times, with a remainder of 3. Therefore, 27/8 equals 3 3/8. Since 3/8 is 0.375, the decimal answer is 3.375.
Method Two: Multiply by the Numerator, Then Divide
The fraction 3/4 means three parts out of four equal parts. The expression can therefore be calculated in two steps: multiply 4.5 by 3, then divide by 4.
4.5 × 3 = 13.5
13.5 ÷ 4 = 3.375
This method is often convenient when a number is multiplied by a fraction. In general, multiplying a quantity by a fraction a/b is equivalent to multiplying the quantity by a and then dividing by b, as long as b is not zero.
Method Three: Convert 3/4 to a Decimal
Divide the numerator, 3, by the denominator, 4:
3 ÷ 4 = 0.75
Then multiply 4.5 by 0.75:
4.5 × 0.75 = 3.375
This method can be especially helpful when using a calculator or when the rest of a problem already uses decimal numbers. It also offers a quick check: 0.75 is three-quarters, so multiplying by 0.75 should give a result equal to 75% of the original amount.
Why the Answer Is 3.375
Multiplication by a fraction does not always make a number larger. When the multiplier is between 0 and 1, the product is a portion of the starting value. Since 3/4 equals 0.75, the calculation asks for 75% of 4.5.
One way to see this is to divide 4.5 into four equal parts. Each part is 1.125. Three of those parts total 3.375:
4.5 ÷ 4 = 1.125
1.125 × 3 = 3.375
This model also clarifies the word “of” in fraction problems. In arithmetic, “three-fourths of 4.5” means 3/4 multiplied by 4.5. The order of the factors does not change the product, so 4.5 × 3/4 and 3/4 × 4.5 have the same answer.
Equivalent Forms of the Result
The value 3.375 can be expressed in several forms. Choosing the right form depends on what the calculation is being used for.
| Form | Value | How It Is Obtained |
|---|---|---|
| Decimal | 3.375 | Divide 27 by 8, or multiply 4.5 by 0.75. |
| Improper fraction | 27/8 | Multiply 9/2 by 3/4. |
| Mixed number | 3 3/8 | Divide 27 by 8; the remainder is 3. |
| Percent of 4.5 | 75% | Three-fourths is equal to 0.75, or 75%. |
These forms are interchangeable, but they may not be equally practical. A decimal is useful in many calculations and on digital devices. A mixed number can be convenient for measurements expressed in fractional units. An improper fraction is often easier to use in further fraction arithmetic.
Using the Calculation in Everyday Situations
Measurements
If a piece of material measures 4.5 feet and someone needs three-fourths of its length, the calculation is 4.5 × 3/4. The result is 3.375 feet, which is also 3 3/8 feet. To express it in inches, multiply by 12: 3.375 × 12 = 40.5 inches. The unit must stay attached to the number throughout the calculation so the result is interpreted correctly.
In a practical measuring task, the final precision may depend on the measuring tool and the material. A ruler marked in eighths of an inch may call for a rounded or converted measurement, while a digital measurement may preserve decimals. The arithmetic result itself remains 3.375 in the original unit.
Recipes and Quantities
A recipe calling for 4.5 cups of an ingredient can be scaled to three-fourths of its original size by multiplying 4.5 by 3/4. The reduced quantity is 3.375 cups, or 3 3/8 cups. In cooking, that amount may be easier to measure using a combination of standard measuring cups and spoons, depending on the ingredients and available equipment.
Scaling a recipe is different from changing an ingredient’s proportions. If every ingredient is multiplied by three-fourths, the recipe’s relative proportions stay the same. Multiplying only one ingredient changes the formula and may affect the final result.
Prices and Portions
If an item costs $4.50 and a discount is three-fourths of its price, the discount amount is $3.375 before considering any store rules, taxes, or rounding. However, a common shopping question is instead to find the price after a 25% discount. Since paying 75% of $4.50 means multiplying by 3/4, the amount before tax is $3.375, which is typically rounded to the nearest cent as $3.38.
This distinction matters: the calculation gives the exact mathematical amount, while money is usually recorded to two decimal places. Rounding should take place at the appropriate stage for the situation, especially when a calculation includes several items or additional percentages.
Common Mistakes to Avoid
- Adding instead of multiplying: The symbol × means multiplication. The problem is not 4.5 + 3/4.
- Reversing the fraction: Three-fourths is 3/4, not 4/3. The numerator is the top number and the denominator is the bottom number.
- Multiplying only by 3: The fraction requires both the numerator and denominator. Multiplying 4.5 by 3 gives 13.5, but that is only an intermediate step; the result must then be divided by 4.
- Misplacing the decimal point: Converting 4.5 to 45/10 and multiplying gives 135/40, which simplifies to 27/8 or 3.375. It is not 33.75.
- Rounding too early: Keeping the exact fraction or full decimal until the end avoids small errors in multistep problems.
- Ignoring units: If 4.5 represents feet, cups, dollars, or another unit, the product initially has that same unit.
How to Check the Result
A quick estimate can catch many errors. Since three-fourths is close to one, the answer should be somewhat less than 4.5. More precisely, 75% of 4.5 should be between half of 4.5, which is 2.25, and the full amount, which is 4.5. The answer 3.375 falls within that range.
A reverse calculation provides another check. Divide 3.375 by 4.5:
3.375 ÷ 4.5 = 0.75 = 3/4
That confirms that 3.375 is three-fourths of 4.5. The fraction route offers a separate check as well: 9/2 × 3/4 equals 27/8, and 27 divided by 8 is 3.375.
Using a Calculator for 4.5 × 3/4
A calculator can evaluate the expression in different ways. One option is to enter 4.5 × 3 ÷ 4. Another is to enter 4.5 × 0.75. Both should display 3.375. If the calculator has a fraction function, the expression can also be entered as 4.5 multiplied by 3/4.
When using a basic calculator, entering multiplication and division from left to right produces the intended result for 4.5 × 3 ÷ 4. For longer expressions, parentheses can make the intended grouping clear. For example, 4.5 × (3 ÷ 4) explicitly identifies three-fourths as the multiplier.
Calculator results should still be checked for entry mistakes. A misplaced decimal, an accidentally reversed fraction, or an extra keystroke can produce a plausible-looking but incorrect answer. Estimating that the result should be less than 4.5 is a simple safeguard.
Related Fraction and Decimal Skills
The calculation combines two useful skills: converting a terminating decimal to a fraction and multiplying fractions. A decimal with one digit after the decimal point can be written over 10; one with two digits after the decimal point can be written over 100, before simplifying. For example, 4.5 becomes 45/10, then 9/2.
To multiply fractions, multiply the top numbers and multiply the bottom numbers. If possible, simplify before or after multiplying. In this problem, 9/2 × 3/4 becomes 27/8. Since the numerator is larger than the denominator, the result is an improper fraction, which can be rewritten as the mixed number 3 3/8.
To convert a fraction to a decimal, divide the numerator by the denominator. Because 3 ÷ 4 is 0.75, multiplying by 3/4 is equivalent to multiplying by 0.75. Recognizing these equivalent forms helps with mental arithmetic, estimation, and checking work across different kinds of problems.