Understanding Fraction Notations
Generally Used Notations
Numerator/Denominator:
The commonest notation for fractions is the numerator/denominator format. The numerator is the quantity above the road, and the denominator is the quantity beneath the road. For instance, within the fraction 1/2, 1 is the numerator and a couple of is the denominator.
Decimal Notation:
Fractions will also be represented in decimal notation. To transform a fraction to a decimal, divide the numerator by the denominator. For instance, 1/2 in decimal notation is 0.5 (1 divided by 2 equals 0.5).
Share Notation:
Percentages are one other strategy to characterize fractions. To transform a fraction to a proportion, multiply the fraction by 100. For instance, 1/2 as a proportion is 50% (1/2 multiplied by 100 equals 50).
| Numerator | Denominator | Decimal | Share |
|---|---|---|---|
| 1 | 2 | 0.5 | 50% |
| 3 | 4 | 0.75 | 75% |
| 1 | 5 | 0.2 | 20% |
Different Notations
Much less widespread notations for fractions embody the next:
- Vinculum Notation: A horizontal line is drawn above the fraction to point the numerator, and a horizontal line is drawn beneath the fraction to point the denominator. For instance, the fraction 1/2 could be written as 1‾2.
- Egyptian Fraction Notation: An Egyptian fraction is a sum of distinctive unit fractions, the place a unit fraction has a numerator of 1. For instance, the fraction 2/5 could be written as 1/3 + 1/15 in Egyptian fraction notation.
- Continued Fraction Notation: A continued fraction is an infinite expression of the shape a0 + 1/(a1 + 1/(a2 + 1/(a3 + …))). For instance, the continued fraction illustration of the golden ratio is [1; 1, 1, 1, …].
Getting into Fractions as Combined Numbers
Utilizing the Devoted Fraction Button
For calculators with a devoted fraction button (sometimes labeled “F” or “FRAC”), observe these steps:
- Press the “F” button.
- Enter the entire quantity a part of the blended quantity.
- Press the “F” button once more.
- Enter the numerator of the fraction.
- Press the “÷” button.
- Enter the denominator of the fraction.
- Press the “=” button to show the blended quantity as a fraction.
Utilizing the “Ab/c” Key
On calculators with no devoted fraction button, you need to use the “Ab/c” key to enter blended numbers:
- Enter the entire quantity a part of the blended quantity.
- Press the “Ab/c” button.
- Enter the numerator of the fraction.
- Press the “÷” button.
- Enter the denominator of the fraction.
- Press the “=” button to show the blended quantity as a fraction.
Instance
To enter the blended quantity 2 3/4 on a calculator, you’ll:
| Calculator Perform | Enter | Outcome |
|—|—|—|
| Utilizing Devoted Fraction Button | F -> 2 -> F -> 3 -> ÷ -> 4 -> = | 2 3/4 |
| Utilizing “Ab/c” Key | 2 -> Ab/c -> 3 -> ÷ -> 4 -> = | 2 3/4 |
Utilizing the Fraction Bar Perform
3. Getting into a Fraction with a Combined Quantity
Many calculators can help you enter fractions as blended numbers. A blended quantity consists of a complete quantity and a fraction. To enter a fraction on this format, observe these steps:
- Enter the entire quantity half.
- Press the “Fraction Bar” perform key (normally denoted by a horizontal line with a diagonal line via it).
Notice: Some calculators might require you to press the “SHIFT” key earlier than urgent the “Fraction Bar” perform key.
- Enter the numerator (prime quantity) of the fraction.
- Press the “Fraction Bar” perform key once more.
- Enter the denominator (backside quantity) of the fraction.
Instance: To enter the blended quantity 2 1/2, the steps could be:
| Step | Keystrokes |
|---|---|
| 1 | Enter the entire quantity 2. |
| 2 | Press the “Fraction Bar” perform key. |
| 3 | Enter the numerator 1. |
| 4 | Press the “Fraction Bar” perform key once more. |
| 5 | Enter the denominator 2. |
The calculator show ought to now present “2 1/2”.
Changing Fractions to Decimals
1. Convert the fraction to an improper fraction
For instance, 2/3 turns into 6/3.
2. Divide the numerator by the denominator
Use your calculator to divide 6 by 3.
3. Verify for a repeating decimal
If the decimal has a sample that repeats, it’s referred to as a repeating decimal. For instance, 6 divided by 3 equals 2.0, which has a repeating decimal of 0.
4. Around the decimal to the specified variety of digits
If the decimal has a repeating sample, you’ll be able to spherical it to the specified variety of digits after the decimal level.
For instance, to spherical 2.0 to 2 decimal locations, you’ll write 2.00.
To spherical 2.0 to 3 decimal locations, you’ll write 2.000.
Desk of Equivalents
| Decimal | Fraction |
|---|---|
| 0.25 | 1/4 |
| 0.33 | 1/3 |
| 0.5 | 1/2 |
| 0.66 | 2/3 |
| 0.75 | 3/4 |
Keyboard Shortcuts for Fractions
Most calculators have a devoted “Fr” or “Frac” button that permits you to enter fractions. In case your calculator doesn’t have this button, you need to use the next keyboard shortcuts:
| Fraction | Keyboard Shortcut |
|---|---|
| 1/2 | Shift + 5 |
| 1/3 | Shift + 6 |
| 1/4 | Shift + 7 |
| 1/5 | Shift + 8 |
| 1/6 | Shift + 9 |
1/6
To enter 1/6 on a calculator with no devoted “Fr” or “Frac” button, use the next steps:
- Press the “Shift” key and maintain it down.
- Press the “9” key.
- Launch the “Shift” key.
This may enter the fraction 1/6 on the calculator show.
Troubleshooting Fraction Enter
If you’re having bother typing a fraction into your calculator, right here are some things to attempt:
- Guarantee that the calculator is within the right mode. Some calculators have a devoted “fraction” mode, whereas others require you to press a particular key to enter fractions.
- Verify the calculator’s show to see whether it is exhibiting the fraction accurately. If the fraction is just not displayed accurately, you could have entered it incorrectly.
- Attempt utilizing a special technique to enter the fraction. For instance, you’ll be able to attempt typing the numerator and denominator individually, or you need to use the calculator’s built-in fraction converter.
Fractions with Entire Numbers
To enter a fraction with a complete quantity, merely kind the entire quantity adopted by an area after which the fraction. For instance, to enter the fraction 1 1/2, you’ll kind “1 1/2”.
Changing Decimal Numbers to Fractions
To transform a decimal quantity to a fraction, you need to use the calculator’s built-in fraction converter. To do that, merely press the “fraction” key after which enter the decimal quantity. The calculator will routinely convert the decimal quantity to a fraction.
Changing Fractions to Decimal Numbers
To transform a fraction to a decimal quantity, you need to use the calculator’s built-in decimal converter. To do that, merely press the “decimal” key after which enter the fraction. The calculator will routinely convert the fraction to a decimal quantity.
Superior Fraction Calculations
With a scientific or graphing calculator, you’ll be able to carry out extra advanced fraction calculations. These calculators sometimes have a devoted “fraction” button that permits you to enter and manipulate fractions instantly. This is tips on how to do it.
Changing Combined Numbers to Improper Fractions
To transform a blended quantity (e.g., 2 1/2) to an improper fraction:
- Multiply the entire quantity by the denominator of the fraction (2 x 2 = 4)
- Add the numerator to the product (4 + 1 = 5)
- Place the sum over the denominator (5/2)
Multiplying and Dividing Fractions
To multiply fractions, multiply their numerators and denominators:
(a/b) x (c/d) = (a x c)/(b x d)
To divide fractions, invert the divisor and multiply:
(a/b) ÷ (c/d) = (a/b) x (d/c) = (a x d)/(b x c)
Including and Subtracting Fractions with Completely different Denominators
So as to add or subtract fractions with totally different denominators, it’s worthwhile to discover a widespread denominator (the least widespread a number of of the unique denominators). Then, convert every fraction to an equal fraction with the brand new denominator and carry out the operation:
| Fraction | Equal Fraction with Frequent Denominator |
|---|---|
| 1/2 | 3/6 |
| 1/3 | 2/6 |
| -> | (3/6) + (2/6) = 5/6 |
Exponents and Radicals with Fractions
When elevating a fraction to an influence, increase each the numerator and denominator to that energy:
(a/b)^n = (a^n)/(b^n)
To take the sq. root of a fraction, take the sq. root of each the numerator and denominator:
√(a/b) = √a/√b
Calculating Percentages with Fractions
To transform a fraction to a proportion, multiply it by 100 and add the p.c signal:
(a/b) x 100% = (a/b) x 100
Utilizing Fractions in Equations
To make use of fractions in equations on a calculator, observe these steps:
1. Press the “Frac” key.
This secret is normally situated above the quantity keys.
2. Enter the numerator of the fraction.
Use the quantity keys to enter the numerator of the fraction.
3. Press the “/” key.
This secret is normally situated between the quantity keys and the “Frac” key.
4. Enter the denominator of the fraction.
Use the quantity keys to enter the denominator of the fraction.
5. Press the “Enter” key.
This may enter the fraction into the equation.
6. Repeat steps 1-5 for every fraction within the equation.
If there are a number of fractions within the equation, you will have to repeat steps 1-5 for every fraction.
7. Carry out the operations within the equation.
As soon as all of the fractions have been entered, you’ll be able to carry out the operations within the equation as normal.
8. Press the “=” key to get the reply.
The calculator will show the reply to the equation.
9. Convert fractions to decimals (Non-compulsory)
If desired, you’ll be able to convert the fractions within the equation to decimals by following these steps:
- Press the “2nd” key.
- Press the “Dec” key.
- Enter the fraction you wish to convert.
- Press the “Enter” key.
The calculator will show the decimal equal of the fraction.
| Fraction | Decimal Equal |
|---|---|
| 1/2 | 0.5 |
| 1/4 | 0.25 |
| 1/8 | 0.125 |
Tips on how to Kind Fractions on a Calculator
To kind a fraction on a calculator, you need to use the next steps:
- Enter the numerator of the fraction.
- Press the divide (÷) key.
- Enter the denominator of the fraction.
- Press the enter key.
For instance, to enter the fraction 1/2 on a calculator, you’ll press the next keys:
1 ÷ 2 = 1/2
Functions of Fractions within the Calculator
Fractions are utilized in a wide range of functions within the calculator.
Percentages
Fractions can be utilized to characterize percentages. To transform a proportion to a fraction, divide the proportion by 100. For instance, to transform 50% to a fraction, you’ll divide 50 by 100, which provides you 1/2.
Ratios
Fractions can be utilized to characterize ratios. A ratio is a comparability of two numbers. To transform a ratio to a fraction, divide the primary quantity by the second quantity. For instance, to transform the ratio 3:4 to a fraction, you’ll divide 3 by 4, which provides you 3/4.
Reductions
Fractions can be utilized to calculate reductions. A reduction is a discount within the value of an merchandise. To calculate a reduction, you need to use the next formulation:
Low cost = (Authentic value – Sale value) / Authentic value
For instance, if an merchandise has an authentic value of $100 and a sale value of $80, the low cost could be (100 – 80) / 100 = 1/5.
Taxes
Fractions can be utilized to calculate taxes. A tax is a cost that’s added to the value of an merchandise. To calculate the quantity of tax on an merchandise, you need to use the next formulation:
Tax = Tax charge x Buy value
For instance, if the tax charge is 8% and the acquisition value is $100, the tax could be 0.08 x 100 = $8.
How To Kind Fractions On A Calculator
Typing fractions on a calculator could be completed in a couple of other ways, relying on the kind of calculator you will have. Listed here are the steps for typing fractions on some widespread varieties of calculators:
Scientific Calculator
1. Enter the numerator of the fraction.
2. Press the “÷” button.
3. Enter the denominator of the fraction.
4. Press the “=” button.
Graphing Calculator
1. Press the “2nd” button.
2. Press the “Frac” button.
3. Enter the numerator of the fraction.
4. Press the “↓” button.
5. Enter the denominator of the fraction.
6. Press the “Enter” button.
Customary Calculator
1. Enter the numerator of the fraction.
2. Press the “÷” button.
3. Enter the denominator of the fraction.
4. Press the “=” button.
5. Press the “Shift” button.
6. Press the “fx” button.
This may convert the fraction to a decimal.
Individuals Additionally Ask About How To Kind Fractions On A Calculator
How do I kind a blended fraction on a calculator?
To kind a blended fraction on a calculator, you need to use the next steps:
- Enter the entire quantity a part of the fraction.
- Press the “÷” button.
- Enter the numerator of the fractional half.
- Press the “↓” button.
- Enter the denominator of the fractional half.
- Press the “=” button.
How do I kind a fraction with a repeating decimal on a calculator?
To kind a fraction with a repeating decimal on a calculator, you need to use the next steps:
- Enter the numerator of the fraction.
- Press the “÷” button.
- Enter the denominator of the fraction.
- Press the “=” button.
- Press the “Shift” button.
- Press the “fx” button.
- Press the “Rcl” button.
- Enter the variety of the register the place you saved the fraction.
- Press the “=” button.
How do I convert a fraction to a decimal on a calculator?
To transform a fraction to a decimal on a calculator, you need to use the next steps:
- Enter the numerator of the fraction.
- Press the “÷” button.
- Enter the denominator of the fraction.
- Press the “=” button.
