Understanding Fraction Notations
Generally Used Notations
Numerator/Denominator:
The most typical 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).
Proportion Notation:
Percentages are one other option to characterize fractions. To transform a fraction to a share, multiply the fraction by 100. For instance, 1/2 as a share is 50% (1/2 multiplied by 100 equals 50).
| Numerator | Denominator | Decimal | Proportion |
|---|---|---|---|
| 1 | 2 | 0.5 | 50% |
| 3 | 4 | 0.75 | 75% |
| 1 | 5 | 0.2 | 20% |
Different Notations
Much less frequent 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 may 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 may 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 Blended Numbers
Utilizing the Devoted Fraction Button
For calculators with a devoted fraction button (sometimes labeled “F” or “FRAC”), comply with 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 should utilize 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 | End result |
|—|—|—|
| 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 Blended Quantity
Many calculators mean you can enter fractions as blended numbers. A blended quantity consists of an entire quantity and a fraction. To enter a fraction on this format, comply with these steps:
- Enter the entire quantity half.
- Press the “Fraction Bar” operate key (often denoted by a horizontal line with a diagonal line by means of it).
Notice: Some calculators could require you to press the “SHIFT” key earlier than urgent the “Fraction Bar” operate key.
- Enter the numerator (prime quantity) of the fraction.
- Press the “Fraction Bar” operate 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” operate key. |
| 3 | Enter the numerator 1. |
| 4 | Press the “Fraction Bar” operate 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. Test 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 a few 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 means that you can enter fractions. In case your calculator doesn’t have this button, you should utilize 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 can enter the fraction 1/6 on the calculator show.
Troubleshooting Fraction Enter
In case you are having bother typing a fraction into your calculator, right here are some things to strive:
- Ensure 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.
- Test the calculator’s show to see whether it is exhibiting the fraction appropriately. If the fraction isn’t displayed appropriately, you’ll have entered it incorrectly.
- Attempt utilizing a distinct technique to enter the fraction. For instance, you’ll be able to strive typing the numerator and denominator individually, or you should utilize the calculator’s built-in fraction converter.
Fractions with Complete 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 should utilize the calculator’s built-in fraction converter. To do that, merely press the “fraction” key after which enter the decimal quantity. The calculator will mechanically convert the decimal quantity to a fraction.
Changing Fractions to Decimal Numbers
To transform a fraction to a decimal quantity, you should utilize the calculator’s built-in decimal converter. To do that, merely press the “decimal” key after which enter the fraction. The calculator will mechanically convert the fraction to a decimal quantity.
Superior Fraction Calculations
With a scientific or graphing calculator, you’ll be able to carry out extra complicated fraction calculations. These calculators sometimes have a devoted “fraction” button that means that you can enter and manipulate fractions immediately. This is the best way to do it.
Changing Blended 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 completely different denominators, you should discover a frequent denominator (the least frequent 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 share, multiply it by 100 and add the % signal:
(a/b) x 100% = (a/b) x 100
Utilizing Fractions in Equations
To make use of fractions in equations on a calculator, comply with these steps:
1. Press the “Frac” key.
This key’s often 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 key’s often 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 can 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’ll need 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 traditional.
8. Press the “=” key to get the reply.
The calculator will show the reply to the equation.
9. Convert fractions to decimals (Elective)
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 need 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 |
The way to Sort Fractions on a Calculator
To kind a fraction on a calculator, you should utilize 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 share to a fraction, divide the share 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 worth of an merchandise. To calculate a reduction, you should utilize the next components:
Low cost = (Authentic worth – Sale worth) / Authentic worth
For instance, if an merchandise has an authentic worth of $100 and a sale worth 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 worth of an merchandise. To calculate the quantity of tax on an merchandise, you should utilize the next components:
Tax = Tax price x Buy worth
For instance, if the tax price is 8% and the acquisition worth is $100, the tax could be 0.08 x 100 = $8.
How To Sort Fractions On A Calculator
Typing fractions on a calculator may be achieved in a number of alternative ways, relying on the kind of calculator you could have. Listed below are the steps for typing fractions on some frequent kinds 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 can convert the fraction to a decimal.
Folks Additionally Ask About How To Sort Fractions On A Calculator
How do I kind a blended fraction on a calculator?
To kind a blended fraction on a calculator, you should utilize 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 should utilize 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 should utilize the next steps:
- Enter the numerator of the fraction.
- Press the “÷” button.
- Enter the denominator of the fraction.
- Press the “=” button.
