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 may 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 technique to symbolize 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 | Share |
|---|---|---|---|
| 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 combined 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 combined 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 combined numbers:
- Enter the entire quantity a part of the combined 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 combined quantity as a fraction.
Instance
To enter the combined quantity 2 3/4 on a calculator, you’d:
| 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 assist you to enter fractions as combined numbers. A combined quantity consists of a complete quantity and a fraction. To enter a fraction on this format, comply with these steps:
- Enter the entire quantity half.
- Press the “Fraction Bar” perform key (often denoted by a horizontal line with a diagonal line by it).
Observe: Some calculators could require you to press the “SHIFT” key earlier than urgent the “Fraction Bar” perform key.
- Enter the numerator (high quantity) of the fraction.
- Press the “Fraction Bar” perform key once more.
- Enter the denominator (backside quantity) of the fraction.
Instance: To enter the combined 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. Examine 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’d write 2.00.
To spherical 2.0 to 3 decimal locations, you’d 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 lets you 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.
It will 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 strive:
- Guarantee that the calculator is within the appropriate mode. Some calculators have a devoted “fraction” mode, whereas others require you to press a particular key to enter fractions.
- Examine the calculator’s show to see whether it is exhibiting the fraction appropriately. If the fraction shouldn’t be displayed appropriately, you might have entered it incorrectly.
- Attempt utilizing a unique methodology to enter the fraction. For instance, you’ll be able to strive 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’d 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 complicated fraction calculations. These calculators sometimes have a devoted “fraction” button that lets you enter and manipulate fractions immediately. This is learn how to do it.
Changing Blended Numbers to Improper Fractions
To transform a combined 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, you want to 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 Widespread 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, elevate 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.
It will 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 want 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 standard.
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 |
Easy methods to Sort 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’d press the next keys:
1 ÷ 2 = 1/2
Functions of Fractions within the Calculator
Fractions are utilized in quite a lot of functions within the calculator.
Percentages
Fractions can be utilized to symbolize percentages. To transform a share to a fraction, divide the share by 100. For instance, to transform 50% to a fraction, you’d divide 50 by 100, which supplies you 1/2.
Ratios
Fractions can be utilized to symbolize 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’d divide 3 by 4, which supplies 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 method:
Low cost = (Unique value – Sale value) / Unique 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 method:
Tax = Tax price x Buy value
For instance, if the tax price is 8% and the acquisition value 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 performed in just a few alternative ways, relying on the kind of calculator you may have. Listed here are the steps for typing fractions on some frequent 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.
Normal 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.
It will convert the fraction to a decimal.
Folks Additionally Ask About How To Sort Fractions On A Calculator
How do I kind a combined fraction on a calculator?
To kind a combined 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.
