Standards in this domain:
Use equivalent fractions as a strategy to add and subtract fractions.
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
1/2 times what equals 1/2? What divided by 1/4 equals 3/5? What is 2 over 3 as a percentage? How to calculate 3/4 plus 1/9 Is 1/2 greater than 1/3? What is 4.56 as a fraction? How to calculate 3/7 divided by 4/5 Equivalent Fractions of 3/9 What is the factorial of 6? 1/2 divided by what equals 3/4? Reduce 5/25 What times 1/3 equals 1/2? (2/3)x-1/3 + (2/3)y-1/3 y' = 0, so that (Now solve for y'.) (2/3)y-1/3 y' = - (2/3)x-1/3, and, Since lines tangent to the graph will have slope $ -1 $, set y' = -1, getting, - y 1/3 = -x 1/3, y 1/3 = x 1/3, ( y 1/3) 3 = ( x 1/3) 3, or y = x. Substitue this into the ORIGINAL equation x 2/3 + y 2/3 = 8, getting x 2/3 + (x) 2/3 = 8, 2 x.
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
Apply and extend previous understandings of multiplication and division.
Instabro 5 3 2 Equals Many
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Instabro 5 3 2 Equals 2/3
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd).
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
Interpret multiplication as scaling (resizing), by:
Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
1Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.
BeatThe metronome is loading, please wait.. 6th grade social studies lesson 1. (You need to have JavaScript enabled for this to work) |
Quick Start Guide
- Set a tempo. Tempo is measured in BPM (beats per minute), and you have the choice of four ways to set it:
- Type a number into the box in the top right corner (overwriting the default value of 120), then press Enter on your keyboard.
- Click the up/down arrows on the spinner.
- Drag the knob of the vertical slider on the right.
- Tap the tempo by clicking a few times in the 'Tap Tempo Here' area.
- Set the number of beats per measure by dragging the slider.
- Start the metronome by pressing the big button labeled START. By the same button you can stop and restart the metronome as many times as you want.
What is a metronome?
A metronome is a practice tool that produces a regulated pulse to help you play rhythms accurately. The frequency of the pulses is measured in beats per minute (BPM).
Diligent musicians use a metronome to maintain an established tempo while practicing, and as an aid to learning difficult passages.
Tempo markings
In musical terminology, tempo (Italian for 'time') is the speed or pace of a given piece. The tempo is typically written at the start of a piece of music, and in modern music it is usually indicated in beats per minute (BPM).
Whether a music piece has a mathematical time indication or not, in classical music it is customary to describe the tempo of a piece by one or more words, which also convey moods. Most of these words are Italian, a result of the fact that many of the most important composers of the 17th century were Italian, and this period was when tempo indications were used extensively for the first time. You can search for these foreign terms in our music glossary.
Traditionally, metronomes display some of the most common Italian tempo markings ('Adagio', 'Allegro', etc.) alongside the BPM slider, but the correspondence of words to numbers can by no means be regarded as precise for every piece. The tempo of a piece will depend on the actual rhythms in the music itself, as well as the performer and the style of the music. If a musical passage does not make sense, the tempo might be too slow. Folder tidy 2 7 2. On the other hand, if the fastest notes of a work are impossible to play well, the tempo is probably too fast.
Time signatures explained
A true understanding of time signatures is crucial towards a correct use of the metronome. Time signatures are found at the beginning of a musical piece, after the clef and the key signature. They consist of two numbers:
- the upper number indicates how many beats there are in a measure;
- the lower number indicates the note value which represents one beat: '2' stands for the half note, '4' for the quarter note, '8' for the eighth note and so on.
You should beware, however, that this interpretation is only correct when handling simple time signatures. Time signatures actually come in two flavors: simple and compound.
- In simple time signatures, each beat is divided into two equal parts. The most common simple time signatures are 2/4, 3/4, 4/4 (often indicated with a 'C' simbol) and 2/2 (often indicated with a 'cut C' simbol).
- In compound time signatures, each beat is divided into three equal parts. Compound time signatures are distinguished by an upper number which is commonly 6, 9 or 12. The most common lower number in a compound time signature is 8.
Unlike simple time, compound time uses a dotted note for the beat unit. To identify which type of note represents one beat, you have to multiply the note value represented by the lower number by three. So, if the lower number is 8 the beat unit must be the dotted quarter note, since it is three times an eighth note. The number of beats per measure can instead be determined by dividing the upper number by three.
To sum up, here are some common examples.
| Time | Type | Beats per measure |
|---|---|---|
| 2/2 | simple | 2 half notes per measure |
| 3/2 | simple | 3 half notes per measure |
| 2/4 | simple | 2 quarter notes per measure |
| 3/4 | simple | 3 quarter notes per measure |
| 4/4 | simple | 4 quarter notes per measure |
| 5/4 | simple | 5 quarter notes per measure |
| 6/4 | compound | 2 dotted half notes per measure |
| 3/8 | simple | 3 eight notes per measure |
| 4/8 | simple | 4 eight notes per measure |
| 6/8 | compound | 2 dotted quarter notes per measure |
| 9/8 | compound | 3 dotted quarter notes per measure |
| 12/8 | compound | 4 dotted quarter notes per measure |
How to practice difficult passages
Sometimes, most of a piece is easy to play except for a few measures. When faced with a challenging passage, practice the problem area at a slow tempo that allows you to play without mistakes: your first goal is to achieve one correct playing of all the notes.
This is very important. Because of muscle memory, you can practice mistakes over and over and learn them just as well as the notes you are supposed to be playing. So during the process of achieving that one correct run through, every mistake must be pounced on.
When you see you can play the passage without mistakes, you can add some BPM and try the passage at the faster tempo. If you can execute the passage 5 times in a row without any mistakes, you can add some BPM again. Repeat this process until you reach the target tempo!
Once you've developed a feel for the right tempo, try turning off the metronome. Your final goal is to play the piece with the pulse in your memory.
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