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Fractions, grade 6

Sixth-grade fractions and decimals.Subjects

The topics, in order:

  • what a fraction is;

  • multiplying and dividing fractions;

  • part of a quantity;

  • decimals;

  • the numbers we know, and the laws of operations.

  • Learning lessons explain a topic with examples, and have a few questions to try.

  • Practice lessons are all questions.

  • Go in order.

How the page works: Using a page.

  1. A fraction as a divisionLearning3 shared equally among 5 is 3/5 – a fraction as the result of a division.
  2. Fractions and decimals on the number lineLearningEvery number has its place on the number line – and between two numbers there is always another one.
  3. Equal fractions, comparing fractionsLearningReducing and expanding – the same number as different fractions; and how to tell which fraction is bigger.
  4. Adding and subtracting fractionsLearningWith the same denominator, with different denominators, and with mixed numbers.
  5. Practice: fractions and the number linePracticeDivisions as fractions and mixed numbers, reducing, comparing, the number line, adding and subtracting fractions.
  6. A whole number times a fractionLearning3 × 2/5 is repeated addition; a whole number times a mixed number, two ways.
  7. Part of a quantity: the value of the partLearningWhat is 2/3 of 24? "Of" is multiplication.
  8. A fraction times a fractionLearningMultiplying fractions as the area of a rectangle; mixed numbers; when multiplying makes a number smaller.
  9. Practice: multiplying fractionsPracticeA whole number times a fraction, a fraction times a fraction, mixed numbers, estimates and word problems.
  10. Finding the part and finding the wholeLearningWhat part of 20 is 4? And 6 is a fifth of what?
  11. Practice: part of a quantityPracticeThe value of a part, which part, the whole quantity – in calculations and word problems.
  12. Dividing fractionsLearningHow many fifths are there in 6? From there to multiplying by the reciprocal.
  13. Practice: dividing fractionsPracticeDividing whole numbers, fractions and mixed numbers by fractions, and word problems.
  14. Decimals as fractionsLearningFrom a fraction to a decimal and back – by expanding and reducing.
  15. Decimals and 10, 100, 1000LearningEach digit moves to the next place – the decimal point seems to move.
  16. Multiplying decimalsLearningMultiply as whole numbers, then put the point back – and check with an estimate.
  17. Dividing decimalsLearningMultiply both numbers by the same 10, 100 … – the result stays the same, and the number you divide by becomes whole.
  18. Repeating decimalsLearningA fraction as a decimal: some end, and some go on forever, repeating.
  19. Practice: decimalsPracticeTimes and divided by 10, 100, 1000; multiplying and dividing decimals; where does the point go?
  20. The numbers we knowLearningWhole numbers, fractions and decimals on one number line; numbers between two numbers; which number fits which context; numbers below zero.
  21. The order and laws of operationsLearningThe order of operations; the commutative, associative and distributive laws for quick calculation; multiplying by a number below 1.
  22. Review: fractions and decimalsPracticeEverything together: fractions and decimals, the four operations, the number line, number sequences, part of a quantity, numbers between numbers, the laws of operations.
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