Positive Fractions Worksheet PDF

Summary

This worksheet covers multiplication and division of positive fractions and mixed numbers. It includes examples, practice exercises, and tables, suitable for secondary school students.

Full Transcript

Name - \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Date - \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ +-----------------------------------+-----------------------------------+ | **TOPIC** | | | |...

Name - \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Date - \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ +-----------------------------------+-----------------------------------+ | **TOPIC** | | | | | | **Multiplication and Division | | | of** | | | | | | **Positive Fractions and Mixed | | | numbers.** | | | | | | **⬇ ⬇** | | +===================================+===================================+ | [\$\\frac{1}{2}\$]{.math.inline} | [\$3\\frac{1}{2}\$]{.math | | |.inline} | +-----------------------------------+-----------------------------------+ **( DON'T DRAW ON THE ASSIGNMENT SHEET )** **If you need help with multiplication tables then you can use the following table:** +-----------------------------------------------------------------------+ | **Que : What is Fraction?** | | | | Ans : A fraction shows a part of something. It is written as two | | numbers: the top number tells how many parts we have, and the bottom | | number tells how many equal parts make a whole. | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | **Examples** | | | | ![](media/image49.png) | +-----------------------------------------------------------------------+ **Worksheet : 1 Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_** ![](media/image52.png) **Worksheet : 2 Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_** +-----------------------+-----------------------+-----------------------+ | **Types of | | | | Fractions** | | | +=======================+=======================+=======================+ | **[Proper | **[Improper | **[Mixed | | Fraction] | Fraction] | Fraction] | | ** | ** | ** | | | | | | **👇👇** | **👇👇** | **👇👇** | | | | | | Proper fractions are | Improper fractions | A mixed fraction is a | | the fractions in | are the fractions in | mixture of a whole | | which the numerator | which the denominator | number and a proper | | is less than its | is less than its | fraction. | | denominator. | numerator. | | | | | **[For | | **[For | **[For | Example]* | | Example]* | Example]* | * | | * | * | | | | | [\$1\\frac{5}{7}\\ \\ | | [\$\\frac{5}{7},\\fra | [\$\\frac{9}{5},\\fra | ,2\\frac{8}{12}\\ ,\\ | | c{8}{12},\\frac{1}{3} | c{3}{2},\\frac{8}{7}\ | 5\\frac{1}{3}\$]{.mat | | \$]{.math | $]{.math | h | |.inline} |.inline} |.inline} | +-----------------------+-----------------------+-----------------------+ ![](media/image7.png) **Worksheet : 3 Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Worksheet : 4 Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_** ![](media/image41.png) +-----------------------------------+-----------------------------------+ | **How to Multiply Fractions? 🤔** | | +===================================+===================================+ | **Let's learn it by example:** | | | | | | **Multiply** | | | [\$\\frac{1}{3}🇽\\frac{3}{5}\$]{. | | | math | | |.inline} | | +-----------------------------------+-----------------------------------+ | **Step 1: Multiply the | [\$\\frac{1\\ 🇽\\ 3}{3\\ 🇽\\ 5} = | | numerators.** | \\frac{3}{15}\$]{.math.inline} | | | | | **Multiply the denominators.** | | +-----------------------------------+-----------------------------------+ | **Step 2: Reduce the resultant | | | fraction\ | | | to its lowest terms, if you | | | can.** | | +-----------------------------------+-----------------------------------+ +-----------------------------------+-----------------------------------+ | **Question 1.** | **Question 2.** | | [\$\\frac{5}{6}🇽\\frac{2}{3}\$]{. | [\$\\frac{3}{5}🇽\\frac{1}{2}\$]{. | | math | math | |.inline} |.inline} | | | | | **Answer:** [\$\\frac{5\\ 🇽\\ | **Answer:** [\$\\frac{3\\ 🇽\\ | | 2}{6\\ 🇽\\ 3} = | 1}{5\\ 🇽\\ 2} = | | \\frac{10}{18}\$]{.math.inline} | \\frac{3}{10}\$]{.math.inline} | | | | | ![](media/image16.png) | WE can not reduce the fraction to | | | lower terms as there is no common | | | factor in denominator and | | | numerator. So the answer will be | | | [\$\\frac{3}{10}\$]{.math | | |.inline}**.** | +-----------------------------------+-----------------------------------+ **Worksheet : 5 Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Worksheet : 6 Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_** ![](media/image13.png) **Worksheet : 7 Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_** +-----------------------------------------------------------------------+ | **How to Divide Fractions? 🤔** | +=======================================================================+ | **When we divide one fraction by another fraction, it's like | | multiplying the first fraction by the second fraction's "flip."** | | | | **The "flip" means we switch the top number (numerator) and the | | bottom number (denominator) of the second fraction.** | | | | **Let's look at a picture to understand how to divide fractions | | better!** | | | | ![](media/image23.png) | +-----------------------------------------------------------------------+ +-----------------------------------+-----------------------------------+ | **Question 1.** [\$\\frac{5}{6} | **Question 2.** [\$\\frac{3}{5} | | \\div \\frac{2}{3}\$]{.math | \\div \\frac{1}{2}\$]{.math | |.inline} |.inline} | | | | | **Answer:** [\$\\frac{5}{6} \\div | **Answer:** [\$\\frac{3}{5} \\div | | \\frac{2}{3} =\$]{.math.inline} | \\frac{1}{2} =\$]{.math.inline} | | [\$\\frac{5}{6}🇽\\frac{3}{2}\\ | [\$\\frac{3}{5}🇽\\frac{2}{1}\\ | | \$]{.math.inline} | \$]{.math.inline} | | | | | [\$\\frac{5\\ 🇽\\ 3}{6\\ 🇽\\ 2} = | [\$\\frac{3\\ 🇽\\ 2}{5\\ 🇽\\ 1} = | | \\frac{15}{12} = | \\frac{6}{5}\$]{.math.inline} | | \\frac{5}{4}\$]{.math.inline} | | +-----------------------------------+-----------------------------------+ **Worksheet : 8 Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Worksheet : 9 Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_** ![](media/image27.png) **Mixed Numbers Or Mixed Fractions** **How to convert Mixed Fractions to Improper Fraction? 🤔** ------------------------------------------------------------ +-----------------------------------------------------------------------+ | **Example: Convert the mixed number** [\$3\\frac{1}{2}\$]{.math | |.inline} **to an improper fraction.** | | | | **[Step 1:]** Let us multiply the denominator with the | | whole number part. Here, we will multiply 3 by 2, that is, 3 × 2 = 6. | | | | **[Step 2:]** Now, we will add this product to the | | numerator. This will be 6 + 1 = 7. | | | | **[Step 3:]** So, 7 will be the new numerator while the | | denominator (2) will remain the same. This means [\$3\\frac{1}{2} = | | \\frac{7}{2}\$]{.math.inline}**.** | +-----------------------------------------------------------------------+ **Worksheet : 10 Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_** ![](media/image36.png) +-----------------------------------------------------------------------+ | **How to Multiply Two Mixed Numbers ? 🤔** | +=======================================================================+ | **[Example]** | | | | ![](media/image46.png) | +-----------------------------------------------------------------------+ **Worksheet : 11 Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_** **⬇ Multiplying mixed numbers ⬇** ![](media/image51.png) +-----------------------------------------------------------------------+ | **Dividing a Mixed Number by Another Mixed Number ? 🤔** | +=======================================================================+ | **First, convert both mixed numbers to improper fractions. Then, take | | the reciprocal of the second fraction and multiply it with the first | | fraction. Finally, simplify the answer you get and convert it into a | | mixed number if required.** | | | | **[Example]** | | | | ![](media/image39.png) | | | | ![](media/image43.png) | +-----------------------------------------------------------------------+ **Worksheet : 12 Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_** **⬇ Dividing mixed numbers ⬇** ![](media/image34.png)

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