Multiplication of Fractions - Mishty Maths PDF

Okay, here is a structured markdown version of the text in the images you sent, with a focus on accuracy and clarity: ## Exercise 7.8 Solve the following by repeated addition. Here is an incomplete table. Here are the first two columns. The third column is just "=" | | | | | --- | --- | --- | | Sq...

Okay, here is a structured markdown version of the text in the images you sent, with a focus on accuracy and clarity: ## Exercise 7.8 Solve the following by repeated addition. Here is an incomplete table. Here are the first two columns. The third column is just "=" | | | | | --- | --- | --- | | Square of plus signs | plus marks | = | | Square of plus signs |plus marks | = | ### Multiplication of Fractions #### Multiplication as Repeated Addition Multiplication is repeated addition of the same number, i.e., $2+2+2+2+2=10$ and $2 \times 5=10$. The same method can be applied for addition of fraction also. i.e., $\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2}= 5 \times \frac{1}{2} = \frac{5}{2} = 2 \frac{1}{2}$ This can be shown as follows: + Image shows a collection of half circles adding up to make full circles. This would visually be 5/2.+ + Image shows a collection of half circles adding up to make full circles. This would visually be 3/2. + Similarly, $\frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4} = \frac{15}{4} = 3\frac{3}{4}$ ### Multiplication of a Fraction by a Number To multiply a number with a proper fraction, we multiply the number with the numerator of the fraction, keeping the denominator same. i.e. $\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = 2$ ## Exercise 7.9 **1.** Multiply and write your answers in the lowest form. * $\frac{6}{7} \times 30 = ?$ * $\frac{6}{8} \times 7 = ?$ * $\frac{3}{4} \times 32 = ?$ * $\frac{5}{9} \times 8 = ?$ * $\frac{8}{9} \times 40 = ?$ * $\frac{5}{2} \times 2 = ?$ **2.** Solve the following riddles on fractions. * a. I am a unit of time on our planet. I am 1/7 of a week. What am I? * b. I am also a unit of time, I am $1/60 \text{ of } 1/60 \text{ of } 1/24$ of the answer to above question (a). What am I? * c. I am a fraction. My denominator is 14. My numerator is not a part of one whol thing!. It is one whole thing!!. And don't you forget it!! What fraction am I? * d. I am a denominator. The numerator of the fraction that I am part of is 5. That fraction is equivalent to the answer to question (c). What number am I? * e. I am a fraction. My numerator is an odd single digit. My denominator is a single digit that is four times greater than my numerator. What fraction am I? ### Multiplication of Proper Fractions **Example:** Find $\frac{2}{3} \text{ of } \frac{3}{4} = \frac{2\times 3}{3\times 4} = \frac{6}{12} = \frac{1}{2}$ *The product of the numerators of the fractions is numerator of thew new fraction. The same applies to the denominators.* **Example:** $\frac{4}{7} \times \frac{5}{11} = \frac{(4 \times 5)}{(7 \times 11)} = \frac{20}{77}$ ### Multiplication of Mixed Numbers Example: Find $2\frac{1}{3} X 2 \frac{1}{4} = ?$ $2\frac {1}{3} X 2\frac {1}{4} = \frac{7}{3} X \frac{9}{4} = \frac{63}{12}$ (change to the new fractions/ always remember to reduce your answer int he lowest term) Example: Raj has 45 marbles of which $ \frac {2}{5} $ are black marbles $\frac {1}{9} $ are green marbles and the remaining are white marbles. How many white Marbles does he have: Total Number of marbles = 45 Number of black marbles =$\frac {2}{5} \times$ 45 = 18 Number of green marbles = $\frac {1}{9} \times$ 45 = 5 Number of white marbles 45 - (18+5) = 45-23= 22 ... The number of white marbles = 22 ### Excercise 7.10: $\check{ }$ Find H.W $ \frac{2}{3}\text { of }15 $ $HW \frac {6}{7} \text{of } 21$ ## Exercise 7.12 ### Division as Repeated Subtraction *Dividing a number by a divisor is the same as subtracting the divisor repeatedly from the given number. Similarly for a fraction, i.e. 10 - 2 = 8 Therefore, 15 - $\frac {6}{2} $ shaded ### Division of Fractions Since division and Multiplication are inverse Operations. Deividing by a fraction is same as multiplying by reciprocal of fraction* Example: find $\frac {2}{5} \div \frac {2}{5} $ =$\frac {1}{8} \div \frac {2}{5} $ $=\frac {1}{8} X \frac {5}{2}$ =$\frac {1 \text{x} 5}{8 \text{x} 2} =\frac {5}{16}$ **Example:** Find howmany $\frac {1}{6}’s $ are in 3? = $1 \frac{3}{4}$ ==End of OCR for the page 4 Please ask if you would like these to be formatted into a different structure.