Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions is an essential study material for students. Basic concepts of Multiplication of Whole Numbers and Fractions are clearly explained to score good marks for students. Also, in-depth knowledge of Chapter 9 Multiplies Whole Numbers and Fractions Big Ideas Grade 4 Math Answer
Key mentioned with a clear explanation. Furthermore, BIM Grade 4 Multiply Whole Numbers and Fractions Answer Key is very convenient for students who are struggling to learn that concept. We have also given extra practice in small groups for the best practice of the students. Every problem is solved and given with a detailed explanation to help the students while their preparation. We have included the BIM Grade 4 Chapter 9 Solution Key in all the ways such as quiz, formative assessment,
homework, or extra practice, etc. Practice in all the ways to get a complete grip on the concept. Provide a bright future for students, by giving the Chapter 9 Multiplies Whole Numbers and Fractions Big Ideas Grade 4 Math Answers as a reference. Lesson: 1 Understand Multiples of Unit Fractions Lesson: 2 Understand Multiples of
Fractions Lesson: 3 Multiply Whole
Numbers and Fractions Lesson:
4 Multiply Whole Numbers and Mixed Numbers Lesson: 5 Problem Solving: Fraction Operations Performance Task Explore and Grow Draw a model of any fraction using unit fractions. Then write an addition equation to represent
your model. Think and Grow: Multiples of Unit Fractions Any fraction can be written as a
multiple of a unit fraction with a like denominator. Answer: Show and Grow Write the fraction as a multiple of a unit fraction. Question 1. Answer: \(\frac{2}{3}\) = \(\frac{1}{3}\) +\(\frac{1}{3}\) = 2 X \(\frac{1}{3}\). Explanation: Question 2. Answer: \(\frac{4}{8}\) = \(\frac{1}{8}\) +\(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) = 4 X \(\frac{1}{8}\). Explanation: We write \(\frac{4}{8}\) in addition equation as \(\frac{4}{8}\) = \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) +\(\frac{1}{8}\) and multiplication as fraction \(\frac{4}{8}\) represents 4 parts that are each \(\frac{1}{8}\) of the whole, \(\frac{4}{8}\) =4 X \(\frac{1}{8}\). Question 3. Explanation: Question 4. Explanation: Apply and Grow: Practice Write the fraction as a multiple of a unit fraction. Question 5. Explanation: Question 6. Explanation: Question 7. Explanation: Question
8. Explanation : Question 9. Explanation : Question 10. Explanation: Question 11. Explanation : We know that the numerator of a unit fraction is always one. So When a fraction is DIG DEEPER! Question 12. Explanation: Question 13. Explanation: Question 13. Think and Grow: Modeling Real Life Example Answer: The worker can garnish \(\frac{1}{12}\) more drinks, \(\frac{7}{12}\) minus \(\frac{1}{2}\) means \(\frac{7}{12}\) – \(\frac{1}{2}\) = \(\frac{1}{12}\), Orange left is 7 X \(\frac{1}{12}\). Explanation: Show and Grow Question 14. Explanation: Question 15. Explanation: Question 16. Answer: Total number of treat bags made are 15 Explanation: Question 17. Explanation: Understand Multiples of Unit Fractions Homework & practice 9.1Write the fraction as a multiple of a unit fraction. Question 1. Answer: \(\frac{2}{12}\)= \(\frac{1}{12}\)+\(\frac{1}{12}\) = 2 X \(\frac{1}{12}\) Explanation: Question 2. Answer: \(\frac{5}{100}\)= \(\frac{1}{100}\)+\(\frac{1}{100}\)+\(\frac{1}{100}\)+ \(\frac{1}{100}\)+\(\frac{1}{100}\) = 5 X \(\frac{1}{100}\). Explanation: Question 3. Explanation: Question 4. Explanation: Question 5. Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanantion: Question 9. Answer: Newton’s fraction = \(\frac{9}{12}\)=\(\frac{1}{12}\) +\(\frac{1}{12}\) + \(\frac{1}{12}\) +\(\frac{1}{12}\) +\(\frac{1}{12}\) +\(\frac{1}{12}\) + \(\frac{1}{12}\) +\(\frac{1}{12}\) +\(\frac{1}{12}\) = 9 X \(\frac{1}{12}\). Explanation: Question 10 Answer: \(\frac{6}{2}\)=\(\frac{1}{2}\)+\(\frac{1}{2}\)+\(\frac{1}{2}\)+ \(\frac{1}{2}\)+\(\frac{1}{2}\)+\(\frac{1}{2}\) = 6 X \(\frac{1}{2}\). Explanation: Question 11. Answer: 4 X \(\frac{1}{5}\) expression does not belong with the other three, as all the other expressions values results are same =\(\frac{5}{4}\) only 4 X \(\frac{1}{5}\) expression is not. Explanation: Question 12. Answer: 6 pancakes i can make. Explanation: Question 13. Explanation : Question 14. Explanation: Question 15. Lesson 9.2 Understand Multiples of FractionsDraw a model for each expression. Then write a multiplication expression to represent each model. Answer: The multiplication expression is \(\frac{2}{6}\) +\(\frac{2}{6}\) +\(\frac{2}{6}\) + Explanation: Structure Explanation: Think and Grow: Multiples of Fractions A multiple of any fraction can be written as a multiple of a unit
fraction with a like denominator. Answer:
Write the product as a multiple of a unit fraction. Then find the product. Question 1. Answer: 2 X \(\frac{4}{5}\) = 2 X 4 X \(\frac{1}{5}\) = 8 X \(\frac{1}{5}\) = \(\frac{8}{5}\). Explanation: Question 2. Answer: 3 X \(\frac{2}{10}\) = 3 X 2 X \(\frac{1}{10}\) = 6 X \(\frac{1}{10}\) =\(\frac{6}{10}\). Explanation: Question 3. Answer: 4 X \(\frac{3}{2}\) = 4 X 3 X \(\frac{1}{2}\) = 12 X \(\frac{1}{2}\) = \(\frac{12}{2}\) = 6. Explanation: Apply and Grow: Practice Write the product as a multiple of a unit fraction. Then find the product. Question 4. Answer: 5 X \(\frac{2}{3}\) = 5 X 2 X \(\frac{1}{3}\) = 10 X \(\frac{1}{3}\)= \(\frac{10}{3}\). Explanation: Question 5. Answer: 6 X \(\frac{5}{8}\)= 6 X 5 X \(\frac{1}{8}\)= 30 X \(\frac{1}{8}\) = \(\frac{30}{8}\). Explanation: Question 6. Answer: 9 X \(\frac{7}{4}\) = 9 X 7 X\(\frac{1}{4}\)= 63 X \(\frac{1}{4}\) = \(\frac{63}{4}\). Explanation: Question 7. Answer: 7 X \(\frac{4}{12}\)=7 X 4 X \(\frac{1}{12}\)= 28 X \(\frac{1}{12}\)= \(\frac{28}{12}\) also 7 X \(\frac{4}{12}\)= 7 X \(\frac{1}{3}\)= \(\frac{7}{3}\). Explanation: Question 8. Answer: \(\frac{9}{6}\) X 8 = 9 X \(\frac{1}{6}\) X 8 = 72 X \(\frac{1}{6}\) = \(\frac{72}{6}\) =12. Explanation: Question 9. Answer: 10 X \(\frac{20}{100}\) = 10 X \(\frac{2}{10}\)=2 X 10 X \(\frac{1}{10}\)= 20 \(\frac{1}{10}\)=\(\frac{20}{10}\)=2. Explanation: Number Sense Question 10. Answer: The unknown number is 2. Explanation: Question 11. Answer: The unknown number is 5. Explanation: Question 12. Answer: The unknown number is 100. Explanation: Question 13. Answer: Yes , without calculating we can plot 5 and \(\frac{3}{6}\) to the left of 5 Explanation: Question 14. Answer: Explanation: We first write the expressions as multiple of unit fraction and find the product so 1. 3 X \(\frac{1}{5}\) can be written as product of 3 X 1 X \(\frac{1}{5}\)= 3 X \(\frac{1}{5}\) = \(\frac{3}{5}\) 2. 3 X \(\frac{2}{5}\) can be written as product of 3 X 2 X \(\frac{1}{5}\) = 6 X \(\frac{1}{5}\) = \(\frac{6}{5}\) 3. 3 X \(\frac{3}{5}\) can be written as product of 3 X 3 X \(\frac{1}{5}\) = 9 X \(\frac{1}{5}\) = \(\frac{9}{5}\) 4. 3 X \(\frac{4}{5}\) can be written as product of 3 X 4 X \(\frac{1}{5}\) = 12 X \(\frac{1}{5}\) = \(\frac{12}{5}\) 5. 3 X \(\frac{5}{5}\) can be written as product of 3 X 5 X \(\frac{1}{5}\) = 15 X \(\frac{1}{5}\) = \(\frac{15}{5}\) further can be simplified as 15,5 goes in 5, so dividing by 5 we get \(\frac{15}{5}\) = 3. Think and Grow: Modeling Real Life A bird keeper uses a \(\frac{1}{3}\) cup scoop to feed 3 birds. He feeds each bird \(\frac{2}{3}\) cup of birdseed. How many times does he
fill the scoop? Answer: Explanation : Question
15. Explanation: Question 16. Explanation: Question 17. Answer: My friend roller skate \(\frac{15}{2}\) miles in all. Explanation: Understand Multiples of Fractions Homework & Practice 9.2Write the product as a multiple of a unit fraction. Then find the product. Question 1. Answer: 2 X \(\frac{2}{3}\) = 2 X 2 X \(\frac{1}{3}\) = 4 X (\(\frac{1}{3}\)) = \(\frac{4}{3}\) Explanation: Question 2. Answer: 3 X \(\frac{5}{8}\) = 3 X 5 X \(\frac{1}{8}\) = 15 X (\(\frac{1}{8}\)) = \(\frac{15}{8}\). Explanation: Question 3. Answer: 4 X \(\frac{8}{2}\) = 4 X 8 X \(\frac{1}{2}\) = 32 X (\(\frac{1}{2}\)) = \(\frac{32}{2}\) =16. Explanation: Question 4. Answer: 5 X \(\frac{9}{10}\) = 5 X 9 X \(\frac{1}{10}\) = 45 X (\(\frac{1}{10}\)) = \(\frac{45}{10}\) = \(\frac{9}{2}\) Explanation: Question 5. Answer: 8 X \(\frac{6}{5}\) = 8 X 6 X \(\frac{1}{5}\) = 48X (\(\frac{1}{5}\)) = \(\frac{48}{5}\) Explanation: Question 6. Answer: 10 X \(\frac{2}{4}\) = 10 X 2 X \(\frac{1}{4}\) = 20 X (\(\frac{1}{4}\)) = \(\frac{20}{4}\) = \(\frac{10}{2}\). Explanation: Question 7. Answer: The expressions equivalent to 4 X \(\frac{7}{8}\) are (4 X 7) x \(\frac{1}{8}\) , \(\frac{28}{8}\),\(\frac{7}{8}\)+\(\frac{7}{8}\)+\(\frac{7}{8}\) + \(\frac{7}{8}\). Explanation: Question 8. Answer: 6 X \(\frac{6}{2}\) is greater Explanation: Question 9. Answer: Explanation: Question 10. Answer: To make a tornado we require 40 cups of water. Explanation: Question 11. Answer: Explanation: Review & Refresh Find the product. Question 12. Explanation: Question 13. Explanation: Question 14. Explanation: Lesson 9.3 Multiply Whole Numbers and FractionsExplore and Grow Use models to help you complete the table. What do you notice about each expression and its product? Construct Arguments Explain how to find the product of a whole number and a fraction without using models. Answer: Explanation: We notice that each expression can be written as the product as a
multiple of a unit fraction, Think and Grow: Multiply Whole Numbers and Fractions You can
find the product of a whole number and a fraction by multiplying the numerator by the whole number. Answer: Explanation: Show and Grow Multiply. Question 1. Answer: 4 X \(\frac{1}{6}\) = \(\frac{4}{6}\) also equals to \(\frac{2}{3}\) Explanation : Already the expression is in multiple of unit fraction so 4 X \(\frac{1}{6}\) = \(\frac{4}{6}\) and further simplification it is equal to \(\frac{2}{3}\) Question 2. Answer: 3 X \(\frac{2}{4}\) = 3 X \(\frac{1}{2}\) = \(\frac{3}{2}\). Explanation: Question 3. Answer: 7 X \(\frac{3}{2}\) = 7 x 3 X \(\frac{1}{2}\) = 21 X \(\frac{1}{2}\) = \(\frac{21}{2}\). Explanation: Apply and Grow: Practice Multiply. Question 4. Answer: 2 X \(\frac{1}{5}\) = \(\frac{2}{5}\). Explanation : Question 5. Answer: 5 X \(\frac{3}{10}\) = \(\frac{15}{10}\)=\(\frac{3}{2}\). Explanation: Question 6. Answer: 6 X \(\frac{7}{8}\)= \(\frac{42}{8}\)= \(\frac{21}{4}\). Explanation: Question 7. Answer: 8 X \(\frac{9}{10}\)= \(\frac{72}{10}\)=\(\frac{36}{5}\). Explanation: Question 8. Answer: 3 X \(\frac{60}{100}\) =\(\frac{180}{100}\) =\(\frac{18}{10}\). Explanation: Question 9. Answer: \(\frac{4}{2}\) X 10 = 20. Explanation : Compare. Question 10. Answer: 7 X \(\frac{2}{4}\) =\(\frac{14}{4}\) is smaller < 5 X \(\frac{3}{4}\)= \(\frac{15}{4}\). Explanation: Question 11. Answer: Explanation: Question 12. Answer: \(\frac{4}{3}\) X 9 = 6 X \(\frac{6}{3}\) both are equal. Explanation: Question 13. Explanation: Question 14. Explanation: Think and Grow: Modeling Real Life Example So, the longer roller-coaster track is about _\(\frac{12}{10}\) _ miles long or \(\frac{6}{5}\) miles long Answer: The longer roller-coaster track is about \(\frac{12}{10}\) miles long or \(\frac{6}{5}\). Explanation: Show and Grow Question 15. Answer: The Burj Khalifa is \(\frac{81}{100}\) kilometers tall. Explanation: Question 16. Explanation: Now we divide \(\frac{18}{5}\) we get the value as 3.6,means between 3 and 4 whole numbers our answer will lie. Question 17. Explanation: Multiply Whole Numbers and Fractions Homework & practice 9.3Multiply Question 1. Answer: 2 X \(\frac{1}{4}\) = \(\frac{2}{4}\)=\(\frac{1}{2}\) Explanation: As the given expression is already a unit fraction we multiply it as 2 X \(\frac{1}{4} = \)\(\frac{2}{4}\) and further both numerator and denominator can be divided by 2 making it as \(\frac{1}{2}\) Question 2. Answer: 3 X \(\frac{3}{5}\)= \(\frac{9}{5}\). Explanation: Question 3. Answer: 1 X \(\frac{6}{8}\)= \(\frac{6}{8}\)= \(\frac{3}{4}\). Explanation: Question 4. Answer: 4 X \(\frac{10}{12}\)= \(\frac{40}{12}\)= \(\frac{10}{3}\) Explanation: Question 5. Answer: 7 X \(\frac{6}{10}\) = \(\frac{42}{10}\)= \(\frac{21}{5}\) Explanation: Question 6. Answer: \(\frac{4}{6}\) X 5 =\(\frac{20}{6}\) =\(\frac{10}{3}\). Explanation: Question 7. Answer: 8 X \(\frac{5}{2}\) = \(\frac{40}{2}\) =20. Explanation: Question 8. Answer: \(\frac{70}{100}\) X 6 = \(\frac{420}{100}\) = \(\frac{42}{10}\). Explanation: Question 9. Answer: 10 X \(\frac{9}{3}\)=\(\frac{90}{3}\)=30. Explanation: Compare. Question 10. Answer: 2 X \(\frac{4}{2}\) = 8 X \(\frac{1}{2}\). Explanation: Question 11. Answer: 9 X \(\frac{1}{5}\) > \(\frac{9}{12}\) Explanation: Question 12. Answer: Explanation: Question 13. Explanation: Question 14. Explanation: Question 15. Explanation: Question 16. Answer: Explanation: Review & Refresh Divide Question 17. Answer: Explanation: Question 18. Answer: Explanation: Step 2: The divisor (7) does not goes into the first digit of the dividend (5), So we take second digit also , The divisor (7) goes into the two digits of the dividend (57) by 8 time(s),there fore put 8 on the top 8 Step 3: Multiply the divisor by the result in the previous step. Therefore, put 8 on top (7 x 9 = 56) and write that answer below the dividend. 8 56 Step 4: Subtract the result in the previous step from the two digits of the dividend (57 -56 = 1) and write the answer below. 8 56 1 Step 5: Move down the 3rd digit of the dividend (1) 8 56 11 Step 6:The divisor (7) goes into the bottom number (11), time(s). Therefore, put 1 on top: 81 56 11 Step 7 : Multiply the divisor by the result in the previous step (7 x 1 = 7) and write that answer at the bottom: 81 56 11 07 Step 8 : Subtract the result in the previous step from the number written above it. (11 – 7 = 04) and write the answer at the bottom 81 56 11 07 4 We stop here as 4 is less than 7 and further we get in decimals , So Question 19. Answer: Explanation: Step 2: The divisor (5) goes into the first digit of the dividend (9) by 8 time there fore put 1 on the top 1 Step 3: Multiply the divisor by the result in the previous step (5 x 1 = 5) and write that answer below the dividend. 1 5 Step 4: Subtract the result in the previous step from the first digit of the dividend (9 -5 = 4) and write the answer below. 1 5 4 Step 5: Move down the 2nd digit of the dividend (2),like below 1 5 42 Step 6:The divisor (5) goes into the bottom number (40), 8 time(s). Therefore, put 8 on top: 18 5 42 Step 7 : Multiply the divisor by the result in the previous step (5 x 8 = 40) and write that answer at the bottom: 18 5 42 40 Step 8: Subtract the result in the previous step from the number written above it. (42 – 40 = 04) and write the answer at the bottom 18 5 42 40 2 Step 9 :Move down the 3nd digit of the dividend (3),like below 18 5 42 40 23 Step 10 : The divisor (5) goes into the bottom number (20), 4 time(s). Therefore, put 4 on top: 184 5 42 40 23 20 Step 11 : Subtract the result in the previous step from the number written above it. (23 – 20 = 03) and write the answer at the bottom 184 5 42 40 23 20 03 We stop here as 3 is less than 5 and further we get in decimals , So Lesson 9.4 Multiply Whole Numbers and Mixed NumbersExplore and Grow Use models to help you complete the table. Structure Answer: Explanation: You can find the product of a whole number and a mixed number by writing the mixed number as a fraction or by using the Distributive Property One Way: Write the mixed number as a fraction, then multiply. Another Way: Use the Distributive Property. Answer: 3 X 1 \(\frac{1}{2}\) = \(\frac{9}{2}\) Explanation: First we write the mixed number as a fraction then multiply, so 1 \(\frac{1}{2}\) = 1+ \(\frac{1}{2}\) = 2 x 1+1 by 2= \(\frac{3}{2}\) now we multiply it with the whole , 3 X \(\frac{3}{2}\) now we write in unit fraction and multiply 3 X 3 X \(\frac{1}{2}\)= 9 X \(\frac{1}{2}\)= \(\frac{9}{2}\). Show and Grow Multiply Question 1. Answer: Explanation: First we write the mixed number as a fraction then multiply, so 2 \(\frac{1}{4}\) = 2 + \(\frac{1}{4}\)=(2 X 4 + 1) by 4 = \(\frac{9}{4}\) now we multiply it with the whole, 3 X \(\frac{9}{4}\) now we write in unit fraction and multiply 3 X 9 X \(\frac{1}{4}\) = 27 X \(\frac{1}{4}\) = \(\frac{27}{4}\), we can write the product as mixed fraction as 4 goes in 6 times. 6 will be our whole number 4 X 6 is 24 and we have 3 left over (27−24), 3 will be our numerator and our denominator will stay the same 4= \(\frac{27}{4}\)= 6 \(\frac{3}{4}\). Question 2. Answer: Explanation: Question 3. Answer: Explanation: First we write the mixed number as a fraction then multiply, so 3 \(\frac{5}{8}\)= 3 + \(\frac{5}{8}\)= (3 X 8 + 5) by 8 = \(\frac{29}{8}\) now we multiply it with the whole, 4 X \(\frac{29}{8}\) now we write in unit fraction and multiply 4 X 29 X \(\frac{1}{8}\)= 116 X \(\frac{1}{8}\) = \(\frac{116}{8}\), we can write the product as mixed fraction as 8 goes in 14 times. 14 will be our whole number 8 X 14 is 112 and we have 4 left over (116−112). 4 will be our numerator and our denominator will be the same 8= \(\frac{116}{8}\)= 14 \(\frac{4}{8}\). Apply and Grow: Practice Multiply. Question 4. Answer: Explanation: First we write the mixed number as a fraction then multiply, so 1 \(\frac{2}{3}\)= 1 + \(\frac{2}{3}\)= (1 X 3 + 2) by 3 = \(\frac{5}{3}\) now we multiply it with the whole, 10 X \(\frac{5}{3}\) now we write in unit fraction and multiply 10 X 5 X \(\frac{1}{3}\)= 50 X \(\frac{1}{3}\) = \(\frac{50}{3}\), we can write the product as mixed fraction as 3 goes in 16 times. 16 will be our whole number 3 X 16 is 48 and we have 2 left over (50−48). 2 will be our numerator and our denominator will be the same 3= \(\frac{50}{3}\)= 16 \(\frac{2}{3}\). Question 5. Answer: Explanation: Question 6. Answer: Explanation: Question
7. Answer: Explanation: First we write the mixed number as a fraction then multiply, so 5 \(\frac{2}{5}\)= 5 + \(\frac{2}{5}\)= (5 X 5 + 2) by 5 = \(\frac{27}{5}\) now we multiply it with the whole, 9 X \(\frac{27}{5}\) now we write in unit fraction and multiply 9 X 27 X \(\frac{1}{5}\)= 243 X \(\frac{1}{5}\) = \(\frac{243}{5}\), we can write the product as mixed fraction as 5 goes in 48 times. 48 will be our whole number 5 X 48 is 240 and we have 3 left over (243−240). 3 will be our numerator and our denominator will be the same 5= \(\frac{243}{5}\)= 48 \(\frac{3}{5}\). Question 8. Answer: Explanation: Question 9. Answer: Explanation: First we write the mixed number as a fraction then multiply, so 9 \(\frac{11}{100}\)= 9 + \(\frac{11}{100}\)= (9 X 100 + 11) by 100 = \(\frac{911}{100}\) now we multiply it with the whole, 6 X \(\frac{911}{100}\) now we write in unit fraction and multiply 6 X 911 X \(\frac{1}{100}\)= 5466 X \(\frac{1}{100}\) = \(\frac{5466}{100}\), we can write the product as mixed fraction as 100 goes in 54 times. 54 will be our whole number 100 X 54 is 5400 and we have 66 left over (5466−5400). 66 will be our numerator and our denominator will be the same 100= \(\frac{5466}{100}\)= 54 \(\frac{66}{100}\). Question 10. Explanation: Question 11. Answer: Yes friend is correct. Explanation: Question 12. Answer: 5 X 6 \(\frac{1}{4}\) < 6 X 5 \(\frac{1}{4}\) Explanation: By drawing models also we can say Think and Grow: Modeling Real Life Example Multiply the number of hours the elephant sleeps by 6. Answer: The koala sleeps 5 hours that day. Explanation: Show and Grow Question 13. Explanation: Question 14. Explanation: Question 15. Answer: Athlete runs more than 80 miles in 1 week so he meets his goal. Explanation: Multiply Whole Numbers and Mixed Numbers Homework & Practice 9.4Multiply Question 1. Answer: 2 X 1 \(\frac{1}{12}\) = \(\frac{26}{12}\) = \(\frac{13}{6}\)= 2 \(\frac{1}{6}\). Explanation: Question 2. Answer: 2 X 3\(\frac{5}{6}\)=\(\frac{46}{6}\) = \(\frac{23}{3}\)= 7 \(\frac{2}{3}\) Explanation: Question 3. Answer: 4 X 3 \(\frac{6}{10}\) = \(\frac{144}{10}\) = \(\frac{72}{5}\) = 14 \(\frac{2}{5}\). Explanation: Question 4. Answer: 2 \(\frac{3}{8}\) X 5 = \(\frac{95}{8}\) =11 \(\frac{7}{8}\). Explanation: Question 5. Answer: 4 X 6 \(\frac{4}{5}\) = \(\frac{136}{5}\) = 27 \(\frac{1}{5}\) Explanation: First we write the mixed number as a fraction then multiply, so 6 \(\frac{4}{5}\) = 6 + \(\frac{4}{5}\) =(6 X 5 + 4) by 5 = \(\frac{34}{5}\) now we multiply it with the whole, 4 X \(\frac{34}{5}\) now we write in unit fraction and multiply 4 X 34 X \(\frac{1}{5}\) = 136 X \(\frac{1}{5}\) = \(\frac{136}{5}\), now we can write the product as mixed fraction as 5 goes in 27 times. 5 X 27 is 135 , 27 will be our whole number and (136−135) we have 1 left over. 1 will be our numerator and our denominator will be the same 5 = \(\frac{136}{5}\)= 27 \(\frac{1}{5}\). Question 6. Answer: 8 \(\frac{20}{100}\) X 10 = \(\frac{8200}{100}\) = 82. Explanation: Question 7. Explanation: Question 8. Answer: Yes friend is correct, because the value is same as 11 \(\frac{2}{10}\) . Explanation: Question 9. Explanation: Question 10. Answer: Athlete B holds 10 kilograms of plate while doing squats. Explanation: Question 11. Review & Refresh Subtract. Question 12. Answer: Explanation: First we write the mixed numbers into fractions and subtract, So 9 \(\frac{1}{4}\) = Question 13. Answer: Explanation: First we write the mixed numbers into fractions and subtract, So 6 \(\frac{1}{3}\) = 6 +\(\frac{1}{3}\) =(6 x 3 + 1) by 3 = \(\frac{19}{3}\) and 2 \(\frac{2}{3}\) = 2 + \(\frac{2}{3}\) = 2 X 3 + 2 by 3 = \(\frac{8}{3}\) now subtracting \(\frac{19}{3}\) – \(\frac{8}{3}\) to subtract a fraction from another we need to first make sure both fractions have the same denominator as both denominators have same value 3 now we can subtract one numerator from the other to make one fraction as 19 – 8 by 3 = \(\frac{11}{3}\) since the numerator is greater than the denominator, we can further simplify it into a mixed fraction as 3 goes in 3 times. 3 X 3 is 9 , 3 will be our whole number and (11−9) we have 2 left over. 2 will be our numerator and our denominator will be the same 3 = \(\frac{11}{3}\) = 3 \(\frac{2}{3}\) . Question 14. Answer: \(\frac{78}{12}\) = \(\frac{39}{6}\) = \(\frac{13}{2}\) = 6 \(\frac{1}{2}\). Explanation: Lesson 9.5 Problem Solving: Fraction OperationsExplore and Grow You want to make 3 batches of the recipe. Explain how to find how much of each ingredient you need. Reasoning Explanation: Think and Grow: Problem Solving: Fraction Operations Example Answer: The temperature shown by the thermometer is 500 Fahrenheit. Explanation: Understand the Problem What do you know?
Make a Plan How will you solve?
Solve So, the temperature shown by the thermometer is _500_ degrees Fahrenheit. Answer: The temperature shown by the thermometer is 500 Fahrenheit. Explanation : Show and Grow Question 1. Explanation: Apply and Grow: Practice Understand the problem. What do you know? What do you need to find? Explain. Answer: Explanation: Question 2. Answer: Explanation: Question 3. Answer: Explanation: Understand the problem. Then make a plan. How will you solve? Explain. Question 4. Answer: Explanation: Question 5. Answer: No friend cannot donate her hair in 8 months as in 8 months it grows to 11 inches long and for Explanation: Given friend’s hair is 7 inches long. Her hair grows about
\(\frac{1}{2}\) inch each month. Question 6. Answer: Tomorrow i will walk father \(\frac{18}{10}\) miles or \(\frac{9}{5}\) miles or 1 \(\frac{4}{5}\) . Explanation: Given today i walked \(\frac{6}{10}\) mile from the Martin Luther King Jr. Memorial Think and Grow: Modeling Real Life Example So, the 60-pound dog eats 10 \(\frac{1}{2}\) more cups of food than the 20-pound dog in 1 week. Answer: The 60-pound dog eats 10 \(\frac{1}{2}\) more cups of food than the 20-pound dog in 1 week. Explanation: Given A 20-pound dog eats 1 \(\frac{1}{2}\) cups and a 60-pound dog eats 3 cups, Show and Grow Question 7. Answer: Explanation: Problem Solving: Fraction Operations Homework & Practice 9.5Understand the problem. Then make a plan. How will you solve? Explain. Question 1. Answer: Friend makes \(\frac{5}{2}\) jars= 2 \(\frac{1}{2}\) jars in that full jars are 2, So 2 jars of raspberry jam he makes. Explanation: Question 2. Question 3. Answer: The height of replica is \(\frac{605}{100}\) =\(\frac{121}{20}\) or 6 \(\frac{1}{20}\) feet. Explanation: Question 4. Answer: For 30 students to complete the Art Project orange sheets required are 11 \(\frac{2}{8}\) and 18 \(\frac{6}{8}\) black sheets of paper is required. Explanation: Question 5. Answer: Explanation: Question 6. Answer: \(\frac{970}{100}\) grams more the bundle of 10 noodles hold than the bundle of 5 noodles or \(\frac{97}{10}\) grams more the bundle of 10 noodles hold than the bundle of 5 noodles or 9 \(\frac{7}{10}\) grams more the bundle of 10 noodles hold than the bundle of 5 noodles. Explanation: Given that bundle of 5 noodles can hold 10 quarters means 5 noodles can hold 10 X 5 \(\frac{67}{100}\) grams first we change mixed fraction to fraction by using multiplication and then add as 5 \(\frac{67}{100}\) = 5 X 6 + 67 by 100 = \(\frac{97}{100}\) now we multiply by 10, 10 X \(\frac{97}{100}\) = 10 X 97 X \(\frac{1}{100}\) = 970 X \(\frac{1}{100}\) = \(\frac{970}{100}\) grams , so 5 spaghetti noodles can hold \(\frac{970}{100}\) grams before breaking, Now given 10 spaghetti noodles can hold 20 quarters means 10 spaghetti noodles can hold 20 X 5 \(\frac{67}{100}\) grams again first we change mixed fraction to fraction by using multiplication and then add as 5 \(\frac{67}{100}\) = ( 5 X 6 + 67 ) by 100 = \(\frac{97}{100}\) now we multiply by 20, 20 X \(\frac{97}{100}\) = 20 X 97 X \(\frac{1}{100}\) = 1940 X \(\frac{1}{100}\) = \(\frac{1940}{100}\) grams , so 10 spaghetti noodles can hold \(\frac{1940}{100}\) grams before breaking now to calculate how many more grams can the bundle of 10 noodles hold than the bundle of 5 noodles we subtract \(\frac{1940}{100}\) grams – \(\frac{970}{100}\) grams as denominators are same first we substract numerators as 1940 – 970 = 970 as numerator and denominator being same 100 we get \(\frac{970}{100}\) grams more the bundle of 10 noodles hold than the bundle of 5 noodles, further can be simplified as 970 and 100 both can be divided by 10 making it as \(\frac{97}{10}\) grams more the bundle of 10 noodles hold than the bundle of 5 noodles and as numerator is greater , we can write in mixed fraction as 10 goes 9 times, 10 X 9 is 90, 9 will be our whole number and (97−90) we have 7 left over. 7 will be our numerator and our denominator will be the same 10, making as 9 \(\frac{7}{10}\) grams more the bundle of 10 noodles hold than the bundle of 5 noodles. Review & Refresh Compare Question 7. Answer: \(\frac{9}{10}\) is greater than > \(\frac{4}{5}\) or \(\frac{9}{10}\) is greater than > \(\frac{8}{10}\) Explanation: Question 8. Answer: \(\frac{3}{8}\) < is less than \(\frac{5}{6}\) or \(\frac{9}{24}\) < is less than \(\frac{20}{24}\). Explanation: Now convert each one of \(\frac{3}{8}\) and \(\frac{5}{6}\) Question 9. Answer: \(\frac{1}{3}\) = is equal to \(\frac{4}{12}\) or \(\frac{1}{3}\) = is equal to \(\frac{1}{3}\) Explanation: Here first we simplify \(\frac{4}{12}\) as both can be divided by 4 if we dividey both numerator and denominator by 4 we get numerator as 1 and denominator as 4 = \(\frac{1}{3}\) now comparing both sides, as values are same so \(\frac{1}{3}\) = is equal to \(\frac{4}{12}\) or \(\frac{1}{3}\) = is equal to \(\frac{1}{3}\). Multiply Whole Numbers and Fractions Performance TaskQuestion 1. a. You fill each glass using a \(\frac{3}{4}\)-cup measuring cup. Complete the table to find the total amount of water in each jar. b. How much more water is in the purple jar than the green jar? c. How many cups of water are used in all? d. Each jar can hold 4 cups of water. Is it possible to add another \(\frac{3}{4}\) cup of water to the purple jar? Explain. e. Which jars are more than half full? f. You add another \(\frac{3}{4}\) cup of water to the green jar. How does that affect the sound? Answer: a. b. Purple jar is 3 cups more than the Green jar or Purple jar is \(\frac{12}{4}\) cups more than the Green jar. c. Total number of cups of water used in all is \(\frac{45}{4}\) cups or 11 \(\frac{1}{4}\) cups. d. No, it is not possible to add another \(\frac{3}{4}\) cup of water to the purple jar as if we add it will become \(\frac{18}{4}\) cups = 4 \(\frac{2}{4}\) = 4 + \(\frac{2}{4}\) cups of water to the purple jar cups which is more than 4 cups it will overflow so it is not possible to add another \(\frac{3}{4}\) cup of water to the purple jar. e. Jars which are more than half full are Orange, Red and Purple. f. After adding add another \(\frac{3}{4}\) cup of water to the green jar it becomes \(\frac{6}{4}\) which is equal to blue color jar, we know the jar that has the least amount of water makes the lowest sound before it was the green jar which had least amount of water so it had lowest sound, so now after adding \(\frac{3}{4}\) cup of water to green jar it has become equal to blue jar so now both green and blue jar has least amount of water so they both make the lowest sound. Explanantion: a. Given we fill each glass \(\frac{3}{4}\)-cup measuring cup so total water cups used for each color are Green 1 means 1 X \(\frac{3}{4}\) cup = \(\frac{3}{4}\) cup Blue 2 of \(\frac{3}{4}\) = 2 X \(\frac{3}{4}\) = 2 X 3 X \(\frac{1}{4}\) = 6 X \(\frac{1}{4}\)= \(\frac{6}{4}\) cups , as both numerator and denominator can be divided by 2 we get \(\frac{3}{2}\) cups Orange 3 of \(\frac{3}{4}\) = 3 X \(\frac{3}{4}\) = 3 X 3 X \(\frac{1}{4}\) = 9 X \(\frac{1}{4}\) = \(\frac{9}{4}\) cups Red 4 of \(\frac{3}{4}\) = 4 X \(\frac{3}{4}\) = 4 X 3 X \(\frac{1}{4}\) = 12 X \(\frac{1}{4}\) = \(\frac{12}{4}\) as both numerator and denominator can be divided by 4 we get numerator as 3 and denominator 1 making Red 4 of \(\frac{3}{4}\) = 3 cups. Purple 5 of \(\frac{3}{4}\) = 5 X \(\frac{3}{4}\) = 5 X 3 X \(\frac{1}{4}\) = 15 X \(\frac{1}{4}\) = \(\frac{15}{4}\) cups. b. To calculate how much more water is in the Purple jar than the Green jar we subtract c. Total number of cups of water are used in all is adding Green, Blue, Orange, Red, d. We got Purple jar contains \(\frac{15}{4}\) cups to this we will add another f. Now we will add another \(\frac{3}{4}\) cup of water to the green jar means Multiply Whole Numbers and Fractions ActivityThree In a Row: Fraction Multiplication Directions:
Answer: Multiply Whole Numbers and Fractions Chapter Practice9.1 Understand Multiples of Unit Fractions Write the fraction as a multiple of a unit fraction. Question 1. Answer: \(\frac{3}{10}\)= \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) = 3 X \(\frac{1}{10}\). Explanation: Question 2. Answer: \(\frac{4}{8}\)= \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) = 4 X \(\frac{1}{8}\). Explanation: Question 3. Explanation: Question 4. Explanation: Question 5. Answer: Newton’s fraction is 5 X \(\frac{1}{6}\), The fraction is already a multiple of a unit fraction = 5 X \(\frac{1}{6}\) , 5 is multiple and \(\frac{1}{6}\) is a unit fraction. Explanation: 9.2 Understand Multiples of Fractions Write the product as a multiple of a unit fraction. Then find the product. Question 6. Answer: 2 X \(\frac{2}{4}\) = 2 X 2 X \(\frac{1}{4}\) = 4 X \(\frac{1}{4}\) = \(\frac{4}{4}\)= 1 Explanation: Question 7. Answer: 3 X \(\frac{9}{12}\) = 3 X \(\frac{3}{4}\) = 9 X \(\frac{1}{4}\) = \(\frac{9}{4}\) Explanantion: Question 8. Answer: \(\frac{3}{5}\) X 4 = 12 X \(\frac{1}{5}\) = \(\frac{12}{5}\). Explanation: Question 9. Answer: \(\frac{8}{10}\) X 7= \(\frac{4}{5}\) X 7 = 28 X \(\frac{1}{5}\) is multiple of unit fraction, The product is \(\frac{28}{5}\). Explanantion: Question 10. Answer: 8 X \(\frac{6}{3}\) = 8 X 2 = 16 as we got \(\frac{6}{3}\) =2, So we get results as whole not in fraction. Explanation: Question 11. Answer: 10 X \(\frac{30}{8}\) = 10 X \(\frac{15}{4}\) = 150 X \(\frac{1}{4}\) = \(\frac{150}{4}\) = \(\frac{75}{2}\). Explanation: 9.3 Multiply Whole Numbers and Fractions Multiply Question 12. Answer: 2 X \(\frac{1}{2}\) = \(\frac{2}{2}\) = 1 Explanation: Already it is in unit fraction so 2 X \(\frac{1}{2}\) = \(\frac{2}{2}\) = 1. Question 13. Answer: 4 X \(\frac{5}{8}\) = \(\frac{20}{8}\) = \(\frac{10}{4}\) = \(\frac{5}{2}\). Explanation : Question 14. Answer: 3 X \(\frac{9}{6}\) = \(\frac{9}{2}\). Explanantion: Question 15. Answer: 5 X \(\frac{7}{12}\) = \(\frac{35}{12}\). Explanation: Question 16. Answer: 7 X \(\frac{30}{100}\) = 7 X \(\frac{3}{10}\) = \(\frac{21}{10}\). Explanation: Question 17. Answer: \(\frac{8}{4}\) X 9 = 2 X 9 = 18. Explanantion: 9.4 Multiply Whole Numbers and Mixed Numbers Multiply Question 18. Answer: Explanation: First we write the mixed number as a fraction then multiply, so 1 \(\frac{1}{4}\)= 1 + \(\frac{1}{4}\)= (1 X 4 + 1) by 4 = \(\frac{5}{4}\) now we multiply it with the whole, 2 X \(\frac{5}{4}\) now we write in unit fraction and multiply 2 X 5 X \(\frac{1}{4}\)= 10 X \(\frac{1}{4}\) = \(\frac{10}{4}\) further we can simplify as 10,4 both can be divided by 2 we get numerator as 5 and denominator as 2, \(\frac{5}{2}\) as numerator is greater than denominator we can write in mixed fraction as 2 goes in 2 times. 2 will be our whole number 2 X 2 is 4 and we have 1 left over (5−4), 1 will be our numerator and our denominator will stay the same 2, \(\frac{5}{2}\)= 2 \(\frac{1}{2}\). Question 19. Answer: Explanation: First we write the mixed number as a fraction then multiply, so 3 \(\frac{10}{12}\)= ( 3 X 12 + 10 ) by 12 = \(\frac{46}{12}\) this can be further simplified as both 46,12 goes by 2 we get numerator as 23 and denominator as 6 , \(\frac{23}{6}\) now we multiply by 3 = 3 X \(\frac{23}{6}\) = \(\frac{69}{6}\) it can be more simplified as both 69,6 goes by 3 we get numerator as 23 and denominator as 2 making \(\frac{69}{6}\) as \(\frac{23}{2}\) as numerator is greater than denominator we can write in mixed fraction as 2 goes in 11 times. 11 will be our whole number 2 X 11 is 22 and we have 1 left over (23−22), 1 will be our numerator and our denominator will stay the same 2, \(\frac{23}{2}\) = 11 \(\frac{1}{2}\). Question 20. Answer: Explanantion: First we write the mixed number as a fraction then multiply, so 2 \(\frac{5}{8}\) = Question 21. Answer: Explanation: First we write the mixed number as a fraction then multiply, so 2 \(\frac{4}{6}\) = ( 2 X 6 + 4 ) by 6 = \(\frac{16}{6}\) this can be simplified as 16,6 both goes by 2 we get numerator as 8 and denominator as 3 we get \(\frac{8}{3}\) now we multiply by 5 we get 5 X \(\frac{8}{3}\) = 5 X 8 X \(\frac{1}{3}\) = 40 X \(\frac{1}{3}\) = \(\frac{40}{3}\) as numerator is greater than denominator we can write in mixed fraction as 3 goes in 13 times. 13 will be our whole number 3 X 13 is 39 and we have 1 left over (40−39), 1 will be our numerator and our denominator will stay the same 3, we get mixed fraction as 13 \(\frac{1}{3}\) . Question 22. Answer: Explanation: First we write the mixed number as a fraction then multiply, so 6 \(\frac{2}{3}\) = ( 6 X 3 + 2 ) by 3 = \(\frac{20}{3}\) now we multiply by 7 X \(\frac{20}{3}\) = 7 X 20 x \(\frac{1}{3}\) = 140 X \(\frac{1}{3}\) =\(\frac{140}{3}\) as numerator is greater than denominator we can write in mixed fraction as 3 goes in 46 times. 46 will be our whole number 3 X 46 is 138 and we have 2 left over (140−138), 2 will be our numerator and our denominator will stay the same 3, we get mixed fraction as 46 \(\frac{2}{3}\) . Question 23. Answer: Explanation: First we write the mixed number as a fraction then multiply, so 9 \(\frac{2}{5}\) = ( 9 X 5 + 2 ) by 5 = \(\frac{47}{5}\) now we multiply by 10 = 10 X \(\frac{47}{5}\) = \(\frac{470}{5}\) this can be further simplified as both can be divided by 5 we get numerator as 94 and denominator as 1 so we get only whole number 94. 9.5 Problem Solving: Fraction Operations Question 24. Explanation: Conclusion: Access the links given in the Big Ideas Math Book 4th Grade Answer Key Chapter 9 Multiply Whole Numbers and Fractions and practice well for the exams. We have solved all the questions in an easy and simple manner. We hope the information provided in this article has brought a smile to your face. Share Big Ideas Math Grade 4 Answer Key Chapter 9 Multiply Whole Numbers and Fractions. How do you multiply fractions by a whole number?How do you multiply a fraction by a whole number?. Write the whole number as a fraction with a denominator of 1.. Multiply the numerators.. Multiply the denominators.. Simplify. , if needed. If your answer is greater than 1, you may want to write your answer as a mixed number.. |